Feljone g. ragma master's thesis

COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE

SECONDARY SCHOOLS IN SAN FERNANDO CITY, LA UNION:

BASIS FOR A TWO-PRONGED TRAINING PROGRAM

A Thesis

Presented to the Faculty

of the Graduate School

College of Teacher-Education

Saint Louis College

City of San Fernando (La Union)

In Partial Fulfillment of

the Requirements for the DEGREE

MASTER OF ARTS IN EDUCATION

MAJOR IN MATHEMATICS

By

FELJONE GALIMA RAGMA

February, 2011

INDORSEMENT

This thesis, entitled, ―COMPETENCE OF MATHEMATICS

TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN SAN

FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED

TRAINING PROGRAM,‖ prepared and submitted by FELJONE GALIMA

RAGMA in partial fulfillment of the requirements for the degree of

MASTER OF ARTS IN EDUCATION MAJOR IN MATHEMATICS, has

been examined and is recommended for acceptance and approval for

ORAL EXAMINATION.

MR.GERARDO L. HOGGANG, MAMT Adviser

This is to certify that the thesis entitled, ―COMPETENCE OF

MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS

IN SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED

TRAINING PROGRAM,” prepared and submitted by FELJONE GALIMA

RAGMA is recommended for ORAL EXAMINATION.

NORA A. OREDINA, Ed.D. Chairperson

EDWINA M. MANALANG, MAEd MARILOU R. ALMOJUELA, Ed.D

Member Member

Noted by:

AURORA R. CARBONELL, Ed.D.

Dean, College of Teacher Education Saint Louis College

APPROVAL SHEET

Approved by the Committee on Oral Examination as PASSED with

a grade of 96% on February 18, 2011.



Member Member

ENGR. ANGELICA DOLORES, MATE-Math

CHED RO I Representative Member

Accepted and approved in partial fulfillment of the requirements for

the degree of MASTER OF ARTS IN EDUCATION MAJOR IN

MATHEMATICS.



This is to certify that FELJONE GALIMA RAGMA has completed

all academic requirements and PASSED the Comprehensive Examination

with a grade of 94% in May, 2010 for the degree of MASTER OF ARTS

IN EDUCATION MAJOR IN MATHEMATICS.



INDORSEMENT

This thesis, entitled, ―COMPETENCE OF MATHEMATICS

TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN SAN

FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED

TRAINING PROGRAM,‖ prepared and submitted by FELJONE GALIMA

RAGMA in partial fulfillment of the requirements for the degree of

MASTER OF ARTS IN EDUCATION MAJOR IN MATHEMATICS, has

been examined and is recommended for acceptance and approval for

ORAL EXAMINATION.

MR.GERARDO L. HOGGANG, MAMT Adviser

This is to certify that the thesis entitled, ―COMPETENCE OF

MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS

IN SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED

TRAINING PROGRAM,” prepared and submitted by FELJONE GALIMA

RAGMA is recommended for ORAL EXAMINATION.



Member Member

Noted by:



APPROVAL SHEET

Approved by the Committee on Oral Examination as PASSED with

a grade of 96% on February 18, 2011.



Member Member

ENGR. ANGELICA DOLORES, MATE-Math

CHED RO I Representative Member

Accepted and approved in partial fulfillment of the requirements for

the degree of MASTER OF ARTS IN EDUCATION MAJOR IN

MATHEMATICS.



This is to certify that FELJONE GALIMA RAGMA has completed

all academic requirements and PASSED the Comprehensive Examination

with a grade of 94% in May, 2010 for the degree of MASTER OF ARTS

IN EDUCATION MAJOR IN MATHEMATICS.



ACKNOWLEDGMENT

The researcher wishes to express his sincerest gratitude and warm

appreciation to the following persons who had contributed much in

helping him shape and reshape this valuable piece of work.

Mr. Gerry Hoggang, thesis adviser, for always giving necessary

suggestions to better this study.

Dr. Nora A. Oredina, chairwoman of the examiners, for her

valuable critique, and most especially, for inspiring the researcher to

pursue his Masterate degree.

Engineer Angelica Dolores, MATE-Math, CHED representative, for

her intellectual comments and recommendations.

Dr. Marilou R. Almojuela and Mrs. Edwina Manalang, panelists,

for their brilliant thoughts.

Dr. Jose P. Almeida, Mrs. Rica A. Perez, Mrs. Rosabel N. Aspiras

for validating the two sets of questionnaire.

Sr. Teresita A. Lara, Sr. Angelica Cruz, Mrs. Evangeline L.

Mangaoang, Mr. Danilo Romero, and Mrs. Loreta Cepriaso for validating

the two-pronged training program.

Principals, heads, teachers and students of the Private Secondary

Schools in the City Division of San Fernando, La Union for lending some

of their precious time in giving their responses to the questionnaires.

Mr. Amado I. Dumaguin, his former Mathematics Coordinator, for

always giving him inspiration and push; and for believing in the

researcher‘s capabilities.

Mr. & Mrs. Felipe and Norma Ragma, researcher‘s parents, for

always being there when the researcher needed some push.

And lastly, to God Almighty for giving the needed strength in the

pursuit of this endeavor.

F. G. R.

DEDICATION

To my Parents Mr. & Mrs Felipe and Norma

Ragma and

To my siblings Darwin, Felinor and Nailyn

This humble work is a sign of my love to you!

F.G.R.

THESIS ABSTRACT

TITLE: COMPETENCE OF MATHEMATICS TEACHERS IN THE

PRIVATE SECONDARY SCHOOLS IN SAN FERNANDO CITY,

LA UNION: BASIS FOR A TWO-PRONGED TRAINING

PROGRAM

Total Number of Pages: 230

AUTHOR: FELJONE G. RAGMA

ADVISER: MR. GERARDO L. HOGGANG, MAMT

TYPE OF DOCUMENT: Thesis

TYPE OF PUBLICATION: Unpublished

ACCREDITING INSTITUTION: Saint Louis College

City of San Fernando, La Union

CHED, Region I

Abstract:

The study aimed at determining the competence level of

mathematics teachers in the private secondary schools in San Fernando

City, La Union with the end goal of designing a validated two-pronged

training program.

Specifically, it looked into the profile of the mathematics teachers

along highest educational attainment, number of years in teaching

mathematics and number of mathematics trainings and seminars

attended; the level of competence of mathematics teachers along content

and instruction; the relationship between teacher‘s profile and content

competence, teacher‘s profile and instructional competence and content

and instructional competence; the major strengths and weaknesses of

the mathematics teachers along content and instruction and; the type

and validity of the training program.

The study is descriptive with two sets of questionnaire as the

primary data gathering instruments. It covered thirteen (13) private

secondary schools in San Fernando City, La Union with heads, faculty,

and students as respondents.

The study found out that all the mathematics teachers are licensed

and majority of them are pursuing graduate studies and had 0-5 years of

teaching experience; 84.62% had very inadequate and 15.39% had

slightly adequate attendance in seminars. It also found out that the

teachers‘ level of content competence was average with a mean rating of

16. They scored highest in conceptual and computational skills but

lowest in problem-solving skills. On the other hand, their level of

instructional competence was very good with a mean rating of 4.24. They

were rated highest in management skills but lowest in teaching skills.

Moreover, the study found that there is no significant difference in

the perceptions between students and teachers and between teachers

and heads but there is a significant difference in the perceptions between

students and heads. Also, there is no significant relationship between

profile and content competence and between content and instructional

competence. On the other hand, there is a significant relationship

between highest educational attainment and instructional competence;

but there is no significant relationship between number of years of

teaching and number of seminars attended to instructional competence.

The teachers‘ conceptual and computational skills are considered

as strengths. On the other hand, reasoning and problem-solving skills

are considered as weaknesses. All the other skills under teaching,

guidance, management and evaluation were considered strengths. The

weakness of Mathematics teachers along instructional competence was

on the quality of utilization of information and communication

technology. In connection to the output of the study, the two-pronged

training program enhances the weaknesses and the sustainability of the

strengths. Its face and content validity was found high.

Based on the findings, the researcher concluded that the

mathematics teachers are all qualified in the teaching profession; they

are very young in the service and are exposed minimally to trainings and

seminars but they still perform well in their teaching; the teachers had

only average competence in terms of their content competence but were

perceived very skillful in teaching Mathematics.

Further, the heads rated instructional competence higher than the

students; but all the respondents considered the teachers very skillful in

teaching. Teachers who have higher educational attainment, number of

years in teaching and seminars do not have higher subject matter

competence and teachers who have higher educational attainment have

higher instructional competence; but, teachers who are more experienced

in teaching and have more seminars do not mean that they have higher

instructional competence than those who are younger and those who

have lesser seminars. It does not also mean that when a teacher has high

content competence, he has high instructional competence as well and

vice versa.

Further, teachers are not so skilled at analysis and problem-

solving and they do not use ICT and other innovative instructional

technology much in their daily teachings but still have very good

teaching performance.

The validated two-pronged training program is timely for the new

and tenured teachers to update and upgrade their content and

instructional competence. Moreover, it is a helpful tool for them to

understand more their subject and know more about the ways on how to

present a subject matter, especially on the use of ICT.

Based on the conclusions, the researcher recommends that the

teachers should be encouraged to enroll in their graduate studies;

incentive scheme for outstanding performance should be devised by

administrators; teachers should always be sent to seminars and

workshops where their participation is necessary; teachers should use

ICT in their teaching and that the school has to provide such ICT

materials; a closer monitoring system has to be applied by the heads; the

proposed two-pronged training program for the Mathematics teachers

should be implemented in the private secondary schools in the City

Division of San Fernando, La Union; a study to determine the efficiency

or efficacy of the two-pronged training program should be undertaken;

and lastly, a parallel study should be undertaken in other subject areas

such as English and Science.

TABLE OF CONTENTS

Page

TITLE PAGE ……………………………………………………………… i

INDORSEMENT …………………………………………………………. ii

APPROVAL SHEET ……………………………………………………... iii

ACKNOWLEDGMENT ………………………………………………….. iv-v

DEDICATION …………………………………………………………….. vi

THESIS ABSTRACT …………………………………………………….. vii-xi

TABLE OF CONTENTS ………………………………………………… xii-xvii

LIST OF TABLES ……………………………………………………….. xviii –xix

FIGURE …………………………………………………………………… xx

Chapter

1 The Problem ……………………………………………… 1

Rationale ……………………………………………. 1-7

Theoretical Framework ………………………….. 7-14

Conceptual Framework …………………………. 15-17

Statement of the Problem ………………………. 19-20

Hypotheses………………………………………… 20-21

Scope and Delimitation ………………………… 21-22

Importance of the Study ……………………….. 22-23

Definition of Terms ……………………………….. 23-26

2 Review of Related Literature ………………………… 27

Profile of High School Mathematics Teachers .. 27

Highest Educational Attainment ………………. 27-28

Number of Years in Teaching Mathematics …. 29-30

Number of Seminars Attended ………………….. 30-31

Level of Content and Instructional Competence .. 31

Subject Matter/Content ……………………………. 32-33

Teaching Skills ………………………………………. 33-37

Guidance Skills ……………………………………… 37-39

Management Skills ………………………………….. 39-40

Evaluation Skills …………………………………….. 40-42

Comparison in Perceived Instructional Competence

Among Respondent Groups ………………………… 42-43

Relationship of Profile and Content

Competence …………………………………………… 43-46

Relationship of Profile and Instructional

Competence ……………………………………………. 46-48

Relationship between Content and

Instructional Competence ……………………….. 48-50

Strengths and Weaknesses in Teachers‘

Competence …………………………………………. 50-52

Training Programs ………………………………….. 52-53

3 Research Methodology …………………………………….. 54

Research Design ……………………………………. 54

Sources of Data …………………………………….. 54-55

Instrumentation and Data Collection …………. 56-58

Validity and Reliability of the Instrument ……. 58-60

Tools for Data Analysis …………………………… 60-64

Data Categorization ……………………………….. 64-66

Proposed Training Program ……………………… 66

Validity of the Training Program ……………….. 66-67

4 Presentation, Analysis and Interpretation of Data… 68

Profile of Mathematics Instructors ……………… 68

Highest Educational Attainment ……………. 68-70

Number of Years in Teaching Mathematics… 70-71

Number of Seminars Attended ……………….. 71-72

Summary of the Profile of Mathematics Teachers.. 73-74

Level of Content Competence ……………………….. 74

Conceptual Skills …………………………………. 74-76

Analytical Skills …………………………………… 76-78

Computational Skills ……………………………… 78-79

Problem-Solving Skills ……………………………. 79-81

Summary of Level of Content Competence.……. 81-83

Level of Instructional Competence ………………………………. 83

Teaching Skills …………………………………………. 83-86

Substantiality of Teaching ………………………. 86-87

Quality of Teachers‘ Explanation ……………… 87

Receptivity to Students‘ Ideas

And Contributions …………………………………. 87-88

Quality of Questioning Procedure ……………… 88

Selection of Teaching Methods …………………. 88

Quality of Information and Communication

Technology Used ………………………………….. 89

Guidance Skills ….…………………………………… 89-90

Quality of Interaction with Students …………. 90-91

Quality of Student Activity ……………………… 91

Management Skills ………………………………….. 91

Atmosphere in the Classroom ………………….. 91-93

Conduct and Return of Evaluation

Materials …………………………………………… 93-94

Evaluation Skills …………………………………….. 94

Quality of Appraisal Questions…………………. 94-96

Quality of Assignment/Enrichment

Activities ……………………………………………. 96

Quality of Appraising Students

Performance ………………………………………… 97

Comparison in the Perceived Instructional

Competence of the Groups of Respondents

Students and Teachers…………………………… 97-98

Students and Heads………………………………. 99-100

Heads and Teachers………………………………. 100-101

Summary of Level of Instructional Competence ……… 102-105

Relationship between Profile and

Content Competence ………………………………………. 105-108

Relationship between Profile and

Instructional Competence ………………………………… 108-111

Relationship between Content and

Instructional Competencies …………………………….. 111-113

Summary of Relationship……………………………………. 113-114

Strengths and Weaknesses along Content Competence… 115-116

Strengths and Weaknesses along

Instructional Competence……………………. 116-121

Teaching Skills…………………………………… 121-122

Guidance Skills …………………………………. 122

Management Skills ……………………………… 122

Evaluation Skills ………………………………… 122-123

Proposed Two-Pronged Training Program ……………… 123-129

Level of Validity of the Proposed ………………………….. 129-13)

Two-Pronged Training Program …………………………. 131-140

Sample Flyer of the Two-Pronged Training Program………. 141

5 Summary, Conclusions and Recommendations ……. 142

Summary ………………………………………… 142-144

Findings …………………………………………… 144-145

Conclusions………………………………………. 146-147

Recommendations ……………………………… 147-149

BIBLIOGRAPHY…………………………………………. 150-161

APPENDICES ……………………………………………. 162-219

CURRICULUM VITAE……………………………………. 210-213

LIST OF TABLES

Table 1…………………………………………………………… 56

Table 2…………………………………………………………… 69

Table 3…………………………………………………………… 71

Table 4…………………………………………………………… 72

Table 5…………………………………………………………… 73

Table 6…………………………………………………………… 75

Table 7…………………………………………………………… 77

Table 8…………………………………………………………… 79

Table 9…………………………………………………………… 80

Table 10………………………………………………………… 82

Table 11………………………………………………………… 84-86

Table 12………………………………………………………… 90

Table 13………………………………………………………… 92-93

Table 14………………………………………………………… 94-96

Table 15………………………………………………………… 98

Table 16………………………………………………………… 99

Table 17………………………………………………………… 101

Table 18………………………………………………………… 103-104

Table 19………………………………………………………… 106

Table 20………………………………………………………… 109

Table 21………………………………………………………… 112

Table 22………………………………………………………… 114

Table 23………………………………………………………… 116

Table 24………………………………………………………… 117-121

Table 25 ……………………………………………………….. 129-130

FIGURE

Figure Page

1 The Research Paradigm ………………………………….. 18

Chapter 1

THE PROBLEM

Rationale

The tremendous task of education today, under the enormous

influx of technological advances and innovations, is still the development

of a learner into a whole person, a complete human being capable of

understanding his own complexity and his intricate society. The teacher,

who is in charge of this global task, needs to cope with the challenges of

the modern times. He has to be equipped with the resources vital in

arousing and sustaining students‘ interest, in facilitating the learning

process, and in evaluating the learning outcomes. He should be a master

of his craft and is genuinely concerned with the total growth and

development of his students (Clemente-Reyes 2002).

Quality education is first and foremost a function of instruction.

Thus, for education to attain and sustain its quality, it should be coupled

with the best preparation for excellent instruction. It is then emphasized

that to be an excellent high school teacher, one should both have full

command of the subject and full knowledge of the teaching-learning

process including course structure and examination system. The

teacher, therefore, should not only have mastery of the subject matter

but also an in-depth understanding of the mind set and standards of

students within the class (http://www.dooyoo.co.uk/discussion/what-

qualities-make-an-excellent-teacher/1039890/).

It is irrefutable that secondary education plays an essential part in

every nation‘s educational system (Darling-Hammond 2008). One high

school subject highly supportive of this is Mathematics.

No one can question the role being played by Mathematics in

education. In fact, Mathematics is one of the basic tool subjects in

secondary education. As such, mathematics teachers contend that the

place of mathematics in the basic education is indispensable

(http://wiki.answers.com/Q/Why_is_Mathematics_Indispensable). It has

been felt that mathematics has both utilitarian and disciplinary uses

necessary for everyone. By the very nature of the discipline, its

application to both science and technology and to the human sciences is

easily recognized by the layman. The bricklayer, the carpenter, and the

nuclear scientist use mathematics of varied complexities

(www.eric.edu/practicalities_mathed). Thus, the role of mathematics in

the holistic formation of every learner is vital (Sumagaysay 2001).

It can be gleaned, therefore, that it is important for students to

develop their potentials and capacities in mathematics to the fullest in all

possible means. In doing this, a sound mathematics curriculum that

would provide each learner the necessary skills and competence in

mathematics is hence necessary. The 2010 Secondary Mathematics

Education Curriculum Guide explicitly presents the Mathematics

Curriculum framework:

The goal of basic education is functional literacy for all. In line with this, the learner in Mathematics should demonstrate core competencies such as problem solving,

communicating mathematically, reasoning mathematically and making connections and representations. These competencies are expected to be developed

using approaches as practical work/ outdoor activities, mathematical investigations/games and puzzles, and the

use of ICT and integration with other disciplines.

With these contents in the Secondary Mathematics Framework,

quality secondary mathematics education, reflective in the best practices

in instruction, would also entail the use of effective approaches and

techniques of teaching, which would equip each learner the needed skills

and competencies. On top of it all, a competent mathematics teacher who

empowers learners to achieve the goals of mathematics education, and

who is efficient and effective in providing quality mathematics instruction

is imperative (Gonzalez 2000).

The country‘s vision for quality education with focus on

Mathematics Proficiency is undoubted. But, our country, of course, is

not relieved from the crises. In fact, Dr. Milagros Ibe of the University of

the Philippines said that the result of a survey on the competence of

Science and Mathematics teachers showed that majority of the teachers

are not qualified to teach the subjects. With this issue at hand, Ibe

remarked that it is easy to understand why the achievement of Filipino

Students in Science and Mathematics was dismally low (Lobo 2000). In

the 2000 issue of the Philippine Journal of Education as cited by Aspiras

(2004), Ibe supports her contention of the connection of teachers‘

competence and students‘ achievement. She stressed that Filipino

students suffer from poor thinking skills; they are only able to recall

concepts but for questions beyond that or which require multiple-step

problem solving, our students appeared to have been stumped. As a

result, math and science skills of students from 42 countries showed

that Filipino students are biting the dust of their global counterparts.

These ideas prompted former President and now Congresswoman Gloria

Macapagal-Arroyo (Educator‘s Journal, 2003). She stressed that in order

for Filipino students to be globally competitive, the national aims to

improve the country‘s educational standards and to upgrade teachers‘

competence have to be pushed (Educator‘s Journal, 2003). Despite these

aims, recent LET results revealed that majority of the secondary teacher-

examinees are not qualified to teach. In April, 2010 the passing rate for

secondary teachers was only 23.32% and in September, 2010 the

passing rate was 25.86%. These rates reveal that teachers, though

possess the needed degree/s are not yet qualified to teach; thus, they are

not competent. However, Lee (2010) clarified that passing the test does

not guarantee content competence. This is because majority of the

passers have rates of 75-79%. He highlighted that rates such as these

reflect fair or if not, poor competence.

On the light of mathematics teacher‘s qualification and

competence, issues arise, too. First, Lobo (2000), as cited by Oredina

(2006) reveals in his article that only 71% of the Mathematics Teachers

claim to have formal preparation in Mathematics. This means that 29%,

who are unqualified to teach mathematics, still teach the subject. In

addition, the Civil Service Commission (CSC) has ruled that the

Department of Education (DepEd) may hire and retain teachers even if

they had not yet registered with Professional Regulation Commission

(PRC) as mandated by Republic Act No.7836 (Educator‘s Journal 2003).

This further implies that a non-registered math teacher or a non-major is

teaching math. Another, teacher handling the same subjects or in the

same year level develops the idea and practice to be stagnant-an ordinary

lecturer in a classroom (Farol 2000). Furthermore, many graduates of

teacher-education institutions, though received formal education, are not

prepared to handle a class of learners (Adams 2002). Further, the UP

Institute of Science and Mathematics Education also revealed that ―many

teachers at all levels do not have the content background required to

teach the subjects they are teaching‖. The survey revealed that only 41%

of mathematics teachers are qualified to teach the subject (Cayabyab

2010). With this reality, it is not surprising why students performed

poorly in Mathematics Achievement Test. This is stressed by Roldan

(2004) in her assertion that students‘ mathematics low performance is

reflective of the weak mathematics teachers‘ influence. Roldan (2004)

revealed that secondary teachers in Region I were proficient only in

concepts and computations but they were deficient in their skills in

problem-solving and the use of teaching strategies. Thus, mathematics

teachers frequently find themselves focusing on mechanics, the answer-

resulting procedures-without really teaching what mathematics is all

about-where it came from, how it was labored on, how ideals were

perceived, refined, and developed into useful theories-in brief, its social

and human relevance (Cayabyab,2010).

It was also disclosed by Bambico (2002) in her dissertation that

that majority of the mathematics teachers in Region I scored 17 out of 35

simple mathematics problems; and their instructional competence

ranged from 54.71% to 78.03% only. These ratings were emphasized to

be weaknesses and the major reasons why the passing rate of the region

in the NAT has not even reached 80% and up.

In the City Division of San Fernando, particularly in the Private

secondary schools, quality mathematics teaching had been given much

emphasis. Several seminars and training-workshops had been organized

to update and upgrade teachers‘ competence. One most recent

Mathematics Seminar was organized by the Association of the Private

Schools last July, 2010. The seminar-workshop on Trends in Teaching

High School Mathematics was an aim to improve the students‘

mathematics performance in the 2009 National Achievement Test (NAT)

(Eligio 2010). The seminar was attended by mathematics teachers in the

Private Schools in La Union where the researcher served as the resource

speaker. This brought out that majority of the teachers could not fully

analyze problems in higher Mathematics such as Geometry and

Trigonometry despite the fact they have graduated with a Mathematics

degree. They were also found to be very young in the service and that

they tend to teach mathematics word problems using one approach.

Even though seminars and trainings were conducted, these only

lasted for few hours and had no follow-ups. Another, only a few are sent

by the participating schools to attend such endeavor.

It is then with these predicaments that the researcher embarked

on the idea to appraise and evaluate the competence of mathematics

teachers along content and instruction. The results, in turn, will be the

foundations of proposing a validated two-pronged training program for

the Mathematics teachers in the Private Secondary Schools of the City

Division of San Fernando for the academic year 2010-2011.

Theoretical Framework

To put this study in its theoretical framework, a discussion on the

competence theories, theories of teaching and learning, the best practices

and approaches of an effective teacher, and the concept of training are

presented. Several theories on learning are also included since teachers

are learners, too. They need to learn first the fundamentals, the

strategies and techniques before they can actually impart knowledge to

their students.

Mathematics involves learning simple skills, calculations, facts and

procedures where memory, most especially practice are the most

essential. It requires a high level of creative and analytic thinking. Thus,

mathematics teachers should know when and what concepts to teach,

when and why students are having difficulties, how to make concepts

meaningful, when and how to improve skills and how to stimulate

productive and creative thinking in order to fully analyze what they are

doing (Subala 2006).

Piaget (1964) opined that as a child acquires knowledge of the

environment, he or she develops mental structures called concepts.

Concepts are rules that describe properties of environment events and

their relations with other concepts. As applied to teachers, when teachers

get familiar with certain concepts and routines, they are able to master

the skills.

Dewey‘s (1896) notion of knowledge for teaching is one that

features inquiry with, and practice as the basis for professional judgment

grounded in both theoretical and practical knowledge. If teachers

investigate the effects of their teaching on student learning and if they

study what others have learned, they come to understand teaching to be

an interesting endeavor. They become sensitive to variation and more

aware of the different purposes and situations. They are assessed on

contingent knowledge to become more thoughtful decision-makers.

According to Thorndike (1926), learning becomes more effective

when one is ready for the activity, practices what he has learned and

enjoys the learning experience. As applied to teachers, they cannot teach

effectively if they have not learned sufficiently.

Thorndike‘s law of exercise states that the more frequently a

stimulus response connection occurs, the stronger association and

hence, the stronger learning. Practice without knowledge of results is not

nearly effective as when the consequences become known to the learner.

Further, concepts are the substance of mathematical knowledge.

Students can make sense of mathematcs only if they understand its

concepts and their meanings or interpretations. An understanding of

mathematical concepts involves around more than mere recall of

definitions and recognition of common examples. The assessment of

students‘ understanding of concepts should be sensitive to the

development nature of concept acquisition. (Arellano 2004)

Bruner‘s (1968) most famous statement is that, any subject can be

taught effectively in some intellectually honest form to any child at any

stage of development. He insisted that the final goal of teaching is to

promote the general understanding of the structure of a subject matter.

To learn and use mathematics requires a substantial mastery of

computation. To master a skill of computation requires constant

practice, repetition and drill. Computational skills are essential in order

to facilitate the learning of new math concepts, to promote productive

thinking in problem solving, research and other creative thinking

activities.

Mathematics teachers have always viewed problem solving as a

preferential objective of mathematics instruction (Subala 2006). It was

not until the National Council of Teachers of Mathematics (NCTM)

published its position paper that problem solving truly came of age. As

its very first recommendation, the council proposed that problem solving

be the focus of school mathematics and performance in problem solving

be the measure of the effectiveness of the personal and national position

of mathematical competence (Taback, 1998).

Bruner (1968) believed that intellectual development is innately

sequential, moving from inactive through iconic to symbolic

representation. He felt it is highly probable that this is also the best

sequence for any subject to take. The extent to which an individual finds

it difficult to master a given subject depends largely on the sequence in

which the material is presented. Further, Bruner also asserted that

learning needs reinforcement. He explained that in order for an

individual to achieve mastery of a problem, feedback must be reviewed as

to how they are doing. The results must be learned at the very time an

individual is evaluating his/her performance.

The above theories suggest that problems and applications should

be used to introduce new mathematical content to help students develop

both their understanding of concepts and facility with procedures, and to

apply and review processes they have learned.

Besides his abilities and competence, a teacher who is tasked to

facilitate the teaching-learning process, also needs a set of teaching

theories. These theories, which are based on the teachers‘ understanding

of the learner and the educative process, become the bases of his ways

on how to influence his students to learn. The 2010 Secondary

Mathematics Curriculum provide the three most important theories.

These are Experiential Learning by David Kolb and Rogers,

Constructivism and Cooperative Learning.

Experiential Learning by Kolb and Rogers presents that significant

learning takes place when the subject matter is relevant to students‘

experience and is purposeful to their personal interest. This further

connotes that human beings have the natural tendencies to learn; as

such, the task of the teacher is just to facilitate learning. Facilitating

learning revolves around (1) setting a positive climate, (2) clarifying the

purpose of the learner, (3) organizing and making available learning

resources, (4) balancing intellectual and emotional components of

learning and (5) sharing feelings and thoughts with learners but not

dominating. Thus, Experiential learning substantiates the Principle of

Learning by doing (http://oprf.com/Rogers).

On the other hand, constructivism roots from the idea that ―one

only knows something if one can explain it‖. This idea was formalized by

Immanuel Kant, who asserted that students are not passive recepients of

information; rather, they are active learners

(www.wikipedia.com/ImmanuelKant). A basic theoretical proposition of

constructivism is that the students are eager participant in the

acquisition of knowledge. So, in the constructivist room, the teacher

serves not as the authority, but the pathfinder of knowledge.

Cooperative Learning Theory by Johnson and Johnson, in

addition, holds that learning is significant when students work together

to accomplish a task. The cooperative tasks are designed to elicit positive

interactions, provide students with different opportunities, and make

students engage in learning. This theory suppports the Multiple-

Intelligence Theory by Gardner (Montealegre 2003).

The Mathematical Framework also necessitates integration. As

such, the Reflective Teaching Theory is vital. This theory is based on the

Ignatian Pedagogy asserting that teaching experience should include

interaction from the students, which calls the plan to implement

reflections that give birth to new insights, knowledge and enlightenment

regarding one‘s self based upon the content of teaching (Crudo 2005).

In addition, in her dissertation on Mathematics Education,

Cayabyab (2010) theorized a mathematics stepping-stone theory. She

stressed that in teaching mathematics, students should be taught that

every mistake, every fault, every difficulty encountered becomes a

stepping-stone to better and higher things. She added that in teaching

and learning mathematics,skills on patience and accuracy are developed.

When a teacher has finished teaching, he therefore administers

strategies for assessment and evaluation to gauge learning. The theory of

Evaluation by Burden and Byrd, as mentioned by Oredina (2006),

pointed out that frequent, continuous and impartial evaluation of

academic performance is vital not only for the growth of institution but

also for the growth of the individual. Evaluation would tell whether

improvement is necessary.

If a teacher wants to be the best teacher for her students, he

should not fail to upgrade and update himself. The concept of training

enters the scene. Training is the process of acquiring specific skills to

perform a better job. It helps people to become qualified and proficient in

doing some jobs (Fianza,2009). Usually, an organization facilitates the

employees‘ learning through training so that their modified behavior

contributes to the attainment of the organization‘s goals and objectives

(Oredina 2006).

Further, training is a complex activity and must be clearly

planned. Design and preparation of training course usually consume

more time than delivery of the material. Successful training requires

careful planning by the trainer. Planning helps the trainer/s determine

that the appropriate participants have been invited to the training course

and that the training is designed to meet their needs in an effective way.

Thus steps in planning for effective training program are a requisite.

According to the PDF article accessed from the internet, the parts of a

training program include objectives, content , materials or resources,

methods or procedures, and evaluation strategy

(www.jifsan.umd.edu/pdf/gaps-en/VI-Effective-Training-Com.pdf).

The abovementioned instructional competency dimensions find its

essence in the general areas cited in the questionnare.These serve as the

building blocks in structuring this research.

Moreover, the theories in teaching and learning, practices and

approaches, and the principles in teaching mathematics show

parallelism in each of the content of the instructional dimensions. These

may also serve in the formulation of the recommendations of the study.

The concept of training serves as the core idea in designing the

output of this pursuit.

Conceptual Framework

The task of a teacher is complex and many-sided and demands a

variety of human abilities and competencies. The abilities and

competencies of a teacher, according to Nava (1999), as cited by

Clemente (2002), are subject matter – mastery of content-specific

knowledge for the effective instruction, classroom management –

creation of an environment conducive to learning, facilitation of learning

– implicit and explicit knowledge of various teaching strategies and

methods to attain instructional objectives, and diagnostic – knowledge of

class needs and goals, abilities and achievement levels, motives,

emotions, which influence instruction and learning. These competence

dimensions were also mentioned by Lardizabal (2001). According to her,

the four dimensions are teaching skills, guidance skills, management

skills, and evaluation skills.

Effective high school mathematics teaching, therefore, involves

mastery of the subject matter on the part of the teacher, understanding

students‘ differences, interest and background, skills in the use of

appropriate methods and techniques, appropriate assessment strategies

and flexibility and sensitivity to adopt to the needs of students. Thus, the

nature of the task of a teacher is not easy. This then implies that the

teacher has to improve if his vision of influencing students to learn is of

prime concern.

One of the most time-tested ways for continuing development of

the professional teachers is the training and in-service educational

program. Its rationale is to help teachers carry out their job better. The

outcome of a well-planned training program is manifested in an

environment of learning suited to the needs of the children

(www.britannicaonlineencyclopedia/training). This then connotes that

when teachers improve for the better, students improve for the better,

too.

Boiser (2000) extends his idea that if one aspires to continue

teaching effectively, he needs to continue upgrading himself. He opines

that to upgrade necessitates reading professional references, enrolling in

advanced courses and attending trainings, conferences and workshops.

Additionally, Lapuz (2007),as cited by Bello (2009), stresses the need for

training and retraining if teachers really wanted to be competent.

It is in this light that the study is thought of, formulated and set

up. This conceptualization is logically designed in the research paradigm

in Figure 1. The paradigm made use of the Input-Throughput-Output

model. The input is composed of the profile of mathematics teachers

along highest educational attainment, number of years in teaching, and

number of trainings and seminars attended. Further, it also contains the

variables on the level of competence along content and instruction. These

variables are indeed necessary to determine how competent the

mathematics teachers in the Private Secondary Schools in the City

Division of San Fernando, La Union are.

The throughput incorporated the processes of analyzing and

interpreting the variables in the input- profile (highest educational

attainment, number of years in teaching, number of seminars attended);

level of competence along content and instruction; the comparison in the

perceived instructional competence among the three respondent groups;

the culled-out strengths and weaknesses,and tests of correlation between

profile and the levels of competence along content and instruction; and

the relationship between the levels of competence along content and

instruction. It also holds the process of conceptualizing and validating

the output of the study.

The output of the study, therefore, is a validated two-pronged

training program for mathematics teachers in the Private Secondary

Schools in the City Division of San Fernando, La Union for academic year

2010-2011.

A. Profile of mathematics teachers

along:

1. Highest educational

attainment;

2. Number of years in teaching

math; and

3. Number of seminars and

trainings

B. Level of competence of

mathematics teachers along:

1. Content

a. conceptual skills

b. reasoning/analytical

skills

c. computational skills

d. problem-solving skills;

and

2. Instruction

a. Teaching/

Facilitating Skills;

b. Guidance Skills;

c. Management

Skills; and

d. Evaluation Skills

A. Analysis and interpretation of:

1. Teachers’ profile

2. Level of competence along

content and instruction

2.1 Comparison in the

perceived instructional

competence among the

respondent groups

3. Relationship between

a. teachers’ profile and

level of competence

along content;

b. teachers’ profile and

level of competence

along instruction; and

c. teachers’

competencies along

content and instruction

4. Strengths and weaknesses

on the level of competence

B. Development of a Proposed

Two-Pronged Training

Program for Mathematics

Teachers

C. Validation of the Two-

Pronged

Training Program

1. face

2. content

A Validated Two-Pronged

Training Program for Mathematics

Teachers

Fig. 1

Research Paradigm

Input Throughput Output

Statement of the Problem

This study aims primarily to determine the level of competence of

mathematics teachers in the Private Secondary Schools in San Fernando for

the academic year 2010-2011 as basis for a validated two-pronged training

program. Specifically, it aims to answer the following questions:

1. What is the profile of the mathematics teachers along:

a. highest educational qualification;

b. number of years in teaching mathematics; and

c. number of mathematics trainings and seminars

attended?

2. What is the level of competence of mathematics teachers along:

a. Content

a.1. Conceptual Skills

a.2. Reasoning/ Analytical Skills

a.3. Computational Skills

a.4. Problem-Solving Skills ; and

b. Instruction

b.1.Teaching Facilitating Skills

b.2. Guidance Skills

b.3. Management Skills

b.4. Evaluation Skills?

2.1 Is there a significant difference in the instructional competence

of the teachers as perceived by the students, heads and

teachers, themselves?

3. Is there a significant relationship between:

a. Teacher‘s profile and competence along content;

b. Teacher‘s profile and competence along instruction; and

c. Competence along content and competence along

instruction?

4. What are the major strengths and weaknesses of the mathematics

teachers along:

a. Content; and

b. Instruction?

5. Based on the findings, what training program may be proposed to

enhance the content and instructional competence of the

mathematics teachers?

5.1 What is the level of validity of the training program along:

a. face; and

b. content?

Hypotheses

The researcher is guided by the following hypotheses:

1. There is no significant difference in the perceived instructional

competence of the teachers among the three respondent groups.

2. There is no significant relationship existing between:

a. Teacher‘s profile and competence along content

b. Teachers‘s profile and competence along instruction

c. Competence along

Scope and Delimitation

The primary aim of this study is to determine the level of

competence of high school mathematics teachers in the Private Schools

of the City Division of San Fernando for the academic year 2010-2011.

The 13 (thirteen) schools include Brain and Heart Center (BHC), Saint

Louis College (SLC), Christ the King College (CKC), Gifted Learning

Center, MBC Lily Valley School, La Union Cultural Institute (LUCI), La

Union Colleges of Arts, Sciences and Nursing (LUCNAS),Union Christian

College (UCC), San Lorenzo Science High Schoool (SLSHS), National

College of Science and Technology(NCST), Central Ilocandia College of

Science and Technology (CICOSAT), Felkris Academy, and Diocesan

Seminary of the Heart of Jesus (DSHJ). Further, there are three (3)

respondent groups: the Mathematics teachers, the heads, and the

students. Each Mathematics teacher in the private schools of San

Fernando is evaluated by one of his/her classes.

Based on the identified strenghts and weaknesses on the level of

content and instructional competence of the mathematics teachers, a

proposed two-pronged training program is formulated. The proposed

training program will be administered to the Private Secondary Schools

in the City Division of San Fernando, La Union. Since it involves

logistics, the administrators of the Private Secondary Schools in the City

Division of San Fernando are asked to validate the proposed two-pronged

training program for teachers.

Importance of the Study

This piece of work will greatly benefit the administrators, heads,

teachers, students, the researcher and future researchers.

To school administrators of the Private Secondary Schools in the

City Division of San Fernando, this study will provide them with data

that can help them formulate the in-service training programs. Further,

they will also be guided in structuring the Faculty Development Program

that is aimed at intensifying and sustaining the skills of the teaching

workforce;

To the Mathematics heads of the City Division of San Fernando,

this study will give them insights about the competence of their teachers.

This will also provide them data in designing the Human Resources

Development Plan;

To Mathematics teachers, this study will give them baseline data of

their strenghts and weaknesses in content and instruction. The output of

the study, on the other hand, will make them more competent, prepared,

directed and helped in carrying out their noble tasks;

To students of the Private Secondary Schools in San Fernando City

Division, this study will lead them to a thoughtful understanding of

mathematics for they are handled by more competent teachers;

To the researcher, a Mathematics teacher and at the same time the

Subject Area Coordinator for Mathematics of Christ the King College, this

study will help him in improving his mathematics teachers‘ competence;

and

To future researchers, who will be interested to conduct similar

studies, this study will motivate them to pursue their research since this

study can be used as basis.

Definition of Terms

To better understand this research, the following items are

operationally defined:

Content Competence. This pertains to the subject matter knowledge of

the Mathematics teachers in the four (4) secondary

Mathematics subjects: Elementary Algebra, Intermediate

Algebra, Geometry, Advanced Algebra, Trigonometry &

Statistics. Further, this also gauges the cognitive skills in

Mathematics along conceptual, analytical, computational and

problem-sloving.

Analytical Skills. This pertains to the skills on

comprehension that requires investigative inquiry and

logical reasoning.

Computational Skills. This pertains to the skills that involve

the fundamental mathematical operations.

Conceptual Skills. This pertains to the skills on learning facts

and simple recall.

Problem-Solving Skills. This pertains to the skills that

require multiple-step plan to come up with a decision

or a solution.

Instructional Competence. This is divided into four dimensions:

teaching/facilitating skills, management skills, guidance skills

and evaluation skills.

Evaluation skills. This is an area on instructional

competence which includes quality of appraisal questions,

quality of assignment/enrichment activities, and quality of

appraising students‘ performance.

Guidance skills. This is an area on instructional competence

which includes quality of interaction and quality of

activity.

Management skills. This is an area on instructional

competence which includes atmosphere in the

classroom,and conduct and return of evaluation materials.

Teaching skills. This is an area on intsructional competence

which includes substantiality of teaching, quality of

teacher‘s explanation, receptivity to students‘ ideas and

contributions, quality of questioning procedure, selection

of teaching methods, and quality of information and

communication technology utilized.

Heads. This pertains to the principals, academic coordinators, subject

area coordinators and department heads.

Level of Competence. This pertains to the degree or extent of

attainment along content and instruction of the Mathematics

teachers.

Mathematics students. These are the students duly enrolled in a private

high school in San Fernando for the academic year 2010-2011.

Mathematics teachers. These are the teachers handling secondary

mathematics in the Private Secondary schools in San Fernando for

the academic year 2010-2011.

Private Secondary schools in San Fernando. These are the non-

government schools owned by private institutions and individuals

where the three groups of respondents came from.

Profile. This contains the variables on highest educational attainment,

number of years in teaching, and number of trainings and

seminars attended.

Highest educational attainment. This pertains to the highest

academic qualification of the high school mathematics teachers

for the academic year 2010-2011.

Number of years in Teaching. This refers to the length of service

a mathematics teacher has in the academe.

Number of Seminars attended. This refers to the frequency of

trainings undergone by a Mathematics teacher for the past 2 years.

Strength. This term refers to a content competence rating of 17 and

above and to an instructional competence rating of 3.51 and

above.

Two-Pronged Training Program. This refers to an action plan devised in

the study to enhance the content and instructional competence of

mathematics teachers of the Private schools in the City Division of

San Fernando.

Weakness. This refers to a content competence rating of below 17 and an

instructional competence rating of below 3.51.

Chapter 2

REVIEW OF RELATED LITERATURE AND STUDIES

A summary of professional literature and studies related to the

present study are presented in this chapter. These helped strengthen the

framework of this study and substantiated its findings.

Profile of Secondary Mathematics Teachers

According to the Executive Summary on Teachers and Institution,

teacher qualifications matter (www.sec.dost.gov.ph). It is with this idea

that the areas on teacher‘s profile are established. The areas include

Highest Educational Attainment, Years in teaching Mathematics and

Numbers of Trainings and Seminars Attended.

Highest Educational Attainment

Republic Act 9293, an act amending section 26 of RA 7836 states

that no person shall engage in teaching or act as a professional teacher

whether in preschool, elementary or secondary level unless the person is

duly registered.

Fianza (2009) revealed in her study that majority of the

respondents possessed the required eligibility to teach secondary

mathematics since most of the teachers were LET/PBET passers and

degree holders of mathematics. She further stressed that 40 out of 56

respondents were bachelor‘s degree holders, 15 had master‘s degree and

1 had doctorate degree.

Bautista, as cited by Binay-an (2002), stressed that teachers, in

general, met the educational requirements in accordance with the Magna

Carta for Public School Teachers. She also stressed that teachers didn‘t

want to remain stagnant in their field.

Eslava (2001) found out that out of the 40 teacher-respondents in

the secondary schools in La Union, only 12 or 30% were AB/BS

graduates, 19 or 47.5% were AB/BS with MA/MS units, or 8 or 20%

were MA/MS graduates and 1 or 2.5 was a PhD/EdD graduate. It was

pointed out that the mathematics teachers value continuing education to

further equip themselves in the issues and concerns about teaching.

In the Education Journal of the District of Thailand year 2009, the

study of Dr. Naree Aware-Achwarin (2005) was noted. The findings of this

published study disclosed that most of the teachers (92.88%) held

bachelor‘s degree; very few teachers (6.23%) held master‘s degree or

higher degrees.

Rulloda (2000), as cited by Oyanda (2003), expressed that teachers

did not want to remain stagnant in their undergraduate degrees. They

endeavored to improve their competencies by updating and upgrading

themselves through the formal process. It was necessary for them to

elevate their professional outlook to make them effective and worthy

members of the profession.

Number of Years in Teaching Mathematics

In the revised guidelines of the appointment and promotions of

teaching and related teaching group (DepEd order No.66, s 2007)

teaching experience is one of the criteria. Thus, the more experienced a

faculty member is the more confident and effective he is in teaching. This

was confirmed and affirmed by the study of Aware-Achwarin (2005). She

stressed that most of the teachers (71.07%) had teaching experience of

more than 10 years.

However, several local studies ran nonparallel to these

international findings. Oyanda (2003) revealed that 136 high school

Mathematics teachers taught for 5-9 years, 132 taught for 0-4 years and

only a few had 20 years or more teaching experience. This implied that

majority of the teacher-respondents were quite young in the service.

Fianza (2009) also revealed that 67% of her respondents were very

young in teaching high school geometry. These respondents are in the

teaching service for less than 4 years.

According to Laroco (2005), 10% of the Private High School

Mathematics teachers in Urdaneta had been teaching for 15-19 years.

30% had 5-9 years of teaching and majority (60%) had taught for 4

years. The same implication was revealed.

Yumul (2001) noted that the length of teaching experience was a

valid indicator of performance. This is also seconded by the study of

Mallare (2001) stating that teaching experience is the best predictor of

mathematics achievement. These assertions can be easily established

since teachers develop their effectiveness as they become aware and

more experienced in the realities and complexities of teaching.

Number of Seminars and Trainings Attended

As teachers become the 21st century teachers, they need to

continually update and upgrade themselves to serve the needs of the so-

called digital learners. One way of doing this is through attending

mathematics seminars or trainings.

Oyanda (2003) revealed that 6 (six) had attended international

trainings and 45 had national trainings. However, 4 revealed that they

had not attended any training. It was pointed out that only a few went to

international seminars/in-service trainings due to financial reasons

including lack of sponsorship from the government and private sectors.

Laroco (2005) brought out that most of the teacher-respondents

only attended seminars within the division level. The 2nd was regional.

The 3rd was at school and 4th was at the national level. This was due also

to financial constraints.

Fianza (2009) divulged that more than fifty percent of the

respondents attended trainings on curriculum, teaching strategies,

management, and assessment methods/ tools. Less than fifty percent of

the respondents attended trainings on content in Geometry. These

seminars are based on school and local.

Cabusora (2004) unveiled that attendance of his teacher-

respondents to seminars and trainings were mostly local and regional.

Oredina (2006) disclosed that the instructors have attended a few

trainings and seminars for professional development. With these,

majority of the teacher-respondents have ―very inadequate‖ participation

in seminars and training workshops. The reasons she stressed were

financial constraints, non-availability of the instructors due to school

commitments and the distance of the seminar venue.

Level of Content and Instructional Competence

The significant factor in achieving quality Secondary Mathematics

Education is teachers‘ competence along content and instruction. Diaz

(2002) supports this by expressing that to be a successful mathematics

teacher, one must be competent in math and in mathematics

instruction. Thus, the levels of competence along the two dimensions

show teachers‘ strengths and weaknesses that serve as basis to develop

and actualize activities that will further improve and enhance

competence. Mathematics teachers can therefore improve the ability of

their learners when they have very good content knowledge of their

subject area and at the same time sound instructional skills.

Subject Matter/ Content

Cabusora (2004) stressed that the first essential of effective

teaching is teacher‘s thorough grasp of the subject matter he teaches.

According to Toledo (1992) and Bagaforo (1998), as cited by Diaz

(2000), teachers, in general, felt moderately competent in their knowledge

and ability in mathematics. It was disclosed that the teachers still lack

the knowledge of mathematics subjects, particularly the higher

mathematics. Thus, it was concluded that teachers did not possess math

competence at level adequate for teaching secondary mathematics. Diaz

(2000) also found out in her study that teachers were moderately

competent in their knowledge in mathematics.

Gundayao (2000) found in her study that the teachers teaching

secondary mathematics in the Province of Quirino had ―good‖ level of

proficiency in Algebra, ―poor‖ in Geometry and ―poor‖ in Trigonometry. In

general, the results were poor because the teachers lacked the

competence in analyzing high level of category in analyzing problems.

Subala (2006) found out in her study that the graduating math

majors of teacher-training institutions in Region I were moderately

competent in Basic Math, fairly competent in Algebra and Statistics and

poorly competent in Geometry and Trigonometry.

Roldan (2004) revealed that her respondents were Above Average in

Math I and II and average in Math III and Math IV. She concluded that

the conceptual skills of the mathematics teachers were very important

and teachers need to consistently update and upgrade their capabilities

to enable them to cope with the challenges of the new millennium. Thus,

teachers needed to improve their skills in the topics of a particular

subject found to be weaknesses.

Teaching or Facilitating Skills

The shift of the teacher‘s role as provider of knowledge to facilitator

of learning or pathfinder of knowledge calls for proper application of

teaching methods to make the learning experiences vital and relevant.

Thus, the effectiveness of teaching Mathematics relies to a great extent

not only upon the teachers‘ educational attainment or skills but also

upon his competence in the subject.

Laroco (2005) unveiled that teachers mostly relied on textbooks to

facilitate the teaching-learning process. She also cited Yumul (2001)

revealing that the adequate instructional materials were not highly

utilized.

Sameon (2002) found out in his study that the most pressing

problems encountered by the instructors were inadequate facilities and

equipment; inadequate knowledge of teaching strategies and approaches.

Likewise, Bello (2009) also divulged that her respondents were

capable in teaching but had not yet achieved the level of competence for

optimum effectiveness. She stressed that teachers have more to enhance

such as on educational technology, technology integration, professional

relationship, community linkages and collaboration.

Also, according to the monitoring and evaluation of the

implementation of the basic education curriculum, there were gross

inconsistencies between the kind of graduates/learners that the schools

desire to produce and the strategies they employ. Instruction was still

predominantly authoritative and text-book based, learning was usually

recipient and reproductive, supervision was commonly prescriptive and

directive; and assessment was focused more on judging rather than on

simproving performance.

The second finding was that teachers wanted to know more about

integrative teaching. Teachers did not feel confident to use the

approaches because of the limited knowledge to operationalize them in

terms of lesson planning, instructional materials development, subject

matter organization, presentation and evaluation. There were still many

teachers who do not have enough knowledge about the key concepts and

approaches. However, they were willing to learn how to be more effective

in facilitating the full development of the students‘ potentials and to be

facilitator of the integrative learning process.

Thirdly, teachers had limited knowledge of constructivism as a

learning process. Learning as a construction process and the learner as a

constructor of meaning is among the basic concepts of the BEC.

Although the concept was unfamiliar to many teachers, it was observable

in some classes where problem solving, inquiry, or discovery approaches

were being used.

Another finding of the team was that several factors constrained

teachers from playing their role as facilitators of the learning process.

The factors that inhibited teachers from playing the facilitators‘ role

effectively were students‘ English deficiency, overcrowded classes, and

insufficient supply of textbooks, prescriptive supervision and an

examination system that encourages authoritative teaching.

However, there were also findings which revealed positive results.

One was the study of Aware-Achwarin (2005) on Teacher Competence of

Teachers at Schools in the Three Southern Provinces of Thailand which

revealed that teachers‘ competence was at high level. The highest was on

―teachership‖.

The second was that of Villanueva (1999), as cited by Binay-an

(2002), which revealed that the instructional abilities of the teachers

were rated high along ability to explain correctly, having a good

command of the language and sufficient knowledge of the subject matter.

Further, the findings of Acantilado (2002) showed that the faculty

members of Tertiary Accredited Programs of SUCs in Region I were highly

competent. Another, Roldan (2004) cited Subala revealing that teacher-

respondents were competent. This finding revealed that the instructors

could be proper sources of assistance and guidance to their students in

analyzing different mathematical problems. She stressed that the more

competent the instructors are the better is the result in terms of the

teaching-learning process.

Grouws and Cebulla (2002), as cited by Fianza (2009) mentioned

that research findings indicated that certain teaching strategies and

methods should be worth careful consideration as teachers strive to

improve their mathematics teaching practice. Teachers should use

textbooks as just one instructional tool among many rather than feel

duty-bound to go through the textbook as one section per day basis. As

technology is used in mathematics classroom, teacher must assign tasks

and responsibilities to students in such a way that they have active

learning experiences with technological tools employed.

Research then suggests that teachers should concentrate on giving

opportunities for all students to interact in problem-rich situations.

Teachers must encourage students to find own solution method and give

opportunities to share and compare their solution method and answer in

small groups. Such solutions were presented by Roldan (2004) as she

cited Diaz (2000). The solutions were: (1) the administration must hire

only competent Mathematics Teachers to teach the subject. This step is

supported by Rivera (2010) citing an article posted on www.eric.ed.gov

conveying that schools are hiring teachers who are competent since

students‘ attainment level is hoped to improve; (2) the administration

should also be fully aware of the importance of faculty development

through the pursuit of graduate courses and attendance to seminars and

in-service training, for such are essential to the teachers‘ professional

growth and development, particularly on effective teaching; (3) teachers

should strive to elevate their level of attitudes along concept and

mathematics from above average to higher level; (4) rigid annual

evaluation of teachers may also be of help for them to assess their

weaknesses, make improvements on such and maintain and sustain

their strengths; (5) moderately competent and competent teachers attend

Saturday and summer classes or workshops to be able to upgrade their

competence; and (6) teachers should be encouraged to attend seminars

and workshops particularly in Mathematics to update them with recent

trends and educational innovations.

Guidance Skills

Educational Guidance is the process of helping students to achieve

the self-understanding and self-direction necessary to make informed

choices and move toward personal goals (Microsoft ® Encarta ® 2009).

One of the innate tasks of a teacher is to promote learning. He

does this by guiding the learning process of students through planning

and organizing meaningful learning experiences, creating a desirable

learning environment, using a variety of instructional materials,

providing for individual differences and appraising students‘ growth and

development.

Diaz (2000) expressed in her study that a teacher who is the

facilitator of learning should also have special knowledge and skills in

guiding, directing and advising learners. She stressed that doing so gives

substance to teacher-students relationship. Thus, in this special task,

the teacher must possess knowledge and skills in assisting students in

their problems.

Graycochea (2000) revealed in his study that his teacher-

respondents were highly competent in providing an environment

conducive to learning. This had been perceived by the teachers, students

and their heads.

The study of Oredina (2006) exposed that mathematics teachers‘

guidance skills were perceived as strengths. She emphasized that the

teacher-respondents were very good in directing, supervising and guiding

the learning process by providing an atmosphere which is

nonthreatening. Further, they were able to provide appropriate level and

needs of the students. In addition, they can direct the work of the

students properly.

Management Skills

The principle of a favorable learning environment is of universal

acceptance. To teach effectively is to manage class effectively, too. This

principle suggests that learning becomes interesting and enjoyable under

favorable working conditions. Good classroom practices; thus, enter the

scene.

Bueno (1999), as cited by Tabafunda (2005), asserts that a sound

classroom can be maintained by employing classroom management

practices. These practices are: (1) structuring the learning environment;

(2) religious preparation of lessons; and (3) maintenance of constructive

pupil-behavior correction. Thus, a successful teacher is one who can

evaluate situations and then apply appropriate styles to address such

situations. (http//www.classroom%20management.03-29-10)

One of the most difficult problems that confront teachers is to

manage classrooms. This is because one cannot fully learn the

techniques of proper management from books or from earning a

bachelor‘s degree.

Achwarin (2005) reveals that among the dimensions of

instructional competence, classroom management was rated the lowest.

Olbinado (2007) in her study entitled, ―Enhancement Program for

Secondary Teachers who are Non-math Majors‖ revealed that the

teacher-respondents were good at classroom management. She stressed

that even though the teachers were not holders of mathematics degree,

they were good at managing classes since most of them were seasoned

teachers.

Oredina (2006) underscored that the teacher-respondents were

very good at guidance skills. This means that the teachers were highly

aware of the importance of extrinsic motivation and strengthen positive

attitudes such as giving commendations and approval.

Evaluation Skills

When a teacher finishes the course of the discussion, he

automatically administers the tools to assess learning. It is through

assessment that students‘ performance is monitored. The purpose of

evaluation is hence necessary.

According to Laroco (2005) there are four principles of educational

assessment. These are: (1) educational assessment always begins with

educational values and standards. Assessment is not an end in itself but

a vehicle for attaining educational goals; (2) educational assessment

works best when it accurately reflects the students‘ achievement/

attainment and understanding of educational goals and standards; (3)

educational assessment works best when it is ongoing, not episodic and

when varied measures are used; and (4) effective educational assessment

provides students with information (e.g. goals, standards, feedback) to

motivate and enable them to attain educational targets. Students should

be aware of what they are being assessed for and should also be given

information on what is needed to attain the expected outcomes.

Sameon (2002) revealed that his respondents perceived themselves

as very competent in assessment. He stressed that the teachers

understood the underlying theories and practices to improve students‘

performance.

Rivera and Sambrano (1999), as cited by Tabafunda (2005),

stressed that effective teaching should be coupled with the art of

questioning. Good questions served as essential in developing students‘

ability to define and exercise judgments.

Oredina (2006) found out in her study that the teacher-

respondents were perceived ―very good‖ in evaluation and assessment.

She revealed that along the four competence dimensions, the skill on

evaluation had the highest rating. This means that the respondents were

highly capable in formulating questions with the purpose of developing

critical thinking; mathematics teachers were competent in providing

reasonable, appropriate, practical and challenging enrichment activities

to substantiate what had been taken in class.

Comparison in the Perceived Instructional Competence Among the

Groups of Respondents

According to the article accessed from

http://en.wikipedia.org/wiki/individual_differences_psychology, ―Every

man is in certain respect (1) like all other men, (2) like some other men

and (3) like no other men‖. Thus, two contrasting ideas are revealed –

individual similarities and differences. This means that any two

individuals may have same perceptions at a time; but they may also have

opposing perceptions at another time. The adage, ―Everyone experiences

different time and space than everyone else but can still find

commonalities at a certain time in space with everyone else‖ supports

this thoughts and contentions very well

(http.//www.newton.dep.anl.gov/askasci/gen06/gen06327.htm).

Commonalities among perceptions exist because there is a

common code (shared representations) for perceptions and actions. This

is contained in the Common Coding Theory

(www.en/wikipedia.org/wiki/common_coding_theory). On the other

hand, differences exist because of different status of people, needs,

personalities, and beliefs. Further, individuals differ in terms of

perception because of selective perception

(www.ask.com/questions_about_selective_perception).

The aforecited thoughts are revealed in a study published in the

web revealing that there is a significant difference in the perceptions

along skills between the teachers and managers/heads. This is due to

the observation that when one holds a position, he has a certain degree

of confidence. He is sure of his capabilities and enjoys certain status

higher than others.

This can be supported through the educational thought presented

by Johnson (2010) on administrative support and cordial teacher-

student relationships. He stresses that these educational principles

integrate the concepts on backing-up, lending hands and sharing

appreciation.

Relationship of Profile and Level of Competence along Content

A teacher cannot share what he does not have. He has to be a

subject matter expert when he intends to instill lasting thoughts in the

minds of his learners.

Several articles posted on the World Wide Web implicitly and

explicitly cite the relationship between profile variables along highest

educational attainment, teaching experiences and number of seminars

attended and subject matter competence.

One article contends that subject matter/ content knowledge is

rooted from teaching experiences and the number of degrees a teacher

holds. (http://doconnor.edublogs.org/finding-e-learning-and-online-

teaching-jobs/)

Another supports this thought by mentioning that subject matter

competence can be attained and maintained through continuing

professional education. It also extended that teachers who are subject

matter expert are the ones who have stayed in service for quite some

time. (jobs.stanlake.co.uk/recruiter/users/jobs.php?id=22).

A published research on Teacher Certification was also accessed.

The study revealed that teachers who had certification, longer years of

professional service and more frequencies of degrees show subject matter

competence (http://www.sedl.org/pubs/policyresearch/resources/ARA-

2004.pdf).

Another web article reveals that instructor-led training workshops

also enhance subject matter expertise and skills.

(http://doconnor.edublogs.org)

http://doconnor.edublogs.org/finding-e-learning-and-online-teaching-jobs/


A national study on teaching expertise, though in the HEIs, by

Clemente-Reyes (2002) expresses that subject matter expertise is gained

through possessing educational achievements, gaining years of

professional teaching service and attending training. She mentioned that

earning a bachelors‘ degree was not sufficient; thus, recommending for

continuing professional education since majority of the teacher experts

were masters degree holders or even doctorate degree holders. Also,

when a teacher is exposed in the teaching profession, he is likely to

expand his horizons in his field; thus, contributing to teaching expertise.

Lastly, she asserted that training helped a lot in gaining additional input.

Such input met or not met by teachers in her formal education can affect

his content knowledge.

Further , the Australian Government commissioned the Australian

Council for Educational Research (2001) to conduct an investigation of

effective mathematics teaching and learning in Australian secondary

schools. The research revealed that teacher knowledge and educational

background is positively, but weakly related to teacher effectiveness. The

more this education has to do with mathematical content and pedagogy,

the more likely it is that teachers will be effective.

Keneddy (2001) also wrote in her article that a prospective teacher

majoring a subject like mathematics or science does not guarantee that

teachers will have the kind of subject matter knowledge they need for

teaching. She further stressed that college-level professional subjects do

not address the most fundamental concepts in disciplines. Instead,

professors provide massive quantities of information, with little attention

given to significance or fundamentals on how to deal with teaching.

Relationship of Profile and Level of Competence along Instruction

Teaching is a systematic presentation of facts, skills and

techniques. It needs certain competencies in order to teach effectively.

One way of assuring this is having a degree in education or any related

degrees. If a teacher wishes to teach in secondary, a field of specialization

is required in order to teach more competently. But having a degree does

not guarantee that one can teach well, he needs constant upgrading of

what he knows.

The study of Estoesta (1999), as cited by Fianza (2009) reveals that

there was a strong relationship between educational attainment and

teaching experiences to instructional competence. She stressed that the

teachers who had higher educational attainment and teaching experience

had high performance rating, thus higher competence. This study is

seconded by the study of Sameon (2002). According to him, teaching

competence is highly correlated to highest educational attainment and

teaching experience.

These findings were also supported by the international study of

Achwarin (2005) arguing that teachers‘ qualification is positively and

significantly related to teachers‘ competence.

Binay-an (2002) extended that length of service and number of

seminars and trainings were significantly related to competence.

Davis (2000), as cited by Binay-an (2002), claimed that teachers

who are younger in the service are more likely to possess greater

competence since they have greater inquisitive mind and zest for

teaching. However, this was not in congruence to the study of Laroco

(2005) claiming that teachers who had longer years in service are in

better position to adjust themselves to different classroom situations;

thus, they are more competent. She concluded that teaching experiences

add to the teaching competence.

Oredina (2006) accentuated that highest educational attainment is

significantly correlated to teaching skills but not significantly correlated

to guidance, management and evaluation skills. She also extended that

number of years in teaching, performance rating and number of

seminars attended are not significantly correlated to the four core

dimensions of instructional competence. These imply that teacher with

higher performance rating, with more number of years of teaching and

seminars were not necessarily more competent than those with less.

Soria (1995), as cited by Laroco (2005), found out that there was

no significant relationship between highest educational attainment and

number of years in teaching and their professional proficiency.

Parrochas (1998) also supported this contention, as cited by

Laroco (2005), by claiming that there is no significant relationship

between highest educational attainment of teachers and mastery level of

pupils.

Relationship of Subject Matter and Instructional Competence

Global goals of education stress the connection between how

teachers let the students know and what the teachers actually know.

Some of these goals are (1) all children should be taught by teachers who

have the knowledge, skills, and commitment to teach children well; (2)

for all teachers to have access to high-quality professional development;

and (3) for teachers and principals to be hired and retained based on

their ability to meet professional standards of practice. It is only with

these clearly stated and directed goals that teaching-learning process will

be meaningful.

Leinhardt, as cited by Subala (2006), disclosed that teaching

practices were often considered as one of the reasons why American

students were not currently demonstrating top achievement in science

and mathematics. He further stressed that teacher‘s knowledge of the

subject matter necessarily influenced their classroom practices.

Moreover, linkages between teacher‘s personal knowledge and

instructional activity had proven elusive despite the considerable level of

concern expressed regarding low levels of mathematics and science

knowledge possessed by pre and in-service teachers.

Binay-an (2002), in her study, ―Determinants of Teaching

Performance‖, pointed out that subject matter expertise is significantly

related to teaching expertise. He made use of the adage, ―One can‘t give

what he does not have‖ to substantiate this.

Cabusora (2004) asserted that subject matter expertise and

exemplary instruction are significantly correlated. He stressed that when

teachers have thorough grasp of the teaching-learning process, they are

likely to perform in instruction.

Diaz (2000) also stressed that teachers who are competent in

instruction are the ones who are competent in their field of expertise.

In the study of Dr. Flordeliza Clemente-Reyes (2002) on ―Unveiling

Teaching Expertise: A showcase of 69 Outstanding Teachers in the

Philippines‖, it was revealed that subject matter expertise was a

contributory factor to teaching expertise. It was stressed that mastery of

content-specific knowledge and the organization of this knowledge affect

effective instruction. If the teachers were not experts in their field, it is

unlikely for them to possess teaching expertise

An international study was cited by an article posted on the

Harvard Educational Review. This study was by Reynolds (1999). In the

study, he exposed that subject matter expertise was not contributory to

success in teaching. With these she expanded the meaning of subject

matter expertise to include an awareness of that expertise as learned.

(http://www.hepg.org/her/abstract/164).

Strengths and Weaknesses in Teachers’ Competence

The teacher is always confronted with different challenges that he

needs to face. Challenges of a teacher might be extrinsic or intrinsic.

Teachers might encounter problems on students‘ population, sizes of

classroom and the like. It can also be that a teacher finds preparing for

a class meaningless. These challenges are undoubted to be contributory

to the teacher‘s success in teaching.

Ordas (2000), as cited by Olbinado (2007), disclosed that schools

were not only faced with great lack of teachers; but with the massive

deficiency in qualified and competent teachers. She further stressed that

teacher training was deficient in terms of frequency and accessibility for

teachers.

Roldan (2004) concluded that secondary mathematics teachers in

Region I were proficient in concept and computations but they were

deficient in their skills in problem-solving and the use of teaching

strategies.

Oyando (2003) revealed in her investigation that teachers were

highly competent in basic mathematics; but were moderately competent

in higher mathematics.

Almeida (1998) and Diaz (1998) revealed that their respondents, in

separate studies, have moderate competence in their field. Diaz (1998)

added that mathematical analysis was wanting.

Verceles (2009) revealed that the use of calculators, especially

computers were all weaknesses. Lecture method was very dominant.

Nuesca (2006) indicated that Philippine Instruction is highly

teacher-centered. She supported this by enumerating the three most

common methods used by Filipino teachers: lecture, discussion and

demonstration.

Fianza (2009) disclosed that math instruction is often approached

in terms of stating and emphasizing rules- the ―tell, show and do‖ model.

Graycochea (2000) revealed that problems on mathematics

teaching were somewhat serious. She stressed that questioning

technique; motivational strategies and management were the

contributory factors in this finding.

Cristobal (2004) found out that Instructors of Lorma Colleges

exhibited capabilities along teaching procedure, substantiality of

teaching and evaluation. The only expressed need is in the use of varied

instructional materials.

Roldan (2004) exposed that the secondary mathematics teachers in

Region I were deficient in the use of teaching strategies. Binay-an (2002)

supported this finding when she exposed that her respondents were not

so competent in using methods and approaches.

Alano (2003) of the Philippine Normal University mentioned that

studies showed that almost half of the teachers teaching the core

subjects have computer units, but only a few among them use such for

classroom instruction.

Oredina (2006) in her dissertation revealed that teacher‘s level of

instructional competence was very good. The evaluation skills were rated

highest while their teaching skills were the lowest.

Two-Pronged Training Programs

To be a successful math teacher, one needs to continually upgrade

himself. With this belief, the Congressional Commission in Education, as

cited by Olbinado (2007), recommended that a periodic assessment of

training needs of school teachers in both public and private schools is

imperative.

Eslava (2001) pointed out that attending service trainings

enhances, with no doubt, the professional qualities of teachers. Laroco

(2005) added this thought expressing that when teachers wanted to

continue improving on their teaching performance, they needed to

undergo necessary training.

Cristobal (2004) claimed that while training remains only one of a

number of alternative approaches towards human resource development,

it remains to be the most utilized instrument for the development of

adults, professionals and paraprofessionals alike in a wide variety of

specific areas.

Fianza (2009) believed that training is a very good approach to staff

development. She opined that quality instruction, especially in

mathematics, can be attained and delivered through enhancing teachers‘

competence.

Roldan (2004) claimed that training should be of prime concern

when quality of education is of prime concern, too. Such training has to

be done before any plan for assigning longer period to the teaching of

Mathematics is implemented.

Lastly, Oredina (2006) discoursed that training allows teachers to

show and share ideas, ask questions, make decisions and share personal

experiences in teaching Mathematics. She stated that this program will

make teachers change their traditional method of teaching to that of a

facilitator of learning.

Chapter 3

RESEARCH METHODOLOGY

This chapter presents, incorporates and discusses the research

design, the sources of data, instrumentation, procedure and the tools for

data analysis.

Research Design

The descriptive method of investigation was used in the study. This

design aims at gathering data about the existing conditions. Calmorin

(2005) describes descriptive design as a method that involves the

collection of data to test hypothesis or to answer questions regarding the

present status of a certain study. Further, Deauna (2003) defines such

design as one that includes all studies that purport to present facts

concerning the nature and status of anything.

Since the comparison on the perceptions of the respondents along

instructional competence and the relationship of the data on the

teachers‘ profile, content and instructional competence were established,

the descriptive-comparative and the descriptive-correlational methods

were employed, respectively.

Sources of Data

The population of this study is composed of three (3) groups of

respondents: (1) heads, (2) High school mathematics teachers in the

Private City schools of San Fernando (3) high school mathematics

students for the academic year 2010-2011.

All the heads with the mathematics teachers were considered. For

the students, one-third of the class population was considered. This is

equivalent to thirty- three and one-third percent (33 1/3 %) of the total

number of students in a class. According to Gay, as mentioned by

Oredina (2006), ten percent (10%) of the population is an acceptable

sample but twenty percent (20%) is required from a small population.

However, to make the findings of this study more reliable and acceptable,

the researcher preferred to implement the statistical idea that the bigger

the sample, the more valid are the results.

The total population of three hundred and fifty-seven (357)

constituted the respondents of this study, broken down as follows: three

hundred eighteen (318) students, twenty six (26) teachers and thirteen

(13) heads. Substitute teachers or on-leave teachers are not considered

as respondents of the study. Table 1 shows the distribution of the

number of specified respondents from the thirteen (13) Private Secondary

Schools of the City Division of San Fernando, La Union for the academic

year 2010-2011.

Table 1

Distribution of Respondents

SCHOOLS

Number of

Students Teachers Heads

Brain and Heart of a Christian (BHC) 33 2 1

Central Ilocandia Institute of Technology

(CICOSAT)

20 2 1

Christ the King College (CKC) 75 5 1

Diocesan Seminary of the Heart of Jesus (DSHJ)

3 1 1

Felkris Academy 8 1 1

Gifted Learning Center (GLC) 7 1 1

La Union Cultural Institute (LUCI) 14 2 1

La Union Colleges of Nursing, Arts and Sciences (LUCNAS)

7 1 1

MBC Lily Valley School 7 1 1

National College of Science and Technology

(NCST)

7 1 1

Saint Louis College (SLC) 90 6 1

San Lorenzo Science School (SLSS) 11 1 1

Union Christian College (UCC) 24 2 1

TOTAL 318 26 13

Instrumentation and Data Collection

To gather the data essential to the realization of this study, two

sets of data gathering instrument were utilized. One was a 60-point

researcher-made mathematics competence test for mathematics teachers

whose content was based on the 2010 Secondary Mathematics

Curriculum. The other is a questionnaire-checklist, the key instrument

in obtaining the data in evaluating the instructional competence of high

school mathematics teachers in the Private Secondary Schools.

The mathematics competence test is divided into 4 areas of

Secondary Mathematics (Elementary Algebra, Intermediate Algebra,

Geometry, Advanced Algebra, Trigonometry and Statistics). Each area

includes 15 questions; each question corresponds to one (1) point.

Further, it was made following the Bloom‘s Taxonomy of Cognitive Skills

for Mathematics (Conceptual, Reasoning/Analytical, Computational, and

Problem-Solving). (Please see appended Table of Specifications)

On the other hand, such questionnaire on instructional

competence was composed of two parts: Part I elicited the profile of the

mathematics teachers along the highest educational attainment, years of

teaching mathematics and number of mathematics trainings and

seminars attended; Part II, on the other hand, drew out the level of

instructional competence along the four areas ─ teaching

skills/facilitating skills, management skills, guidance skills, and

evaluation skills. The statements in the questionnaire for student-

respondents were rephrased in such a way that these are parallel to the

statements in the questionnaires for teachers and heads. This rewording

ensured that the student-respondents clearly understood the details for

assessment.

Each of the teacher-respondent took the mathematics competence

test not exceeding one hour or sixty (60) minutes in one sitting/ session.

The administration of the test was conducted during their free periods,

lunch breaks, and after the class hours as agreed upon by the researcher

and the teacher-respondents, themselves. Such being the case, the

researcher took him almost 2 months to gather the required data. Also,

each teacher was evaluated by his/ her students in one of his/her

classes, heads and himself.

With the permission of the school heads of the thirteen private

secondary schools, copies of the two sets of instrument were given to the

respondents to accomplish. In the mathematics competence test,

teachers were not allowed to use calculators. This was made sure by the

researcher during his proctoring of tests. The fully accomplished

questionnaires were retrieved personally by the researcher.

Validity and Reliability

The mathematics competence test was a researcher-made test

whose content was based on the 2010 UBD-Secondary Education

Curriculum. The questionnaire-checklist, on the other hand, was a

combination of the FAPE Performance Evaluation Tool, Institutional

Supervisory Instrument of Christ the King College and the questionnaire-

checklist utilized by Oredina (2006) in her study, ―Mathematics

Instruction in the HEIs in La Union: Basis for a Training Program‖. Since

the key instruments were based on several manuscripts, their validity

and reliability were established. The Education Supervisor for

Mathematics; a Master Teacher II of La Union National High School; the

Academic Coordinator of Christ the King College and the members of the

reading committee served as the validators of the two sets of

questionnaires. The computed validity rating for the Mathematics

competency test was 4.63, which means that the Mathematics

competency test is of very high validity. On the other hand, the computed

validity rating for the Instructional competence test was 4.71 indicating a

very high validity, too. Further, all the suggestions cited by the validators

were incorporated, especially on the competence test where the radical

symbols and fractional bars have to be encoded using the equation editor

to avoid unnecessary misconception. Conversely, their internal

consistency or reliability was determined using the Kuder-Richardson 21

formula. The first one was used to get the reliability of the content

competence test while the second was used to get the reliability of the

instructional competence checklist. The formulas are (Monzon-Ybanez

2002):

𝐾𝑅21 = 𝑘

𝑘−1 1 −

𝑥 𝑘−𝑥

𝑘𝜎2

where:

k = number of items

𝑥 = mean of the distribution

𝜎2= the sample variance of the distribution

or

(Garett 1966): 𝐾𝑅21 =[𝑛𝜎𝑡

2−𝑀(𝑛−𝑀)]

(𝑛−1)(𝜎𝑡2)

where:

n = product of the number of items in the test and the highest

scale

𝜎𝑡2 = variance

𝑀 = mean

Through the assistance of the Education Supervisor for

Mathematics, Dr. Jose P. Almeida, a dry run of the questionnaires was

administered to 20 students, 5 mathematics teachers and 1 Mathematics

head of La Union National High School. The mathematics competence

test had a reliability coefficient of 0.93, denoting that the competence test

was very highly reliable. Alternatively, the questionnaire checklist was

found to have very high reliability having a computed coefficient of 0.96.

Tools for Data Analysis

The data which were gathered, collated and tabulated were

subjected for analysis and interpretation using the appropriate statistical

tools. The raw data were tallied and presented in tables for easier

understanding.

For problem 1, frequency counts and rates were used to determine

the status of the profile of the respondents along highest educational

attainment, years in teaching mathematics. A scoring scheme seen in

data categorization together with frequency counts and rates were used

to treat the number of seminars and trainings attended. The rates were

obtained by using the formula below:

R = n x 100

N

where: R - rate

n - number of frequencies gathered by each item

N - the total number of cases

100 – constant

For problem 2.a, mean and rates were utilized to determine the

mathematics competence; whereas for problem 2.b., weighted mean was

employed to determine the level of instructional competence along the

four areas.

The formula for mean is as follows (Ybanez 2002):

M = ∑x N

Where: M – mean

x – sum of the product of the extent of the variables and

their corresponding frequency

N – number of respondents

For problem 2.1, t-test independent (t-test between means), taken

two at a time was used to determine the difference in the perceptions of

the respondents. The formula for t-test for means

(http://en.wikipedia.org/wiki/Student%27s_t-test) is:

where:

= estimator of the common standard deviation of the two

samples

n = number of participants, 1 = group one, 2 = group two.

n – 1 = number of degrees of freedom for either group

n1 + n2 – 2 = the total number of degrees of freedom, which is used

in significance testing.

t = degree of difference

For problem 3.a, 3.b and 3.c, the Pearson-r moment of correlation

was used to determine the significance of relationship between teachers‘

profile and teachers‘ level of content competence, profile and

http://en.wikipedia.org/wiki/Standard_deviation

instructional competence and level of content competence and

instructional competence. The formula (Ybanez 2002) is:

𝑟 =N ∑XY − ∑X (∑Y)

(N∑X2− ∑X 2 )(N ∑ – ∑Y 2)2

where: X – observed data for the independent variable

Y – observed data for the dependent variable

N – size of sample

r – degree of relationship between X and Y

The computed correlation coefficients were subjected to

significance; thus the formula used

(http://faculty.vassar.edu/lowry/ch4apx.html) is:

𝑡 =r

1 − r2

n − 2

where: r – computed correlation coefficient

n-2 – degree of freedom

t – degree of significance for r

For problem 4, the major strengths and weaknesses were deduced

based on the findings, particularly on the level of competence (content

and instruction) through statistical ranking. An area was considered

strength when it received a descriptive rating of very good or excellent;

otherwise, the area was considered a weakness.

The MS Excel Data Analysis Tool and STATEXT were employed in

treating the data.

Data Categorization

For the mathematics competence test, the Scale System is utilized.

Ave. No. of Descriptive Equivalent rating DER class Teachers who

Got the correct Answer

22-26 Outstanding strength

17-21 Above Average Competence strength

12-16 Average Competence weakness

7-11 Fair Competence weakness

0-6 Poor Competence weakness

For the mathematics trainings and seminars attended by teachers,

data were categorized according to levels: school, local, national and

international. Each level corresponds to a particular number of points.

The scales below clarify the categorization:

Level Frequency Point Equivalent

School 1 1

Local 1 2

Regional 1 3

National 1 4

International 1 5

No. of points Descriptive Equivalent rating

40 and above Very Adequate (VA)

31-40 Moderately Adequate (MA)

21-20 Fairly Inadequate (FA)

11-20 Slightly Inadequate (SI)

1-10 Very Inadequate (VI)

For the level of instructional competence, the 5-point Likert Scale

below is incorporated:

Points Ranges DER DER Class

5 4.51-5.00 Excellent (E) Strength

4 3.51-4.50 Very Good (VG) Strength

3 2.51-3.50 Good ( G) Weakness

2 1.51-2.50 Fair (F) Weakness

1 1.00-1.50 Poor (P) Weakness

Moreover, the major strengths and weaknesses are drawn out from

the ratings given. Such ratings are ranked; hence, the ranking system

was used. The item that gets the highest mean value in the strengths

was ranked first indicating that it is regarded as the foremost strength.

These procedures also apply in the items considered as weaknesses.

Finally, the scales for interpretation on the degree of relationship of

the identified correlates are as follows (Ybanez 2002):

±1.00 -perfect correlation

±0.91-0.99 -very high correlation

±0.71-±0.90 -high correlation

±0.41-±0.70 -marked correlation

±0.21-±0.40 -low correlation

±0.01-±0.21 - negligible correlation

0.00 - no correlation

Proposed Training Program

The proposed training program includes the following parts:

rationale, objectives, content, methodology, training management,

participants, duration, logistics and success indicator (Cayabyab, 2010).

A training program is set for content competence; another program

is set for instructional competence. The trainers considered for the

training program were some of the speakers met by the researcher in the

seminars/workshops he attended, the Education Supervisor for

mathematics, and some of his professors in mathematics.

Validity of the Training Program

To establish the validity, acceptability and functionality of the

proposed training program, it was presented to the Administrators of the

Private Secondary Schools in the City Division of San Fernando, La

Union.

The validation was guided by the following point assignments:

Points Ranges DER

5 4.51-5.00 Very High (VH)

4 3.51-4.50 High (H)

3 2.51-3.50 Moderate (M)

2 1.51-2.50 Fair/Slight (F/S)

1 1.00-1.50 Low/Poor (L/P)

Chapter 4

PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA

In this chapter, the data gathered were subjected to statistical

analysis and systematically presented to manifest the levels of content

competence along conceptual skills, reasoning/analytical skills,

computational skills and problem-solving skills; and instructional

competence of the mathematics instructors along teaching skills,

management skills, guidance skills and evaluation skills. The identified

strengths and weaknesses were the foundations for formulating and

structuring a proposed two-pronged training program for the

Mathematics teachers in the City Division of San Fernando, La Union.

Profile of the Mathematics Teachers

The first problem of the study focused on the profile of the

Mathematics Teachers in the Private Secondary Schools in the City

Division of San Fernando to provide basic but relevant information on

teachers‘ competence both for content and instructional competence.

Highest Educational Attainment

Table 2 shows the highest educational attainment of Mathematics

Teachers. Out of the 26 teacher-respondents, 11 or 42.31% are licensed

teachers, 14 or 50.00% are pursuing graduate studies and 2 or 7.69%

Table 2

Distribution of Teacher-Respondents

According to Highest Educational Attainment

Educational Attainment Frequency Rate

BSED/BSE/AB/BS graduate

(Non-licensed)

0 0%


(Licensed)

11 42.31%


w/ MS/MA units

13 50.00%

MS/MA graduate 2 7.69%

with EDd/PHd units 0 0%

EDd/Phd graduate 0 0%

Total 26 100%

are Master‘s degree holders. This means that the Mathematics teachers

are qualified to teach in the Secondary schools since they have met the

necessary requirements stipulated in the Magna Carta for Public School

Teachers and Republic Act 9293, which both require secondary teachers

to be duly registered before engaging themselves in the teaching

profession. It is also noticeable that majority of the teachers value

continuing education since half of the total population are currently

enrolled in their Master‘s program. This finding accepts the null

hypothesis that 50% of the respondents are pursuing their graduate

studies. Also, it runs parallel to the studies of Fianza (2009), Eslava

(2001) and Rulloda (2000) stressing that generally, the teachers meet the

basic requirements for teaching and do not want to be stagnant because

they want to elevate their professional outlook to make them effective

and worthy members of the profession.

Number of Years in Teaching Mathematics

Table 3 reveals the distribution of teacher-respondents according

to the number of years in teaching Mathematics. It further reveals that

18 or 65.38% have been teaching from 0-5 years, 2 or 7.69% from 6-10

years, 1 or 3. 85% from 11-15 years, 4 or 15.39% from 16-20 years, 1 or

3.85% from 21-25 years, and 1 or 3.85% has been teaching for more

than 25 years. These data give a general impression that the

Mathematics teachers of the Private Schools in San Fernando City, La

Union are very young in the profession. It means that the general turn-

over of teachers in the private schools is high, especially in small schools

where teachers stay only up to 1-2 years since they desire to be

employed in the public schools or work abroad, where higher

compensation, more incentives and other benefits abound. Therefore, it

rejects the null hypothesis of the study that 50% of the teacher-

respondents have teaching experience of below 5 years. This finding runs

parallel to the studies of Oyanda (2003) and Fianza (2009) revealing that

the teachers are generally quite young in the service. Their findings

revealed that more than half of their respondents have less than 5-year

teaching experience.

Table 3


According to Number of Years in Teaching Mathematics

Years Frequency Rate

0-5 years 17 65.38%

6-10 years 2 7.69%

11-15 years 1 3.85%

16-20 years 4 15.39%

21-25 years 1 3.85%

26 years and above 1 3.85%

Total 26 100%

However, the finding of this study does not support the finding of

Aware-Achawarin (2005) when he revealed that 71.07% of his teacher-

respondents were tenured in the teaching profession since they have

been teaching for more than 10 years.

Number of Seminar/Trainings Attended (for the last two years)

Table 4 presents the distribution of the teacher-respondents

according to the number of seminars/trainings attended for the last two

years.

Out of the 26 respondents, 22 or 84.62% have ―very inadequate‖

attendance or participation in trainings and seminars while the

remaining 4 or 15.39% have ―slightly adequate‖ attendance to seminars

and trainings. This finding rejects the null hypothesis of the study

stating that 50% of the teacher-respondents have adequate attendance to

Table 4


According to Seminars Attended

No. of Points Earned

for the past 2 years

Descriptive Equivalent Frequency of

Teachers

Rate

0-10 Very Inadequate 22 84.62%

11-20 Slightly Adequate 4 15.39%

21-30 Adequate 0 0%

31-40 Moderately Adequate 0 0%

40 and above Very Adequate 0 0%

Total 26 100%

seminars/trainings for the past two years. This implies that the teachers

have not been sent to seminars and trainings where their participation

was highly expected. This is caused by financial constraints, non-

availability of teachers due to school commitments and the distance of

the venue of the seminar.

The finding of the current study is supported by the finding of

Oredina (2006), which disclosed that majority of the teacher-respondents

have ―very inadequate‖ participation in seminars and training

workshops. This was due to financial constraints. However, it does not

jibe with the finding of Fianza (2009), which revealed that more than 50%

of her respondents have attended trainings on curriculum, teaching

strategies, management and assessment methods.

Summary of Profile of Mathematics Teachers in the Private

Secondary Schools in San Fernando City, La Union

Table 5 reveals that majority of the Mathematics teachers in the

Private Secondary Schools in the City Division of San Fernando possess

the necessary requirements in the teaching profession. Thus, they are

Table 5

Summary Table of Profile of Mathematics Teachers in the Secondary

Schools in San Fernando City, La Union

Variables Frequency Rate

A. Highest Educational Attainment 0 0%

BSEd/AB/BS Graduate (Non-licensed)

BSEd/AB/BS Graduate (Licensed) 11 42.31%

BSEd/AB/BS Graduate w/ MS/MA units 13 50.00%

MS/MA graduate 2 7.69%

With EDd/PHd units 0 0%

EDd/PHd graduate 0 0%

Total 26 100%

B. No. of Years in Teaching Mathematics

0-5 years

17 65.38%

6-10 years 2 7.47%

11-15 years 1 3.85%

16-20 years 4 15.39%

21-25 years 1 3.85%

26 years and above 1 3.85%

Total 26 100%

C. No. of Seminars Attended

(0-10) Very Inadequate

22

84.62%

(11-20) Slightly Inadequate 4 15.39%

(21-30) Fairly Inadequate 0 0%

(31-40) Moderately Adequate 0 0%

(41 and above) Very Adequate 0 0%

Total 26 100%

qualified to teach in the secondary schools. Also, they value continuing

education by enrolling in graduate school programs; however, they are

very young in the service and their attendance to seminars is very

inadequate.

Level of Subject Matter/ Content Competence

The succeeding tables present the subject matter/ content

competence of the Mathematics teachers in the private secondary schools

in the City Division of San Fernando as revealed in the results of the

Mathematics competence test along conceptual skills, reasoning/

analytical skills, computational skills and problem-solving skills.

Conceptual Skills

Table 6 shows the subject matter competence of the teacher-

respondents along conceptual skills. There are twenty-four (24 or

92.31%) teachers who got the items correctly in Elementary Algebra,

eighteen (18 or 69.23%) in Intermediate Algebra, fourteen (14 or 53.85%)

in Geometry, and seventeen (17 or 65.38%) in Advanced Algebra,

Trigonometry and Statistics. Thus, the teachers have ―outstanding‖

competence‖ in Elementary Algebra, ―above average competence‖ in

Intermediate Algebra, ―average competence‖ in Geometry and ― above

average competence‖ in Advanced Algebra, Trigonometry and Statistics.

Generally, there are eighteen (18 or 69.23%) teachers who got the items

correctly for conceptual skills; thus, they have above average competence

Table 6

Subject Matter Competence of the Teacher-Respondents along

Conceptual Skills

Area of Mathematics

Average no.

of teachers

who got the

items

correctly

Rate

DER

Elementary Algebra 24 92.31% Excellent

Intermediate Algebra 18 69.23% Above Average

Geometry 14 53.85% Average

Advanced Algebra, Trigonometry,

and Statistics

17 65.38% Average

Mean 18 69.23% Above Average

in conceptual skills. This rejects the null hypothesis of the study that the

teachers have average competence in content along conceptual skills.

This means that the teachers have mastered the basic mathematical

terms, definitions and concepts in mathematics. This is attributed to the

reason that they have finished their degrees in Mathematics and that

majority of them are continuing their graduate studies. Such being the

case, the teachers can impart to the students the basic mathematical

concepts needed in the understanding of more complex analysis of

mathematical problems. It is very true that definitions, theorems,

postulates and other facts in mathematics should be well understood by

anyone first before he/she can fully understand the rudiments of

Mathematics. As Mina (2002) explained, knowledge, concepts, principles

and ideas are very necessary in teaching because these start the

acquisition of further learning. Further, it implies that the teachers need

to continually upgrade and update their knowledge in the subject they

are teaching to be able to achieve excellent competence. Roldan (2004)

stressed this in her study that conceptual skills of the teachers are very

important because these serve as the foundations of their math skills.

The finding of the study does not jibe with the studies of Toledo

and Bagaforo, as cited by Diaz (2000), revealing that the teachers felt

moderately competent in their knowledge in mathematics. It was

concluded that the teachers did not possess mathematics competence at

a level very adequate for teaching secondary mathematics.

Reasoning/ Analytical Skills

Table 7 shows the subject matter competence of the teacher-

respondents along reasoning/ analytical skills. There are twelve (12 or

46.15%) teachers who got the items correctly in Elementary Algebra,

sixteen (16 or 61.54%) in Intermediate Algebra, nineteen (19 or 73.08%)

in Geometry, and fourteen (14 or 53.85%) in Advanced Algebra,

Trigonometry and Statistics. Thus, the teachers have ―average

competence‖ in Elementary algebra, ―average competence‖ in

Intermediate Algebra, ―above average competence‖ in Geometry and

―average competence‖ in Advanced Algebra, Trigonometry and Statistics.

Generally, there are fifteen (15 or 57.69%) teachers who got the item for

Table 7


Reasoning/Analytical Skills

Area of Mathematics Average no. of

teachers who got

the items

correctly

Rate DER

Elementary Algebra 12 46.15% Average

Intermediate Algebra 16 61.54% Average

Geometry 19 73.08% Above Average

Advanced Algebra, Trigonometry, and

Statistics

14 53.85% Average

Mean 15 57.69% Average

reasoning/ analytical skills correctly; thus, the teachers have ―average

competence‖ in terms of their reasoning/ analytical skills. This accepts

the null hypothesis of the study that the teachers have average

competence in content along reasoning/analytical skills. This implies

that the teachers can satisfactorily lead the students in comprehending

mathematical problems. Further, it is evident that in Geometry, the

subject that requires more analysis and probing, the teachers achieved

higher competence than the other subjects. It means that they received

more training in reasoning in this subject than the other subjects. This is

very true since Geometry focuses much on deductive reasoning as a tool

in analyzing geometric problems and illustrations. This finding also

means that the teachers needed upgrading of their reasoning competence

to be able to lead students to analyze all types of problems, especially the

most complex ones. Roldan emphasized this in her study that teachers

really needed to be excellent in comprehension. This finding does not

corroborate with the study of Gundayao (2000) when she generalized

that the teachers lacked the reasoning competence since they have poor

skills in analyzing different categories of mathematical problems.

Computational Skills

Table 8 discloses the subject matter competence of the teacher-

respondents along computational skills.

The table divulges that there are nineteen (19 or 73.08%) teacher-

respondents who got the items correctly in Elementary Algebra, nineteen

(19 or 73.08%) in Intermediate Algebra, twenty-one (21 or 87.50%) in

Geometry, and twelve (12 or 46.15%) in Advanced Algebra, Trigonometry

and Statistics. Thus, the teachers possess ―above average competence‖ in

Elementary Algebra, ―above average competence‖ in Intermediate

Algebra, ―above average competence‖ in Geometry and ―Average

Competence‖ in Advanced Algebra, Trigonometry and Statistics.

Generally, there are eighteen (18 or 69.23%) teachers who got the item

correctly in computational skills; thus, they have ―average competence‖

in terms of their computational skills. This accepts the null hypothesis of

the study that the teachers have average competence in content along

computational skills. This means that the teachers are good sources of

processes, procedures, and techniques in solving items in Mathematics.

Table 8


Computational Skills


teachers who got

the items

correctly

Rate DER

Elementary Algebra 19 73.08% Above Average

Intermediate Algebra 19 73.08% Above Average

Geometry 21 87.50% Above Average


Statistics

12 46.15% Average

Mean 18 69.23% Above Average

Subala (2006) stressed this when she concluded that when teachers have

average competence or above, they can satisfactorily direct students in

the correct process of solving mathematical items. Roldan stressed that

mathematics teachers needed to be experts in computation because

when teachers are experts of this skill, it is expected that students can

master this skill, too.

A closer look at the table makes it evident that the teachers have

much lower computational competence in Advanced Algebra,

Trigonometry & Statistics than the other subjects. This is due to the fact

that this is a more complex subject than the other subjects.

Problem-Solving Skills

Table 9 illustrates the subject matter competence of the teacher-

respondents along problem-solving skills.

Table 9


Problem-solving Skills


teachers who got

the items

correctly

Rate DER

Elementary Algebra 11 42.31% Fair

Intermediate Algebra 10 38.46% Fair

Geometry 13 50.00% Average


Statistics

12 46.15% Average

Mean 12 46.15% Average

It demonstrates that there are eleven (11 or 42.31%) teachers who got

the items correctly in Elementary Algebra, ten (10 or 38.46%) in

Intermediate Algebra, thirteen (13 or 50.00%) in Geometry, and twelve

(12 or 46.15%) in Advanced Algebra, Trigonometry and Statistics. Thus,

the teachers possess ―fair competence‖ in Elementary Algebra, ―fair

competence‖ in Intermediate Algebra, ―average competence‖ in Geometry

and ―average competence‖ in Advanced Algebra, Trigonometry and

Statistics. Generally, there are twelve (12 or 46.15%) teachers who got

the items correctly in problem-solving skills; thus, they have ―average

competence‖ in problem solving skills. This accepts the null hypothesis

of the study that the teachers have average competence in content along

problem-solving skills. This means that the teachers can guide their

students in analyzing, interpreting and solving word problems in

Mathematics. Since this is the case, it can be inferred that the students

in the Private Secondary Schools is San Fernando City can analyze, solve

and interpret word problems. This is rooted to their average competence

in analyzing skills and above average competence in computation skills

since a good foundation of analytical and computational skills are

necessary in solving word problems.

Further, among the four subject matter skills, this is the area that

received the lowest mean score. This is due to the fact that these skills

require more rigorous analysis and computation before one can actually

come up with an approach to the problem and eventually a correct

solution.

Summary on the Level of Content Competence of the Mathematics

Teachers

Table 10 reveals that the teachers have above average competence

in Elementary Algebra, average competence in Intermediate Algebra,

above average competence in Geometry; and average competence in

Advanced Algebra, Trigonometry and Statistics. Generally, the teachers

have ―average subject matter competence‖ in Mathematics. This accepts

the null hypothesis of the study that the teachers have average subject

matter competence. This means that the teachers know what to teach

since they have ―good‖ proficiency in the Mathematics subjects offered in

the Secondary schools. Since they have average

Table 10

Summary on the Level of Content Competence of the Mathematics

Teachers along Conceptual, Reasoning /Analytical, Computational and

Problem-solving Skills

Area of

Mathematics

Conceptual

Skills

Reasoning/

Analytical

Skills

Computational

Skills

Problem-

Solving

Skills

Mean DER

Elementary Algebra 24 12 19 11 17 Above

Average

Intermediate 18 16 19 10 16 Average

Algebra

Geometry 14 19 21 13 17 Average

Advanced Algebra,

Trigonometry, and

Statistics

17 14 11 12 14 Average

Grand Mean 18 15 18 12 16

Average DER Above

Average

Average Above

Average

Average

competence in Mathematics, it can be inferred that they know what to

teach; hence, they are qualified to teach secondary mathematics. Since

they are qualified to teach, the students can get adequate concepts and

skills in mathematics.

The finding of this study is supported by the findings of Toledo

and Bagaforo, as cited by Diaz (2000), which asserted that the teachers

have average competence in their knowledge and ability in mathematics.

They emphasized that the teachers needed updating and upgrading of

subject matter competence to possess the needed competence situated at

a level very adequate for teaching secondary mathematics. This was even

stressed by Roldan (2004) that even if the teachers have average or above

average competence, the teachers need to consistently upgrade their

knowledge and capabilities in teaching so as to cope with the challenges

of the new millennium. However, this does not jibe with the study of

Gundayao (2000) which revealed that the teachers, in general, have poor

proficiency in the Mathematics subject they are teaching. He stressed

that the competence was poor because the teachers lacked the

competence in analyzing complex mathematical principles, concepts and

problems.

Level of Instructional Competence

The subsequent tables reflect the instructional competence of the

Mathematics Teachers in the Private Secondary Schools in the City

Division of La Union as perceived by themselves, heads and the students.

There were four areas in which the teachers were appraised, namely:

teaching/facilitating skills, guidance skills, management skills and

evaluation skills.

Teaching/ Facilitating Skills

Table 11 shows the mathematics teachers‘ level of instructional

competence along teaching/ facilitating skills. The table reveals that the

teachers have high level of competence as shown by the mean rating of

4.07, which is interpreted as very good.

Table 11

Level of Instructional Competence of the Teacher-Respondents Along


Instructional Competence Dimensions Students Teachers Heads WM DER

1. Substantiality of Teaching

a. show confidence and exhibit mastery of the subject matter

4.41 4.33 4.63 4.46 Very

Good

b. show awareness of the developments of the subject matter as seen in the utilization of key concepts, relationships, and different perspectives related to the content area

4.28 4.30 4.48 4.35 Very

Good

c. align classroom instruction with national standards, school’s vision-mission and educational philosophy

3.99 4.19 4.41 4.19 Very

Good

d. focus on and cover all important aspects of the subject matter

4.26 4.22 4.37 4.28 Very

Good

e. connect students’ prior knowledge, life experiences, and interests in the instructional process

4.15 4 4.19 4.11 Very

Good

f. provide values clarification and integration considering the applications of the subject area to the students’ practical life

4.08 3.96 4.22 4.09 Very

Good

g. engage students in in-depth and varied experiences that meet the diverse needs and promote holistic growth

4.23 4.04 4.26 4.18 Very

Good

h. relate ideas and information within and across content areas

3.79 4.04 4.26 4.03 Very

Good

Sub-mean 4.15 4.14 4.35 4.21 Very

Good

2. Quality of teacher’s explanation

I…

a. make abstract concepts clear for students’ understanding

4.18 4.37 4.33 4.29 Very

Good

b. ask students how they got a particular answer 4.29 4.48 4.37 4.38 Very

Good

c. encourage students to probe into reactions, answers and responses

4.35 4.33 4.30 4.33 Very

Good

d. use knowledge of students’ development to make learning experiences meaningful and accessible for every student

4.13 4.19 4.37 4.23 Very

Good

Sub-mean 4.24 4.34 4.34 4.31 Very

Good

3. Receptivity to students’ ideas and contributions

I…

a. lead students to ask or initiate thought-provoking questions

3.95 4.15 4.07 4.06 Very

Good

b. integrate and elaborate students’ questions and contributions into the class discussion

4.14 4.22 4.11 4.16 Very

Good

c. demonstrate flexibility and responsiveness in adjusting instruction to meet students’ needs, ideas and contributions

4.1 4.19 4.22 4.17 Very

Good

Sub-mean 4.06 4.19 4.13 4.13 Very

Good

4. Quality of questioning procedure

a. pose thought-provoking questions that promote high-order thinking skills

4.24 4.15 4.33 4.24 Very

Good

b. encourage students to explain ideas and ask questions about the content

4.19 4.22 4.22 4.21 Very

Good

c. provide time for student to think, ponder on and express response

4.25 4.22 4.30 4.26 Very

Good

d. pose follow-up questions to clarify initial question when a student is unable to respond effectively

4.20 4.15 4.37 4.24 Very

Good

e. emphasize on essential ideas and problems 4.24 4.19 4.37 4.27 Very

Good

f. ensure that factual information and skills are applied to ideas and problems

4.25 4.15 4.19 4.20 Very

Good

Sub-mean 4.23 4.18 4.30 4.24 Very

Good

5. Selection of teaching methods

a. determined on behavioral objectives and appropriate to the content area

4.16 4.04 4.22 4.14 Very

Good

b. used in expressing ideas and problems (projects, themes, panel discussion, demonstration, etc)

4.21 3.85 4.15 4.07 Very

Good

c. emphasizing on and eliciting students’ inquiry 3.94 3.89 4.15 3.99 Very

Good

d. used to address individual differences and develop multiple intelligences

3.94 3.78 4.15 3.96 Very

Good

e. intended to engage students in learning and supportive of theories of collaborative and cooperative learning

4.14 4.07 4.26 4.16 Very

Good

Sub-mean 4.08 3.93 4.19 4.07 Very

Good

6. Quality of information and communication technology used

I use…

a. computers for designing and printing instructional materials

3.54 3.59 3.85 3.66 Very

Good

b. the principles of computer-aided and computer-based instruction

3.26 3.33 3.77 3.45 Good

c. multi-media resources, including technologies such as the internet, in the development and sequencing of instruction

3.08 3.33 3.7 3.37 Good

d. computerized grading sheets (without received corrections)

3.53 3.70 4.04 3.76 Very

Good

e. overhead/LCD projector 3.19 2.96 3.56 3.24 Good

Sub-mean 3.32 3.38 3.78 3.49 Good

Grand Mean 4.01 4.03 4.18 4.07 Very

Good

Legend:

WM – Weighted Mean

DER – Descriptive Equivalent Rating

This finding is beyond the null hypothesis that the teachers have good

performance levels in their instructional competence along

teaching/facilitating skills.

Substantiality of Teaching. This aspect of the

teaching/facilitating skills received an average rating of 4.21, which is

interpreted as very good. This is the area rated third highest among the

areas under this skill. It means that the teachers exhibit the subject

matter competence required in teaching secondary mathematics. This is

even supported by the result of the mathematics test that the teachers

have average subject matter competence. Being subject matter experts,

the teachers were perceived to be skillful in the utilization of key

concepts, relationships, and different perspectives related to the content

area. Thus, it implies that the students can have adequate

comprehension of the subject matter. This slightly affirms the result of

the competence test revealing that the teachers have ―average

competence‖ in the Mathematics subject they are teaching.

The Quality of Teacher’s Explanation. This area received a

rating of 4.31, interpreted as ―very good‖. This is the area with the

highest rating among the areas under teaching/facilitating skills. It can

be inferred that the teachers are able to explain mathematical concepts

since they have mastered the mathematical facts and concepts needed in

their subject. With their mastery, the teachers are able to make abstract

concepts clear. Further, the teachers were also perceived to be skillful in

involving students in finding and explaining how they got their answers

and in probing into their answers, reactions and responses. This is

supported by the study of Villanueva (1999), which revealed that the

teachers were rated very high along ability to explain correctly as evident

in their content of the answer and command of the language of

instruction.

Receptivity to students’ Ideas and Contributions. This area was

rated a mean value of 4.13, interpreted as very good. This finding

suggests that the teachers can demonstrate flexibility and

responsiveness in adjusting teaching to meet students‘ needs, ideas and

contributions. Furthermore, the teachers are skilled in leading students

in initiating thought-provoking questions. Rivera (2010) stressed that

when teachers want students to learn, they have to provide opportunities

for all students to interact in problem-rich situations, ask questions and

probe into each question. Thus, teachers have to encourage students to

find their own solution methods and give occasions for students to share

and compare solution methods and answers in the groups.

Quality of Teaching Procedure. The very high rating of 4.24

signifies that the teachers have the ability to ask thought-provoking

questions to find out if the students have understood the lesson very

well. This means further that the teacher can formulate questions that

develop the critical thinking ability of the students. If questions are

understood, the teachers are able to follow up to find out the extent of

students‘ understanding; if questions are unanswered, the teachers are

able to reformulate or rephrase the questions so as to fit students‘

understanding.

Selection of Teaching Methods. In connection to the selection of

teaching methods, the teachers were perceived ―very good‖ in all the

identified skills with a mean value of 4.07. This means that the teachers

are highly skilled in employing several approaches, methodologies and

techniques with emphasis on student inquiry and on collaborative and

cooperative learning. Grouws and Cebulla (2002), as cited by Fianza

(2009), mentioned that when teachers want to improve mathematics

teaching, certain strategies and methods of teaching should be

considered to a great extent by the teachers, themselves.

Quality of Information and Technology Utilized. The lowest

mean rating of 3.49, interpreted as good, was given to the quality of

information and communication technology used. This implies that the

teachers recognize to a lower degree the relevance of technology in

teaching mathematics. They do not often use instructional gadgets such

as the overhead projector, LCD projector and the like, although they have

received very good rating in terms of computerization of grades and some

instructional materials.

This finding corroborates with the study of Bello (2009) stressing

that the instructors have to improve more on educational technology and

technology integration.

This also finds support from the study of Oredina (2006) asserting

that the lowest area rated by her respondents was on quality of

information and communication technology used since utilization of ICT

was seldom.

Guidance Skills

Relative to the guidance skills, the mathematics teachers were

evaluated along quality of interaction with students and quality of

students‘ activity. As revealed in Table 12, level of Instructional

competence of the Teacher-Respondents along guidance skills, the

mathematics teachers were rated a grand mean of 4.24, which is

interpreted as very good.

Table 12


Guidance Skills


1. Quality of Interaction with students

a. arouse, maintain and sustain students’ interests

3.98 4.19 4.48 4.22 Very Good

b. give students recognition (phrases and reinforcements)

4.18 4.22 4.41 4.27 Very Good

c. regard students’ errors/mistakes as fruitful opportunities for learning

4.06 4.3 4.48 4.28 Very Good

d. make use of teaching as guide in helping students improve their work

4.25 4.37 4.44 4.35 Very Good

e. communicate high and realistic expectations from students

4.10 4.07 4.33 4.17 Very Good

Sub-mean 4.11 4.23 4.43 4.26 Very Good

2. Quality of students’ activity

a. activities are purposeful, relevant and experiential

4.2 4.37 4.26 4.28 Very Good

b. students are developing increased self-reliance and responsibility

4.1 4.19 4.37 4.22 Very Good

c. learning activities are appropriate for students’ developmental tasks

4.05 4.22 4.37 4.21 Very Good

d. time allocation is flexible to allow continuity of productive activities

4.06 4.11 4.44 4.20 Very Good

e. resources and facilities are appropriate for the learning activities

4.12 4.07 4.37 4.19 Very Good

Sub-mean 4.11 4.19 4.36 4.22 Very Good

Grand Mean 4.11 4.21 4.40 4.24 Very Good

Legend:

WM – Weighted Mean


Quality of Interaction with Students. The teachers were

perceived to have very good competence in helping students improve on

their work, in providing encouragement, recognition and in developing

self-reliance and responsible self-direction to students for a more

effective learning. This means that the teachers are highly aware of the

importance of extrinsic motivation to maintain, strengthen and sustain

positive attitudes such as giving commendations and approval. Also, they

excel in encouraging students to learn and improve their performance.

This finding is supported by the study of Graycochea (2000) which

revealed that teachers were very highly competent in providing an

environment conducive to learning.

Quality of Students’ Activity. As regards the quality of students‘

activity, the rating received by the teachers was 4.22, interpreted as very

good. This implies that the teachers are highly capable in providing

learning activities that are appropriate for students‘ developmental tasks.

The highest area rated was the area on ―activities are purposeful,

relevant and experiential‖. Kolb and Rogers stressed that significant

learning takes place when the subject matter is relevant to students‘

experience and is purposeful to their personal interest.

Management Skills

Table 13 presents the instructional competence of the mathematics

teachers in terms of their management skills. It is revealed that the level

of management skills of the mathematics teachers was very good with a

grand mean rating of 4.37.

Atmosphere in the classroom. The three respondent groups

indicated their highest response on the ability of the teacher to instill

mutual respect, order and discipline as attested by the mean of 4.42.

This entails that the teachers are skilled classroom managers. They have

the ability to create and sustain desirable behavior during classroom

instruction. They also have that certain ―command‖ over the class that

effective classroom managers possess. According to Bueno, as cited by

Tabafunda (2005), a sound classroom can be achieved and maintained

through maintenance of constructive student-behavior correction.

The teachers are also found to be skilled in establishing,

communicating, modeling and maintaining standards of responsible

behavior by incorporating creative and constructive discipline techniques

rather than coercive and restrictive ones. This means that there is a

thriving harmonious relationship existing between the teachers and their

students. A genuine expression of care on the part of the teacher makes

an atmosphere conducive to learning, a learning atmosphere of safety

and free of threat (Lardizabal, 1991).

Table 13


Management Skills

Instructional Competency Students Teachers Heads WM DER

1. Atmosphere in the classroom

I…

a. create and encourage positive social interaction, active engagement and self-regulation for every student

4.27 4.26 4.44 4.32 Very

Good

b. am enthusiastic and maintain a warm friendly atmosphere conducive to learning

4.24 4.33 4.30 4.29 Very

Good

c. establish, communicate, model, and maintain standards of responsible student behavior

4.32 4.33 4.30 4.32 Very

Good

d. instill mutual respect, order and discipline 4.32 4.41 4.52 4.42 Very

Good

e. incorporate creative and constructive discipline techniques rather than coercive and restrictive discipline techniques

4.28 4.19 4.30 4.26 Very

Good

f. develop and implement classroom procedures and routines that support learning and enforce school policies among students

4.23 4.30 4.37 4.30 Very

Good

g. cultivate students’ deep sense of controlling for their direction

4.15 4.22 4.37 4.25 Very

Good

h. am organized, punctual and manage class time well; accomplish the objectives and procedures set for the time period

4.15 4.22 4.33 4.23 Very

Good

Sub-mean 4.25 4.28 4.37 4.30 Very

Good

2. Conduct and return of evaluation materials

I…

a. correct test papers, quizzes, assignments/requirements carefully

4.31 4.56 4.52 4.46 Very

Good

b. return corrected test papers, quizzes, requirements promptly

4.25 4.30 4.56 4.37 Very

Good

c. conduct efficiently quizzes/ examinations to avoid cheating

4.31 4.44 4.59 4.45 Very

Good

Sub-mean 4.29 4.43 4.56 4.43 Very

Good

Grand Mean 4.27 4.36 4.47 4.37 Very

Good

Legend:

WM- Wieghted Mean


Conduct and Return of Evaluation Materials. In connection to

the conduct and return of evaluation materials, the teachers were

perceived to be very good in all the areas included. This reflects that the

teachers conduct efficiently quizzes to avoid cheating, and after the

administration of tests, the teachers are able to correct and return the

said evaluation materials. Cabusora (2001) emphasized that competence

and efficiency of a teacher is also reflected in his ability to return

promptly corrected test papers.

Evaluation Skills

Table 14 presents the instructional competence of the mathematics

teachers along evaluation skills. It is reflected that the teachers have very

good evaluation skills as attested by the mean value of 4.32. This implies

that the teachers are able to maintain, enhance and sustain learning

through their skill in evaluating learning outcomes; thus, they are able to

determine students‘ strengths and weaknesses as basis for an improved

classroom interaction.

Quality of Appraisal Questions. The teachers are found to be well

adept in the preparation of well-framed test questions covering the

subject matter taken in the class and in asking questions that lead to the

summary of the salient points of the lesson. These bring out the idea that

Table 14


Evaluation Skills


1. Quality of Appraisal questions

I am able to…

a. frame questions to find out students’ understanding

4.33 4.33 4.44 4.37 Very

Good

b. ask questions, integrated in varying techniques, that lead to the synthesis of the salient points of the lesson

4.28 3.70 4.30 4.09 Very

Good

c. prepare well-framed questions covering the subject matter taken in class

4.20 4.37 4.37 4.31 Very

Good

d. guide students in goal setting and assessing their own learning

4.16 4.15 4.44 4.25 Very

Good

e. provide students substantive, timely, and constructive feedback for specific area for improvement (write comments on paper/talk to students privately)

4.01 4.15 4.22 4.13 Very

Good

Sub-mean 4.20 4.14 4.36 4.23 Very

Good

2. Quality of assignment/ enrichment activities

I provide and consider…

a. varying authentic assessments to gauge the extent of authentic learning

4.20 4.08 4.37 4.22 Very

Good

b. assignment/ enrichment activities to supplement the day’s lesson and/or aligned to classroom instruction

4.25 4.22 4.48 4.32 Very

Good

c. subject requirements that are practical and challenging

4.25 4.19 4.44 4.29 Very

Good

d. adequate time for students to complete assignments/ requirements

4.27 4.41 4.59 4.42 Very

Good

e. availability of materials in giving assignments and subject requirements

4.19 4.37 4.52 4.36 Very

Good

Sub-mean 4.23 4.25 4.48 4.32 Very

Good

3. Quality of appraising students’ performance

I…

a. observe the standard grading system of the school

4.37 4.52 4.74 4.54 Excellent

b. grade/ score students objectively and accurately

4.37 4.48 4.70 4..52 Excellent

c. encourage students’ participation in creating rubrics

4.15 4.04 4.30 4.16 Very

Good

d. utilize criteria/ rubrics in checking requirements

4.21 4.30 4.56 4.36 Very

Good

Sub-mean 4.28 4.34 4.58 4.40 Very

Good

Grand Mean 4.24 4.24 4.47 4.32 Very

Good

Legend:

WM- Weighted Mean


the teachers are well-skilled in directing the class to probe into situations

that develop critical analysis through the formulation of very good

questions. This finding corroborates with study of Sameon (2002) which

stressed that teachers perceived themselves as very competent in

assessment. It means, therefore, that the teachers understood the

underlying principles and theories in test construction to improve

students‘ performance. According to Rivera and Sambrano (1999), as

cited by Tabafunda (2005), effective teaching should be coupled with the

art of questioning. Good questions serve as essential in developing

students‘ ability to define and exercise judgments.

Quality of Assignment/Enrichment Activities. The teachers

were perceived very good in providing quality assignment/ enrichment

activities as attested by the mean rating of 4.32. This means that the

teachers are highly capable in providing varying authentic assessments

to gauge the extent of learning. Further, they were also found to be well-

skilled in providing activities that supplement the day‘s lesson. Similarly,

they were found very good in providing time to complete requirements

and projects that are practical and challenging. This finding is supported

by the finding of Oredina (2006) divulging that her respondents were very

competent in providing reasonable, appropriate, practical and

challenging enrichment activities to substantiate what the students have

learned in class.

Quality of Appraising Students’ Performance. Relative to the

quality of appraising students‘ performance, the mathematics teachers

were perceived very good in observing the grading system of the school,

in grading students objectively, in encouraging students in creating,

utilizing rubrics/ criteria in checking requirements. This finding suggests

that the teachers are skilled evaluators, interpreters and users of

evaluation results or learning outcomes. This study is supported by the

study of Sameon (2002) revealing that the respondents perceived

themselves as very competent in assessment. He stressed that the

teachers understood the underlying principles and practices in

evaluation and assessment.

Comparison on the Perceived Instructional Competence between

Students and Teachers

Table 15 presents the comparison between the perceived

instructional competence between the students and teachers. The

perceptions have ―insignificant‖ difference in the teaching skills,

―significant‖ difference in guidance skills, ―insignificant‖ in management

skills and ―insignificant‖ in evaluation skills. Generally, there is no

significant difference in the perceptions of students and teachers as

regards the teachers‘ instructional competence. This finding accepts the

null hypothesis of the study that there is no significant difference in

perceptions of the group of respondents.

Table 15


Students and Teachers

Instructional Skills Mean

(Students)

Mean

(Teachers)

Computed t-

value

t- critical

@ 0.05

Decision Interpretation

Teaching/

Facilitating

4.01 4.03 0.07 2.23 Do not

reject Ho

Not

significant

Guidance 4.11 4.21 5.00 4.30 Reject Ho Significant

Management 4.27 4.36 1.10 4.3 Do not

reject Ho

Not

significant

Evaluation 4.24 4.24 0.65 2.78 Do not

reject Ho

Not

significant

Grand Mean 4.12 4.17 0.5 2.06 Do not

reject Ho

Not

significant

This means that the students and teachers evaluated the teachers‘

competence without discrepancy. This is rooted to the fact the teachers

and the students are the ones who interact with each other on a daily

basis, so they know very well what transpires and what does not in the

classroom. This can also be explained using the educational thought by

Johnson (2010) on teacher-student relationships. He stressed that

backing up, sharing and appreciation helped maintain commonalities in

perceptions of teachers and their students.


Students and Heads

Table 16 presents the comparison between the perceived

instructional competence between the students and heads. There exists

an ―insignificant‖ difference in the teaching skills, ―significant‖ difference

in guidance skills, ―insignificant‖ difference in management skills and

―significant‖ difference in evaluation skills. Generally, there is a

significant difference in the perceptions of the students and heads as

regards the instructional competence of the mathematics teachers. This

rejects the null hypothesis of the study on the difference of the

perceptions.

Table 16


Students and Heads


(Students)

Mean

(Heads)

Computed t-

value

t- critical

@ 0.05


Teaching/

Facilitating

4.01 4.03 1.01 2.23 Do not

reject Ho

Not

significant

Guidance 4.11 4.40 8.14 4.30 reject Ho Significant


reject Ho

Not

significant

Evaluation 4.24 4.47 3.50 2.78 reject Ho significant

Grand Mean 4.12 4.33 2.28 2.06 reject Ho significant

This means that the heads rated the teachers comparatively higher than

the students. This is rooted to the period of interactions of the two

groups of respondents: the students on a daily basis; while the heads on

occasional basis. The students interact with the teachers daily during

class interactions. They could assess when a teacher comes to class

prepared or not. On the other hand, the head sees the class interaction

during observation, a period when the teacher has prepared much for the

teaching-learning process. This is supported by the thought presented by

the article on www.ask.com that differences exist because of the different

status of people, needs, personalities, interactions and beliefs.


Teachers and Heads

Table 17 manifests the comparison on the perceived instructional

competence between the teachers and their heads. There exists an

―insignificant difference‖ in terms of teaching skills, ―significant‖ in

guidance skills, ―insignificant‖ in management skills and ―insignificant‘

in evaluation skills. Generally, there exists an insignificant difference in

the perceptions of the two respondents. This finding accepts the null

hypothesis of the study that there is no significant difference in the

perceptions of the respondents. This can be explained through citing the

Common Coding Theory. According to the theory, commonalities among

perceptions of two groups of respondents exist because there is a

Table 17


Teachers and Heads


(Teachers)

Mean

(Heads)

Computed t-

value

t- critical

@ 0.05


Teaching/

Facilitating

4.03 4.18 0.94 2.23 Do not

reject Ho

Not

significant

Guidance 4.21 4.40 4.59 4.30 reject Ho Significant


reject Ho

Not

significant

Evaluation 4.24 4.47 2.68 2.78 Do not

reject Ho

Not

significant

Grand Mean 4.16 4.33 1.83 2.06 Do not

reject Ho

Not

significant

common code or shared representations for perceptions and actions.

(www.en/wikipedia.org/wiki/common_coding_theory). Thus, the teachers

and their heads share a common goal in instruction, that is, to impart

quality education to the students. The insignificant difference can also be

explained by citing an excerpt in the Magna Carta for Public School

Teachers asserting that teachers should always need to back up each

other as sign of professionalism (Magna Carta for Public School

Teachers: Teacher as Professionals).

Summary of the Level of Instructional Competence of Mathematics

Teachers in the Private Secondary Schools in the City of San

Fernando, La Union

Table 18 reflects the summary of instructional competence of

mathematics teachers. It is gleaned from the table that the instructional

competence of the teachers obtained a grand mean of 4.24, interpreted

as very good. This rejects the null hypothesis of the study that the

teachers have only average/moderate instructional competence.

All the levels of skills were rated very good with management skills

as the highest and teaching skills as the lowest. Along teaching skills,

one indicator was rated good only, that is on the quality of

communication and information technology used. This implies that the

teachers are not very familiar and unskillful in utilizing instructional

technology; thus, they are not very competent along this area. This is

also rooted to the access to such technologies. In the researcher‘s

observation during the proctoring of tests, teachers, especially the ones

in the big schools, own laptops. This gives an idea that the math

teachers have limited access to projectors since other math teachers and

teachers of other subjects also desire to use information and

communication technology in facilitating the teaching-learning process.

Preparation of instructional technology is also a cause of this. Creating

interactive slides, researching up-to-date clips including the setting up of

the gadgets is also a complex task. Reinhardt, as cited by Oredina

(2006), emphasizes that using ICT in teaching develops the proficiency

desired among the students since features of computers such as video

presentations; animations and the like are better instructional objects

than chalkboards and transparencies.

Table 18

Summary of the Level of Instructional Competence of Mathematics

Teachers in the Private Secondary Schools in the City of San Fernando,

La Union

Level of Instructional

Competence

Students Teachers Heads Mean DER

A. Teaching/ Facilitating Skills


4.15 4.14 4.35 4.21 Very

Good

2. Quality of Teachers’

Explanation

4.24 4.34 4.34 4.31 Very

Good

3. Receptivity to students’ ideas 4.06 4.19 4.13 4.13 Very

and contributions Good

4. Quality of questioning

procedure

4.23 4.18 4.30 4.24 Very

Good

5. Selection of teaching methods 4.08 3.93 4.19 4.07 Very

Good

6.Quality of information and

communication technology used

3.32 3.38 3.78 3.49 Good

Sub-Mean 4.01 4.03 4.18 4.07 Very

Good

B. Guidance Skills

1. Quality of interaction with

students

4.11 4.23 4.43 4.26 Very

Good

2. Quality of students’ activity 4.11 4.19 4.36 4.22 Very

Good

Sub-Mean 4.11 4.21 4.40 4.24 Very

Good

C. Management Skills

1.Atmosphere in the Classroom 4.25 4.28 4.37 4.30 Very

Good

2.Conduct and return of

evaluation materials

4.29 4.43 4.56 4.43 Very

Good

Sub-Mean 4.27 4.36 4.47 4.37 Very

Good

D. Evaluation Skills

1. Quality of appraisal questions

4.20 4.14 4.36 4.23 Very

Good

2.Quality of

assignment/enrichment

4.23 4.25 4.48 4.32 Very

Good

activities

3.Quality of appraising students’

performance

4.28 4.34 4.58 4.4 Very

Good

Sub-Mean 4.24 4.24 4.47 4.32 Very

Good

Grand Mean 4.16 4.21 4.38 4.24 Very

Good

Legend:

WM- Weighted Mean


The very good evaluation given by the respondent groups to almost

all the skills is pinpointing to a laudable instructional competence of the

mathematics teachers in the Private schools in the City Division of San

Fernando. This means that the mandate of the Department of Education

(DepEd) to provide Quality Education for All (EFA) is present such that

the realization of the goals and objectives of Mathematics teaching is

achievable, especially in the Secondary schools.

The studies of Acantilado (2002), Subala, as cited by Roldan (2004)

and Oredina (2006) support the finding of the study. Their studies

emphasized that their teacher-respondents were highly competent.

Subala explained that since the teachers were competent, they can be

proper sources of assistance and guidance to their students in analyzing

different mathematical concepts. It is noteworthy that the perceived

instructional competence of teachers is in line with the goal of DepEd of

achieving and providing sound functional literacy to the students.

(Secondary Education Curriculum Framework, 2010).

Relationship Between Profile and Level of Content Competence

Table 19 manifests the relationship existing between profile

variables and content competence variables. It further reveals that

highest educational attainment is significantly correlated to

computational skills but not with conceptual skills, analytical and

problem-solving skills. This means that when a math teacher has higher

educational attainment, he has higher computational skills; but not

necessarily conceptual, analytical and more so with problem-solving skill

since such skill requires complex analysis with accurate solutions to deal

with certain mathematical problems. This can be explained through

citing an article by Keneddy (2001). Her article explained that a

prospective teacher majoring a subject like mathematics or science does

not guarantee that teachers will have the kind of subject matter

knowledge and skills they need for teaching.

Moreover, the table shows that number of years of teaching is

significantly correlated to problem-solving skills but not conceptual,

analytical and computational skills. Thus, a teacher who is more tenured

Table 19

Relationship Between Profile and Level of Content Competence

Profile Conceptual

Skills

Analytical Skills Computational

Skills

Problem-solving

Skills

Highest Educational

Attainment

0.23 Low

t= 1.16

0.32 Low

t= 1.90*

0.57* marked

t= 3.40*

0.05 Negligible

t=0.25

Number of Years in

Teaching

0.37 Low

t= 1.95*

0.19 negligible

t= 0.95

0.27 low

t= 1.37

0.42 * marked

t= 2.27*

Seminars Attended 0.49* marked

t= 2.75*

0.31Low

t= 1.60

0.19 Negligible

t= 0.95

0.06 Negligible

t= 0.29

Legend *- The relationship is significant

df = n-2 = 24; t critical value = 1.711

in teaching mathematics has higher competence in problem solving. It is

true that when someone is more exposed to certain routine, he is able to

master it.

The table also presents that the number of seminars attended is

significantly correlated to conceptual skills but not to analytical,

computational and problem-solving. This implies that when a teacher

frequently attends seminar-workshops, he has more content knowledge

of a certain discipline. It is with attending seminars that changes or

developments of an area of learning are taught and learned.

A further examination of the table reveals that all the marked or

substantial correlations (highest educational attainment- computational

skills, number of years in teaching-problem solving skills, seminars

attended- conceptual skills) had been found to be significant. This means

that the relationship existing among the cited variables are significant. It

can be strongly inferred that once a teacher has higher educational

qualifications, he is more competent in terms of computational skills;

once a teacher becomes more tenured in the teaching profession, he is

more competent along problem-solving skills; and, once a teacher has

attended more seminars, he is more competent in terms of conceptual

skills.

It can also be noted that even the correlations between highest

educational attainment-analytical skills and number of years in

teaching- conceptual skills, which were found to be low, are significant.

This means that there is really no strong connection between having

higher educational qualifications and competence along analytical skills,

and number of years in teaching and conceptual skills.

The finding of this study is supported by the ideas of web-article

writers suggesting that subject matter competence can be attained and

sustained through continuing professional education and teaching

experiences. Also, the data fully support the contention of Clemente-

Reyes (2002) in her study. Reyes expresses that subject matter expertise

is gained through possessing educational achievements, gaining years of

professional teaching service and attending training. She mentioned that

earning a bachelors‘ degree was not sufficient; thus, recommending for

continuing professional education since majority of the teacher experts

were masters degree holders or even doctorate degree holders. Also,

when a teacher is exposed in the teaching profession, he is likely to

expand his horizons in his field; thus, contributing to teaching expertise.

Lastly, she asserted that training helped a lot in gaining additional input.

Such input met or not met by teachers in her formal education can affect

his content knowledge.

Relationship Between Profile and Level of Instructional Competence

Table 20 discloses the relationship existing between profile

variables and instructional competence variables. It shows that highest

educational attainment is significantly correlated to teaching skills,

guidance skills, management skills and evaluation skills. This implies

that when a teacher has higher educational achievement, he is likely a

master of the teaching-learning process— he can facilitate classroom

instruction, can provide needed guidance to his students, is an effective

classroom manager, and a good evaluator of learning outcomes. Since

the computed correlation coefficients were found to be significant, there

exists a strong relationship between the variables correlated. It can be

strongly expressed that when a teacher possesses higher educational

attainment, he is likely more competent in instruction.

Table 20

Relationship Between Profile and Level of Instructional Competence

Profile Teaching

Skills

Guidance Skills Management

Skills

Evaluation Skills

Highest Educational

Attainment

0.71 * high

t = 4.94*

0.54 * marked

t=3.14*

0.51 * marked

t=2.90*

0.61* marked

t=3.77*

Number of Years in

Teaching

0.18 low

t=0.90

0.24 Low

t=1.21

0.28 Low

t=1.43

0.33 Low

t=1.71*

Seminars Attended 0.21 low

t=1.05

0.41* marked

t=2.20*

0.24 Low

t=1.21

0.41 * marked

t=2.20*


df = n-2 =24; t critical value= 1.711

This finding is supported by the study of Sameon (2002) stating that

highest educational attainment is strongly correlated to teaching

competence. Also, this corroborates with the international study of

Achwarin (2005) arguing that teachers‘ qualification is positively and

significantly related to teachers‘ instructional competence.

The table also illustrates that number of years of teaching does not

correlate with teaching, guidance, management and evaluation skills.

This means that the skills under instructional competence (teaching,

guidance, management, evaluation) are not necessarily brought about by

the number of years a teacher has spent in teaching. Further, a teacher

who has a 30-year teaching experience is not necessarily more competent

than a teacher who is still earning his teaching experience.

Moreover, the correlation between number of years of teaching to

teaching skills, guidance skills and management skills were found to be

insignificant. This means that the relationship is not strong enough to

contend that a teacher who stayed long in the service does not

necessarily have higher competence along teaching, guidance and

management skills. On the other hand, the correlation between the

number of years of teaching to evaluation skills was found to be

significant. This means that it is safe to assert that a teacher who stayed

in the service for a longer period of time does not necessarily have higher

evaluation skills.

These findings run parallel to the study of Oredina (2006)

revealing that number of teaching experience is not significantly

correlated to the four instructional competence dimensions. However,

these findings do not corroborate with the study of Davis (2000), as cited

by Binay-an (2002), which claimed that teachers who are younger in the

service are more likely to possess greater competence since they have

greater inquisitive mind and zest for teaching. Further, these were not

also in congruence to the study of Laroco (2005) claiming that teachers

who had longer years in service are in better position to adjust

themselves to different classroom situations; thus, they are more

competent. She concluded that teaching experiences add to the teaching

competence.

Same table also exposes that the number of seminar-workshops

attended by the teachers is significantly related to guidance and

evaluation skills but not to teaching and management skills. This means

that the more seminar-workshops a teachers attends, the teacher

becomes more competent in guiding students and in evaluating their

learning. This can be strongly asserted since the correlation for these

variables have been found to be significant.

It further means that a teacher who has more seminars or

trainings is not more competent in teaching and managing a class

compared to a teacher with less number of seminars.

Relationship Between Content and Instructional Competence

Table 21 unveils the relationship existing between content and

instructional competence of the mathematics teachers. It relates that

conceptual skill is significantly related to guidance skills. Thus, a teacher

who is more competent along concepts is more likely a good source of

guidance. However, conceptual skill is not correlated to teaching skills,

management and evaluation skills; thus, a teacher who possesses more

conceptual skills does not necessarily mean that he can teach well,

manage class effectively and evaluate learning outcomes accurately.

Table 21

Relationship Between Content and Instructional Competence

Cognitive Skills Teaching

Skills

Guidance Skills Management

Skills

Evaluation

Skills

Conceptual Skills 0.25 Low

t=1.26

0.45* marked

t=2.47*

0.31 Low

t=1.60

0.33 Low

t=1.71*

Analytical Skills 0.23 Low

t=1.15

0.37 Low

t=1.95*

0.27 Low

t=1.37

0.33 Low

t=1.71*

Computational Skills 0.35 Low

t=1.83*

0.37 Low

t=1.95*

0.21 Low

t=1.05

0.25 Low

t=1.27

Problem-Solving skills 0.22 Low

t=1.10

0.16 Negligible

t=0.79

0.17 Negligible

t=0.85

0.14 Negligible

t=0.69


df=n-2=24; t critical value = 1.711

Moreover, analytical, computational and problem-solving skills do not

correlate with teaching, guidance, management and evaluation skills.

This means that when teachers possess high skills along analysis,

computational and problem-solving, they do not necessarily possess

skills along teaching-facilitating, guidance, management and evaluation

lls. An international study which was cited by an article posted on the

Harvard Educational Review supports this finding very well. This study

was by Reynolds (1999). In the study, he exposed that subject matter

expertise was not contributory to success in teaching. With these she

expanded the meaning of subject matter expertise to include an

awareness of that expertise as learned.

(http://www.hepg.org/her/abstract/164). This means that when a

teacher has more content competence, it does not necessarily follow that

he can teach better. On the other hand, these findings do not support

several studies, which include that of Binay-an (2002), Cabusora (2004),

Diaz (2000), and Clemente-Reyes (2002) which revealed that subject

matter expertise was a contributory factor to teaching expertise. It was

stressed that mastery of content-specific knowledge and the organization

of this knowledge affect effective instruction. If the teachers were not

experts in their field, it is unlikely for them to possess teaching expertise.

Summary on the Relationship existing among Profile, Instructional

and Subject Matter Competence

Table 22 summarizes the relationship existing between profile and

content competence, profile and instructional competence, and

competence along content and instruction.

It further reveals that the computed correlation coefficients

between the profile variables and content competence profile are all

below the substantial coefficient of 0.41; thus profile (highest educational

attainment, number of years of teaching and number of seminars

attended) is not significantly related to content competence.

Summary on the Relationship existing among Profile, Instructional and

Subject Matter Competence

Table 22

Highest

Educational

Attainment

Number of Years

of Teaching

Number of

Seminars Attended

Instructional

Competence

Content

Competence

0.40 low

t = 3.10*

0.38 low

t = 2.01*

0.31 low

t = 1.60*

0.38 low

t = 2.01*

Instructional

Competence

0.64* Marked

t = 4.08*

0.28 low

t = 1.43

0.35 low

t = 1.83*

Legend: * Significant

df=n-2=24; t critical value = 1.711

Moreover, it divulges that highest educational attainment is

significantly correlated to instructional competence with a correlation

coefficient of 0.64, which is interpreted as marked or substantial

correlation. However, the number of teaching experience and number of

seminars attended do not correlate with instructional competence.

It also reveals that the computed correlation coefficient between

instructional competence and content competence is 0.38, interpreted as

low correlation. This means that instructional competence and content or

subject matter competence are not significantly related.

Strengths and Weaknesses of Mathematics Teachers Along Content

Competence

Table 23 manifests the strengths and weaknesses of the

mathematics teachers along the content/subject matter competence

dimensions such as conceptual skills, analytical/reasoning skills,

computational skills and problem-solving skills. As basis for determining

the strengths from weaknesses, a mean rating lower than 17 is

considered a weakness; otherwise, it is considered as strength. They are

ranked accordingly for an organized presentation. The strengths are

ranked in such a way that the item that garnered the highest mean value

obtained the first rank to indicate that it is regarded as the foremost

strength; the lowest mean value under the strength is ranked first

indicative that it is a foremost weakness.

Analytical skills and problem-solving skills are considered

weaknesses; conceptual and computational skills are considered as

strengths. Generally, the teachers have a grand mean below 17; thus, the

teachers are found to be weak in terms of their subject matter/ content

competence. This accepts the null hypothesis of the study that the

teachers‘ weaknesses are on analytical and problem-solving skills and

their strengths are on conceptual and computational.

Table 23

Strengths and Weaknesses of Mathematics Teachers along Content

Competence

The foremost weakness is problem-solving. This is due to the fact

that this skill encompasses all the other skills. One should know enough

mathematical facts, should know how to reason out and probe deeper,

and of course, should know how to compute before he can actually deal

with mathematical problems.

Area of Content

Competence

Strength Rank Weakness Rank

Conceptual Skills 18 1.5

Analytic/Reasoning

Skills

15 2

Computational

Skills

18 1.5

Problem-Solving

Skills

12 1

Grand Mean 16

Strengths and Weaknesses of Mathematics Teachers Along

Instructional Competence

Table 24 manifests the strengths and weaknesses of the

mathematics teachers along the instructional competence dimensions

such as teaching/facilitating skills, guidance skills, management skills

and evaluation skills. As basis for determining the strengths from

weaknesses, all items rated 3.50 and above are strengths; otherwise,

weaknesses. They are ranked accordingly for an organized presentation.

The strengths are ranked in such a way that the item that garnered the

highest mean value obtained the first rank to indicate that it is regarded

as the foremost strength; the lowest mean value under the strength is

ranked first indicative that it is a foremost weakness.

Table 24

Strengths and Weaknesses of Mathematics Teachers

Instructional Competence

Instructional Competency

Strength

Rank

Weakness

Rank A. Teaching / Facilitating Skills


I...


4.46 1


4.35 2


4.19 4


4.28 3


4.11 6


4.09 7


4.18 5


4.03 8


I…


4.29 1

b. ask students how they got a particular answer 4.38 2


4.33 3


4.23 4


I…


4.06 3


4.16 2


4.17 1


I…


4.24 4


4.21 5


4.26 2


4.25 3

e. emphasize on essential ideas and problems 4.27 1


4.20 6


I use teaching methods which are…


4.14 2


4.07 3

c. emphasizing on and eliciting students’ inquiry 3.99 4


3.96 5


4.16 1


I use…


3.66 2


3.45 3


3.37 2


3.76 1

e. overhead/LCD projector 3.24 1

B. Guidance Skills


I…

a. arouse, maintain and sustain students’ interests 4.22 4

b. give students recognition (phrases and reinforcements)

4.27 3


4.28 2


4.35 1


4.17 5


I ensure that…


4.28 1

b. students are developing increased self-reliance and responsibility

4.22 2


4.21 3


4.20 4


4.19 5



I…


4.32 2.5


4.29 5


4.32 2.5

d. instill mutual respect, order and discipline 4.42 1


4.26 6


4.30 4


4.25 7


4.23 8


I…

d. correct test papers, quizzes, assignments/requirements carefully

4.46 1

e. return corrected test papers, quizzes, requirements promptly

4.37 3

f. conduct efficiently quizzes/ examinations to avoid cheating

4.45 2

4. Evaluation Skills


I am able to…


4.37 1


4.09 5


4.31 2


4.25 3


4.13 4




4.22 5


4.32 3


4.29 4


4.42 1


4.36 2


I…


4.54 1

b. grade/ score students objectively and accurately 4.52 2


4.16 4

d. utilize criteria/ rubrics in checking requirements 4.36 3


In general, teaching skills were considered as strengths of the

teachers as regards substantiality of teaching, quality of teacher‘s

explanation, receptivity to students‘ ideas, quality of questioning

procedure and selection of teaching methods. However, the quality of

information and communication technology used was regarded as

weakness. Thus, it entails that the teachers are very good facilitators of

the teaching learning process. They are able to execute their function

effectively. They are effective pathfinders of knowledge who can instill the

essentials of their subject in the students. But, they need to improve

along the quality of information and communication technology utilized

the mere fact that they were found wanting along this area. The reason

for this weakness may be the accessibility of the teachers to these kinds

of technology.

Guidance Skills

All the indicators under this area were perceived as strengths. This

implies that the Mathematics teachers are very good in directing,

supervising, and guiding the teaching-learning process. They are able to

provide an atmosphere conducive to humane learning. Also, they provide

activities which are relevant and purposeful for the students, and which

they can direct and control to aim for optimum learning. Such being the

case, the students are trained to become responsible element of the

teaching-learning process.

Management Skills

The indicators of this skill are all perceived as strengths. A further

comparison of the four skills gives an idea that this area is the skill rated

the highest, the foremost strength. This means, in general, that the

teachers are very good classroom managers. As such they are able to

instill mutual respect, good behavior and discipline among students

since they, themselves, model good behavior that their students emulate.

Evaluation Skills

Like all the indicators under guidance and management skills, all

the indicators under evaluation skills are perceived strengths by the

three groups of respondents. This means that the teachers are able to

gauge the extent of learning of their students.

In synthesis, all the identified skills along teaching, guidance,

management and evaluation were perceived to be strengths by the three

groups of respondents, except in the quality of information and

communication utilized, which is considered a weakness; thus, a

primary concern.

The finding of the current study runs parallel to the studies of

Cirstobal (2004), Oredina (2006), and Bello (2009). In their studies, all

the other areas were perceived strengths such as in teaching procedure,

methodologies, assessment strategies, guidance, and management but

the three divulged that the teachers lacked the necessary competence in

technology utilization and integration.

Proposed Two-Pronged Training Program for Mathematics Teachers

of the Private Secondary Schools in the City Division of

San Fernando, La Union

I. Rationale

The task impressed by the educative process on the shoulders of

the teachers is not easy. Despite this, teachers still strive for the best to

provide the quality education every student deserves. Teachers still

desire to be the best for their students. If this ideal holds greater than

the challenges, then the teacher should not fail to upgrade and update

himself. In doing so, teachers certainly improve their weaknesses and

sustain or intensify their strengths. Indeed, training is necessary.

. Training is the process of acquiring specific skills to perform a

better job. It helps people to become qualified and proficient in

performing their tasks. Through training, people‘s behavior towards a

task becomes modified. Such modified behavior contributes to the

successful attainment of goals and objectives.

The proposed two-pronged training program is based upon the

identified strenghts and weaknesses of the mathematics teachers‘

competence along content and instruction. The items rated the lowest in

content competence dimensions (reasoning/analytical and problem-

solving skills which were average competence), and instructional

competence dimensions (Information and Communication Technology

(ICT) utilization) are considered priorities. The other dimensions

considered very good are still included for sustainability and possible

enhancement.

The insufficiency of Information and Communication Technology

used in the private secondary schools in the City Division of San

Fernando is theorized to be a contributory factor in the low rating given

to the quality of ICT used. To improve such, each school should upgrade

its facilities in terms of technology, besides training the teachers in the

use of such technology.

The training program shoud be implemented during the pre-

services of the institution so that the attendance of the teachers will be

assured. The teachers will simultaneously have their training. Follow-up

will be done, if necessary. Assessment will be done on the last day of the

program.

Post-test will be done to ensure mastery of the subject matter.

Demonstration lesson, on the other hand, will be conducted to see the

extent of manifestation of instructional competence. In the selection of

topics to be taught, the area with the lowest competency rating will be

considered.

II. General Objectives

1. Improve content and instructional pedagogical competencies;

2. Apply and adopt technology and utilize varied instructional

materials in teaching mathematics;

3. Utilize the different motivating techniques and classroom

interactive activities;

4. Develop the proper techniques in the art of questioning and

classroom management; and

5. Construct reliable and valid evaluative materials to measure

students‘ achievement.

III. Training Course Contents

A. Content Competence

1. Problem-Solving Skills

2. Reasoning/Analytical Skills

3. Computational Skills

4. Conceptual Skills

B. Teaching Skills

1. Information and Communications Technology

2. Instructional Aids and Devices

3. Methodology/Strategies and Approaches in Classroom

Interaction

4. Art of Questioning

C. Guidance Skills

1. Motivating Techniques

D. Management Skills

1. Classroom Management and Discipline

E. Evaluation Skills

1. Evaluative Techniques

IV. Methodologies

Lectures integrated with Interactive discussion with, application,

skill builders, and follow-up workshops will be the main methodologies of

the training course. Partcipants will be engaged in different set-ups:

individual for the lecture, solving and application, pair for the

brainstorming and group for the workshops.

The teacher-participants can sometimes be asked to share their

know-how and procedures about certain situations so that the

discussion will be more substantial, fruitful and participative.

V. Training Management

The mathematics training shall be under the over-all management

of the prinicipal with the assistance of the academic coordinator and the

mathematics coordinator.

The facilitators for the proposed training program were chosen

based on their qualifications, trainings and seminars attended and

organized, and competence along the different areas of concern. Most of

the facilitators were speakers of the different seminar-workshops

attended by the researcher. Such being the case, their expertise have

really been considered in choosing their area for training.

For Content Competence Training Name Position Experiences/Qualifications/ Area/s of Concern Mr. Gerry Hoggang Head, Mathematics BSEd, MAMT Saint Louis College Elementary Algebra High School

Dr. Jose Almeida Education Supervisor I BSEd, MATE, PHd Mathematics, DepEd Intermediate Algebra Mrs. Edwina Manalang Faculty BSED, MAED Saint Louis College Geometry Dr. Ramir Austria Head, Mathematics Instruction BSEd, MAEd-Math, EDd.Mgt. University of the Cordilleras - Advanced Algebra, Trigo and Stat

For Instructional Competence Mr. Jayson Toquero Instructional Media Center-In charge BSIT, MS Comp Ed Units CKC-High School - Info. and Com. Tech utilized Dr. Nora A. Oredina Head, Mathematics BSEd, MATE, EDd Saint Louis College -test construction Mrs. Debbie Graffil Principal BSED, MAED St Paul College, Manila -classroom management Mrs. Gloria Cruz Principal BEED, MAED STC, QC -guidance skills, lesson planning

VI. Participants

All mathematics teachers of the Private Secondary Schools in the

City Division of San Fernando, La Union

VII. Duration

5 days (refer to the proposed program of activities) VIII. Logistics

Honoraria for speakers (1,500/speaker) P12000.00

Meals/Snacks for the speakers (P150/speaker) P 1200.00

Seminar Kits (P50/teacher) P 1300.00

Others:

Documentation, LCD projectors

Laptop (c/o IMC officer)

Certificates (c/o secretary)

TOTAL P14,500.00

IX. Success Indicator

The mathematics teachers of the private secondary schools in the

City Division of San Fernando, La Union shall improve on their content

competence: conceptual, reasoning/analytical, computational and

problem-solving skills; and instructional: teaching/facilitating, guidance,

management and evaluation skills by 25 percent.

Level of Validity of the Two-Pronged Training Program

It can be seen from the Table that the level of face and content

validity of the proposed two-pronged training program as perceived by

the validators was high. This suggests that the proposed program is

highly functional, acceptable, appropriate, timely, implementable and

sustainable.

Table 25

Level of Validity of the Two-Pronged Training Program

Level of Validity Weighted

Mean

Descriptive

Equivalent

I. Face 4.17 High

II. Content

a. Functionality

4.50

High

b. Acceptability 4.50 High

c. Appropriateness 4.33 High

d. Timeliness 4.17 High

e. Implementability 3.83 High

f. Sustainability 3.83 High

Average 4.20 High

Over-all Rating 4.19 High

A VALIDATED TWO-PRONGED TRAINING PROGRAM FOR MATHEMATICS TEACHERS

Area of

Concern

Objectives Methods/

Strategies

Content Materials

Needed

Time

Frame

Human

Resource

Logistics Outcomes

A. Content

Competence

Problem

Solving

Skills

Through the

conduct of

lecture, test-

retest, skill

builders

strategies, the

mathematics

teachers

should be

able to:

- examine

different word

problems,

mathematics

illustrations or

items

accurately

- solve

-lecture

-Skill-building

Algebra I

-real number

system

-First degree

equations and

inequalities in

one variable

-rational

algebraic

expressions

-linear

equations in 2

variables

-systems of

linear

equations

Problem Sets

Compass

1 day

May 24, 2011

(Morning)

Participants:

All math

teachers

Speaker:

Mr. Gerry

Hoggang

Snacks:

P 300.00

Honorarium

There is a

significant

increase in

the

mathematics

competence

pretest and

mathematical

problems with

ease and

accuracy

-develop

additional

techniques in

solving word

problems

exercises

-sharing-

discussion

Test-retest

strategy

Algebra II

-Quadratic

Equations

-variations

-Sequences

and Series

Geometry

-Writing Proofs

-Triangle

congruence

Supplemental

Materials

Overhead/

or LCD

projectors

Laptops

1 day

Participants:

All math

teachers

Speaker:

Dr. Jose P.

Almeida

Participants:

All math

P3000.00

Snacks:

posttest

-inequalities

-Similarity

-Circles

-Coordinate

Geometry

Math IV

-Functions

Quadratic

Polynomial

Exponential

Logarithmic

Circular

-trigonometric

Identities and

Equations

-Counting

techniques and

May 24, 2011

(Afternoon)

teachers

Speaker:

Mrs. Edwina

Manalang

Participants:

All math

teachers

Speaker:

Dr. Ramir

Austria

P 300.00

Honorarium

P3000.00

probability

-Intro to

Statistics

Area of

Concern

Objectives Methods/

Strategies

Content Materials

Needed

Time

Frame

Human

Resource

Logistics Outcomes

A. Content

Competence

Through the

conduct of

lecture, test-

retest, skill

builders

strategies, the

mathematics

teachers

should be

able to:

- examine

different word

problems,

mathematics

illustrations or

Algebra I

-real number

system

-First degree

equations and

inequalities in

one variable

-rational

algebraic

expressions

-linear

equations in 2

Participants:

All math

teachers

Speaker:

Mr. Gerry

Hoggang

Snacks:

There is a

significant

Reasoning/

Analytical

Skills

items

accurately

-use

deductive or

inductive

reasoning in

solving

exerices

-lecture

-Skill-building

exercises

-sharing-

discussion

Test-retest

strategy

variables

-systems of

linear

equations

Algebra II

-Quadratic

Equations

-variations

-Sequences

and Series

Geometry

-Writing Proofs

-Triangle

Problem Sets

Compass

Supplemental

Materials

Overhead/

or LCD

projectors

Laptops

1/2 day

May 23, 2011

(morning)

Participants:

All math

teachers

Speaker:

Dr. Jose P.

Almeida

P 300.00

Honorarium

P3000.00

increase in

the

mathematics

competence

pretest and

posttest

congruence

-inequalities

-Similarity

-Circles

-Coordinate

Geometry

Math IV

-Functions

Quadratic

Polynomial

Exponential

Logarithmic

Circular

-trigonometric

Identities and

Equations

-Counting

1 /2day

May 23, 2011

(afternoon)

Participants:

All math

teachers

Speaker:

Mrs. Edwina

Manalang

Participants:

All math

teachers

Speaker:

Dr. Ramir

Austria

techniques and

probability

-Intro to

Statistics

Area of

Concern

Objectives Methods/

Strategies

Content Materials

Needed

Time

Frame

Human

Resource

Logistics Outcomes

A. Content

Competence

Through the

conduct of

lecture, test-

retest, skill

builders

strategies, the

mathematics

teachers

should be

able to:

Algebra I

-real number

system

-First degree

equations and

inequalities in

one variable

-rational

algebraic

Participants:

All math

teachers

Speaker:

Mr. Gerry

Hoggang

Conceptual

Skills

Computatio-

nal skills

- restate on

their own the

different basic

mathematical

concepts,

theorems,

postulates,

laws and

properties/

axioms

- solve

mathematical

problems

mentally

-improve

performance

in the

mathematics

competency

test

-lecture

-Skill-building

exercises

-panel discussion

-sharing-

discussion

Test-retest

strategy

expressions

-linear

equations in 2

variables

-systems of

linear

equations

Algebra II

-Quadratic

Equations

-variations

-Sequences

and Series

Geometry

Overhead/

or LCD

projectors

Laptops

Problem sets

1 day

May 25, 2011

Participants:

All math

teachers

Speaker:

Dr. Jose P.

Almeida

Snacks:

P 300.00

Honorarium

P3000.00

There is a

significant

increase in

the

mathematics

competence

pretest and

posttest

-Writing Proofs

-Triangle

congruence

-inequalities

-Similarity

-Circles

-Coordinate

Geometry

Math IV

-Functions

Quadratic

Polynomial

Exponential

Logarithmic

Circular

-trigonometric

Identities and

Participants:

All math

teachers

Speaker:

Mrs. Edwina

Manalang

Participants:

All math

teachers

Equations

-Counting

techniques and

probability

-Intro to

Statistics

Speaker:

Dr. Ramir

Austria

Area of

Concern

Objectives Methods/

Strategies

Content Materials

Needed

Time

Frame

Human

Resource

Logistics Outcomes

B. Through the

Instructional

Competence

Teaching

Facilitating

Skills

(utilization of

ICT)

conduct of

lecture,

seminar-

workshop,

demonstration

panel

discussion,

and hands-on

activities, the

mathematics

teachers should

be able to:

- use ICT

gadgets such

as projectors,

laptops,

computers and

the like

-acquaint

themselves in

the basic usage

of the features

of MS

PowerPoint

-lecture

Basic features

of MS

PowerPoint,

Excel, MS

LCD

Projector

1 day

Participants

All Math

teachers

Snacks:

P600.00

95% of the

teachers have

improved on

the use of ICT

slides such as

hyperlinking,

videos, photos,

and the like

-use MS Excel,

Geogebra, MS

Math, MathLab

and Statext

-familiarize

themselves

with the

different

interactive

classroom

activities that

supplement

classroom

instruction

-structure

thought

provoking

questions that

-workshop

-demonstration

-panel discussion

Math, Math

Lab, Geogebra,

Statext

Internet

Mathematical

Softwares

May 26, 2011

Speaker:

Mr. Jayson

Toquero

Honorarium

P1500.00

in instruction

develop the

critical and

analytical

thinking of the

students

Area of

Concern

Objectives Methods/

Strategies

Content Materials

Needed

Time

Frame

Human

Resource

Logistics Outcomes

B.

Instructional

Competence

Through the

conduct of

lecture,

seminar-

workshop,

demonstration

panel

discussion,

and hands-on

activities, the

mathematics

teachers

should be

able to:

Guidance

Skills

(Motivating

techniques)

- use the

varied

motivating

techniques in

instruction

-acquire and

utilize skills

and

techniques in

improving

classroom

instruction

-lecture

-workshop

-demonstration

-panel discussion

Motivating

techniques

LCD

Projector

Laptop

Internet

Mathematical

Softwares

1 day

May 27, 2011

Participants

All Math

teachers

Speaker:

Mrs.Gloria

Cruz

Snacks:

P800.00

Honorarium

P1500.00

95% of the

teachers have

improved on

motivating

techniques,

classroom

discipline,

assessment

strategies)

Management

skills

(Classroom

discipline)

Evaluation

skills

(assessment

strategies)

-construct well-

framed test

questions with

table of

specifications

Classroom

Discipline

techniques

-Authentic

assessment

Strategies

Articles on

Classroom

situations

Test samples

Participants

All Math

teachers

Speaker:

Mrs. Deffie

Graffil

Participants

All Math

teachers

Honorarium

P1500.00

Honorarium

P1500.00

Speaker:

Dr. Nora A.

Oredina

Prepared by: Noted by: Approved by:

MR. FELJONE G. RAGMA MRS. EVANGELINE L. MANGAOANG SR. TERESITA A. LARA, ICM Researcher HS Principal School Directress

Chapter 5

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This chapter incorporates the summary, findings, conclusions and

recommendations of the study.

Summary

The study aimed at determining the competence of Mathematics

teachers in the private secondary schools of San Fernando City, La

Union as basis for a proposed two-pronged training program.

Specifically, it sought to find answers to the following questions:

6. What is the profile of the mathematics teachers along:

a. highest educational qualification;

b. number of years in teaching mathematics; and

c. number of mathematics trainings and seminars

attended?

7. What is the level of competence of mathematics teachers along:

a. Content

a.1. Conceptual Skills

a.2. Reasoning/ Analytical Skills

a.3. Computational Skills

a.4. Problem-Solving Skills ; and

b. Instruction

b.1.Teaching Facilitating Skills

b.2. Guidance Skills

b.3. Management Skills

b.4. Evaluation Skills?

2.1 Is there a significant difference in the instructional competence

of the teachers as perceived by the students, heads and

teachers, themselves?

8. Is there a significant relationship between:

a. Teacher‘s profile and competence along content;

b. Teacher‘s profile and competence along instruction; and

c. Competence along content and competence along

instruction?

9. What are the major strengths and weaknesses of the mathematics

teachers along:

a. Content; and

b. Instruction?

10. Based on the findings, what training program may be

proposed to enhance the content and instructional competence of

the mathematics teachers?

5.1 What is the level of validity of the training program along:

a. face; and

b. content?

The descriptive survey method was used in this study. Data were

gathered with the use of two sets of questionnaire. One is a teacher-made

competence test to determine the content competence. The other one is

questionnaire-checklist to determine the instructional competence.

Respondents were heads, teachers and their students.

Findings

The following are the salient findings of the study:

1. a) All the mathematics teachers are licensed and majority of them

are pursuing graduate studies.

b) Majority of the teacher-respondents, 17 or 65.38%, had 0-5

years of teaching experience.

c) 84.62% had very inadequate and 15.39% had slightly adequate

attendance in seminars.

2. a) The teachers‘ level of subject matter/content competence was

average with a mean rating of 16. They scored highest in

conceptual and computational skills but lowest in problem-solving

skills.

b) The teachers‘ level of instructional competence was very

good with a mean rating of 4.24. They were rated highest in

management skills but lowest in teaching skills.

2.1) There is no significant difference in the perception between

students and teachers; there is a significant difference in the

perception between students and heads; and there is no significant

difference in the perception between teachers and heads.

3. a) There is no significant relationship between profile (highest

educational attainment, number of years of teaching, number of

seminars attended) to content competence.

b) There is a significant relationship between highest

educational attainment and instructional competence; but there is

no significant relationship between number of years of teaching

and number of seminars attended to instructional competence.

c) There is no significant relationship existing between content

competence and instructional competence.

4. a) Conceptual skills and Computational skills are considered as

strengths. On the other hand, reasoning/analytical skills and

problem-solving skills are considered as weaknesses.

b) All the other skills under teaching, guidance, management

and evaluation were considered strengths. The weakness of

Mathematics teachers along instructional competence was on the

quality of utilization of information and communication technology.

5. The two-pronged training program enhances the weaknesses

and the sustainability of the strengths.

5.1 The training program along face and content validity was

high.

Conclusions

In the light of the above-cited findings, the following conclusions

are drawn:

a) The mathematics teachers in the secondary schools of the City

Division of San Fernando, La Union are all qualified in the teaching

profession.

b) The teachers are very young in the service because of the high

turn-over rate of the private schools. The rate may be rooted to the

teachers‘ desire to be employed abroad or in the public schools.

c) The mathematics teachers are exposed minimally to trainings

and seminars but they still perform well in their teaching.

2. The teachers had only average competence in terms of their

content competence but were perceived very skillful in teaching

Mathematics.

2.1 The heads rated instructional competence higher than the

students; but all the respondents consider the teachers very skillful

in teaching.

3. a) Teachers who have higher educational attainment, number of

years in teaching and seminars attended do not have higher subject

matter competence.

b) Teachers who have higher educational attainment have higher

instructional competence; but, teachers who are more experienced in

teaching and have more seminars do not mean that they have higher

instructional competence than those who are younger and those who

have lesser seminars.

c) It does not mean that when a teacher has high content

competence, he has high instructional competence as well and vice

versa.

4. Teachers are not so skilled at analysis and problem-solving and

they do not use ICT and other innovative instructional technology

much in their daily teachings but still have very good teaching

performance.

5. The proposed two-pronged training program is timely for the new

and tenured teachers to update and upgrade their content and

instructional competence. Moreover, it is a helpful tool for them to

understand more their subject and know more about the ways on

how to present a subject matter, especially on the use of ICT.

5.1 The administrators of the private secondary schools in the City

Division of San Fernando, La Union considered the two-pronged

training program valid.

Recommendations

Based on the conclusions of the study, the researcher recommends

the following:

1. The teachers have to be encouraged to enroll in their graduate

studies, especially in line with their fields of specialization so that

their competence will be elevated.

2. Incentive Scheme for outstanding performance should be devised

by administrators to enhance or sustain teaching performance;

and keep outstanding teachers in the service.

3. Teachers should always be sent to seminars and workshops where

their participation is necessary. If funding isn‘t enough, there

should be mechanisms such as improving faculty development

plan to remedy the predicament. Further, if a teacher is sent for a

seminar, he has to echo the essentials of the seminar to his/her

area members.

4. Teachers should use ICT in their teaching. On the other hand,

the school has to provide the materials in order for the teacher to

integrate technology to instruction.

5. A closer monitoring system has to be applied by the heads to

ensure that teachers utilize ICT in their teaching. If materials are

scarce, scheduling should be done.

6. The proposed two-pronged training program for the Mathematics

teachers should be implemented in the private secondary schools

in the City Division of San Fernando, La Union.

7. A study to determine the efficiency or efficacy of the two-pronged

training program should be undertaken.

8. A parallel study should be undertaken in other subject areas such

as English and Science.

BIBLIOGRAPHY

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APPENDICES

Sample Computation of Reliability of the Questionnaires

For the College Algebra test:

𝐾𝑅21 = 𝑘

𝑘−1 1 −

𝑥 𝑘−𝑥

𝑘𝜎2

where:

k = number of items

𝑥 = mean of the distribution

𝜎2= the sample variance of the distribution

𝐾𝑅21 = 𝑘

𝑘−1 1 −

𝑥 𝑘−𝑥

𝑘𝜎2

𝐾𝑅21 = 30

30−1 1 −

8.9 30−8.9

30 5.15 2

r = 0.79

Sample Computation on the Validity

College Algebra Test

CRITERIA Validators Mean

A B C D E

1. The directions are

specific and can be

understood well by the

students.

4.8

2. The questions are

encoded correctly. There

are no grammatical errors

and lapses.

4.8

3. The sentences are

formulated in a manner

that the target students

can understand.

4. Mathematical

expressions and equations

are encoded correctly. They

are easily understood for

easier calculations.

4.4

5. The test items cover the

course contents as

indicated in the table of

specifications.

4.6

7. There are provisions for

students to write solutions

on the question sheets.

4.6

6. Generally, the test items

are representations of what

they are ought to measure.

4.6

4.6

Overall Mean 4.0 5.0 4.43 4.71 5.0 4.63

Summary of Suggestions:

Sample Computation on the Validity of the

Instructional Competence Questionnaire-Checklist

Criteria Validators

A B C D E Mean

1. Are the items representative

of the concepts being

measured?

4 5 5 5 5 4.8

2. Are the questions free from

grammatical error?

4 5 5 5 5 4.8

3. Are the items perfectly clear

and unambiguous? Is the

general frame and reference

from which these are asked,

and from which the answers

should be given clear?

4 5 5 4 5 4.6

4. Are the test items stable,

relatively deep-seated, well-

considered, non-superficial,

non-ephemeral, but

something which is typical of

the subject area?

4 5 5 5 5 4.8

5. Do the test item pull? That

is, can these be responded

to by a large enough

proportion of examinees to

permit validity? Are the test

items engaging enough to

get response with some

4 5 5 5 5 4.8

depth and reality?

6. Are the options of reasonable

range of variations?

4 5 5 4 5 4.6

7. Are the test items sufficiently

inclusive? Are full scope and

intent of the test items so

clearly indicated that the

test takers will not omit

parts of the options through

lack of certainty as to what

the test items desired.

4 5 4 5 5 4.6

Overall Mean 4.0 5.0 4.86 4.71 5.0 4.71

Sample Computation on the Validity of the

Two-Pronged Training Program

Criteria Validators Mean

A B C D E F

I. Face 4 5 5 4 4 3 4.17

II. Content

a.Functionality

5

5

5

5

4

3

4.50

b.Acceptability 5 5 5 5 4 3 4.50

c.Appropriateness 5 5 5 4 4 3 4.33

d.Timeliness 5 5 5 4 4 2 4.17

e.Implementability 4 4 5 4 4 2 3.83

f.Sustainability 4 4 4 5 4 2 3.83

Average 4.67 4.67 4.83 4.5 4.0 2.50 4.20

Overall Mean 4.34 4.83 4.92 4.25 4.0 2.78 4.19

MATHEMATICS COMPETENCE TEST

NAME:________________________________SCHOOL_______________:SCORE::______

INSTRUCTIONS: Select the letter of the correct answer. Write your answers on the space provided for.

CALCULATORS ARE NOT ALLOWED! (30)

_____1.Which axiom supports the idea that 2x +y = y +2x?

a. commutative b. associative c. inverse d. identity

_____2. Which of the following statements is always true?

a. The quotient of two numbers is not always an integer.

b. The quotient of two numbers is not always a fraction.

c. The quotient of two number is not always rational

d. All statements are true except a

e. Statements a, b and c are true.

_____3. San Fernando’s temperature, which is 40◦C, is how many ◦F?

a.104 b. 77 c. 400 d. 273.4

_____4. Len borrowed P10,000 at 10% simple interest. If she paid an interest and principal at the end of 18

mos., how much did she pay?

a.P11,550 b. P18000 c.P11500 d. P10010

_____5. From a 100cm x 100cm x 60cm block of marble, a pyramid with square base of 100cm and a

height of 60cm is carved. What is the volume of the marble carved in scientific notation?

a. 2x105 b. 4x104 c. 4x105 d. 5x102

_____6.If the sum of x and y is subtracted from the sum of their squares, the answer is N. What is the

relevant equation?

a. x+y- x2+y2 =N b.(x2+y2)-(x+y)=N c.(x+y)2 -(x+y)=N d. (x-y) + (x+y)2=N

_____7. Which of the following is not a polynomial?

a. 5x2 +2x -1 b. x3- 3.4x+7 c. 4

𝑥−2𝑥3−5 d.

𝑥2

2

_____8.Which of the following describes an identity equation?

a.4a-7=1 b. x= y+1 c.3(8-10)=-8+2 d. 4(7-2) =18

_____9. RJ and JR are traveling north in separate cars on the same highway. RJ is at 65kph and JR is at

70kph. RJ passes Dau Exit at 2:30p.m. JR passes the same exit at 2:45p.m. At what time will JR

catch up to RJ?

a. 3:25p.m. b.6:00p.m. c. 5:30 p.m. d. he can’t catch up

_____10. If 1

𝑢+

1

𝑣=

1

𝑓 then what is the formula for v?

a.v = u - 2f b. v= 𝑓𝑢

𝑢+1 c. v=

𝑓𝑢

𝑢−𝑓 d. v =

1

𝑢+

1

𝑓

_____11. What is the complete factored form of 𝑎3−𝑏3−𝑎2𝑏+𝑎𝑏2−𝑎+𝑏

2𝑎−2𝑏 ?

a. (a-b)(a2+b2-1) b. 𝑎2+𝑏2−1

2𝑎 c.

𝑎2+𝑏2+1

2 d. 2a2+2b2-2

_____12. Which of the following lines has an undefined slope?

a. Vertical b. horizontal c. skewed to the right d. skewed to the left

_____13. If three vertices of a parallelogram are A(2,0), B(4,4), C(6,0), find the vertex D if D is in the 4th

quadrant. a. (1,-1) b.(4,-4) c.(2,-4) d.(4,-1)

_____14.The line with equation 2y= - 4x +8 is perpendicular to a line whose one point is (2,-3). What is the

equation of the line?

a.y=𝑥−8

2 b. y=

𝑥+2

2 c. y = -2x +1 d. y= 2x+1

_____15. For how many different positive integers n is 0<10-√n<1?

a.19 b. 21 c. 23 d. 18

_____16. To solve x2 +8x =-5 by completing the square, what number must be added to both sides of the

equation?

a. 64 b. 8 c. -64 d. 16

_____17. What is the complete factored form of𝑥3−8

2𝑥2+4𝑥+8?

a. x-2 b. 𝑥−2

2 c. 2 (x-2) d. not factorable

_____18. For what values of k will kx2 +11x -2 =0 have unequal roots?

a.k >0 b. k> 1

4 c. k <

121

8 d.k >

−121

8

_____19. In the quadratic equation y= x2-8x +3, what is the minimum point?

a.(13,4) b.(-13,4) c.(4,-13) d.(-4,13)

_____20. For what values of x will 4𝑥2−9

𝑥4−5𝑥2+4 be meaningless?

a.±1,±2 b. ±1,±3 c.±1,0 d. 0

_____21. What is the simplified form of 2𝑦−14

𝑦2−2𝑦−35÷

6𝑦3

𝑦2−25?

a. 𝑦−5

3𝑦 b.

𝑦−5

3𝑦3 c. 𝑦+5

𝑦 d.

𝑦−5

𝑦

_____22.What is the value of (81/256)-3/4?

a. 64

27 b.

1

4 c.

24

5 d.

27

64

_____23.If 62(3x-2)=324, what is x?

a.4 b.3 c.1 d.0

_____24. If 𝑎

𝑏 : 𝑎𝑏

𝑏: 6

3:_______ a.

63

3 b.

18

3 c. 2 d.

18

3

_____25. If 𝑥3𝑦3 + 𝑥4𝑦63= 4𝑥𝑦, then xy3 is equal to? a.31 b.63 c.96 d.15

_____26. y varies directly with x such that and y =12 when x=4. What is the equation of variation?

a. xy=k b. y=-3x/12 c.4x=12y d. y=3x

_____27. The distance of a body falls from rest is directly proportional to the square of the time it falls. If an

object falls 256 feet in 4 seconds, how far will it fall in 8 seconds?

a.128ft b.1024ft c.64ft d. none among the options given

_____28. What is the general term for the sum of the first 100 whole numbers?

a. 𝑎𝑛 = 100(1 + 100) b. 𝑎𝑛 =99(0+99)

2 c. 𝑎𝑛 =

100(1+100)

2 d. 𝑎𝑛 =

100(0+99)

2

_____29.Find the 11th term of the sequence 25,50,75… a.250 b.200 c.275 d.300

_____30. Suppose a ball always rebounds 1/3 of the height from which it falls and the ball is dropped from a

height of 24 feet. What is the general tem of its sequence whose sequences are the heights from

which the ball falls? a.an = 24(1/3)n b. an = (8)n c. an = 24(1/3)n-1 d. an = 8n-1

_____31. Which of the following geometric statements is stated correctly?

a. A polygon is a plane figure formed by two or more non-collinear segments such that each

segment intersects exactly two others, one at each endpoint.

b. Among skew, perpendicular, parallel and intersecting lines, only skew lines are non-coplanar.

c. An angle is formed by rays that have a common endpoint.

d. A segment bisector is a ray that divides a segment into two congruent parts.

e. All statements are stated correctly.

_____32. E is the midpoint of segment FL. If FE = 4x2 –x +12 and EL = 3x2 +x +60, what are the possible

lengths of FL?

a. 260 and 162 b. 144 and 200 c. 520 and 364 d. 8 and -6

C D

A B

M

E

J

J

B

J

D

M

J

O

D

_____33. <a and <b are both right angles. Which can justify the conclusion that the two right angles, <a and

<b, are congruent?

a. Definition of right angles b. definition of congruent angles

b. Right angles theorem c. Transitive property of Equality

_____34.Which among these is a geometric corollary?

a. Law of Substitution b. Supplement Theorem

c. Supplement Postulate d. Definition of Linear Pair

_____35. Angles C and A are same-side interior angles. What type of angles are they if m<A=m<C?

a. right b. acute c. obtuse d. can’t be determined due to limited data

_____36. Which of the following is not a triangle congruence postulate?

a. SAS b.SSS c. AAA d. ASA

_____37.(Refer to the figure at the right) If M is the midpoint of AC and BD, which postulate

can be used to prove that the 2 ∆s are congruent?

a. SAS b. ASA c. AAS d. AAA

_____38. Which inequality describes an obtuse triangle?

a. c2 ≠ a2+b2 b. c2 > a2+b2 c. c2 < a2+b2 d. c 2≤ a2+b2

_____39. Which is correct for the angles of a rectangle and square?

a. Two consecutive angles are supplementary

b. Two nonconsecutive angles are congruent

c. One of the four angles is right.

d. all statements

_____40. The consecutive angles of a parallelogram are (3x +4) and (2x+6) degrees. What is the measure

of (3x+4)?

a. 10 b. 106 c.74 d. b or c

_____41. The diagonals of an isosceles trapezoid are denoted by 2x2+3 and x2+28. What is the length of

one diagonal? a.43 b. 53 c.5 d.106

For nos. 42-43, refer to circle E at the right.

_____42. What is the measure of <IEB if its 1/8 of a revolution?

a.45 b. 10 c. 170 d. 135

_____43. IF m<IEB=73, what is the measure of <IOB?

a.73 b. 143.5 c. 36.5 d. 287

_____44. What is the other endpoint of a segment with one endpoint at (3,-7) and the midpoint at (2,0)?

a. (1,7) b. (-4, 3)

c. (3, 4) d. (7,1)

_____45. The line through (-2,-1) with a slope of 3/8 also passes through the point (6,y) What is the

coordinate of y?

a. y=1 b. y = -1 C. y=2 d. y =-2

_____46. Which correspondence is a function?

a. One-to-one b. one-to-many c. many-to-one d. a and b e. a and c

_____47. If y = x/4, how many sixths of y does 1/12 of x represent?

a. 0 b.1 c.2 d.3

_____48. For what values of x is x2 + 5x -14 greater than 0?

a. x< -7; x >2 b. x> -7; x >2 c. x> 7; x >2 d. x> -7; x >-2

_____49. Which polynomial has the integral roots of -1/3 and 1 ± 2?

a. 3x3-5x2-5x-1=0 b. 3x3-5x2-5x+1=0

b. 3x3+5x2+5x-1=0 d. 3x3+5x2-5x+1=0

_____50. What is the domain of y = 3𝑥2 + 5 ?

a. x ≥ ±5/3 b. x ≥ ± 5/3 c. x ≥ -5/3 d. the set of reals (R)

_____51. If x = log8 87 then what is the value of x?

a. 1 b. 8 c. 7 d. 0

_____52. If x = eln5, then what is the value of x?

a. 0 b. e c. 1 d. 5

_____53. Which is a coterminal angle of -150 degrees?

a. 30 b. 210 c. 510 d.330

_____54. The second hand of a clock is 10.5cm. What is the linear speed of the tip of this second hand as it

passes around the clock face?

a. 2 cm/sec b. 3.3 cm/sec c.1.099cm/sec d. 1.315cm/sec

_____55. Which of the following is equal to ( 3/2, 1/2)?

a. [5∏/6, 17∏/6, 29∏/6, 41∏/6] b. [7∏/6, 19∏/6, 31∏/6, 43∏/6]

b. [11∏/6, 23∏/6, 35∏/6, 47∏/6] d. [∏/6, 13∏/6, 25∏/6, 37∏/6]

_____56. What is the solution of cos2 x+ sin x = 1; 0≤ x ≤∏/4?

a. ∏/2 b. 90 c. ∏/2, 7∏/6, 11∏/6 d. no solution

_____57. Two dice are tossed. How many possible outcomes are there?

a. 12 b. 24 c. 36 d. 42

_____58.In how many ways can 4 people be seated in a round table?

a.12 b. 6 c. 24 d. 30

_____59. Which of the following is equal to the median?

a. 5th decile b. 50th percentile c. 2nd quartile d. all

_____60.When gathering raw data using a 5-point Likert Scale, what is the appropriate statistical tool to be

used to determine the desired data necessary to interpret results?

a. Standard deviation b. Variation c. weighted Mean d. Frequency count

ANSWER KEY TO MATHEMATICS COMPETENCE TEST

ITEM

NO.

Answer ITEM

NO.

Answer

1 A 31 B

2 E 32 C

3 A 33 B

4 C 34 B

5 C 35 A

6 B 36 C

7 C 37 A

8 C 38 B

9 B 39 D

10 C 40 B

11 C 41 B

12 A 42 A

13 B 43 C

14 A 44 A

15 D 45 B

16 D 46 E

17 B 47 C

18 D 48 B

19 C 49 A

20 A 50 D

21 B 51 C

22 A 52 D

23 A 53 B

24 C 54 C

25 B 55 D

26 D 56 D

27 B 57 C

28 D 58 B

29 C 59 D

30 C 60 C

TEST SPECIFICATIONS FOR MATHEMATICS COMPETENCE TEST

AREA OF

MATHEMATICS

GRADING

PERIOD

CONTENT

STANDARDS

Knowledge Comprehension/

Analysis

Application Synthesis/

Evaluation

Pts

Total

Pts

%

Conceptual

Skills

Analytical/

Reasoning

Skills

Computational

Skills

Problem-

Solving

Skills

E

L

E

M

E

N

T

A

1ST

Real Number

System

#1 #2 2

3 1/3%

Measurements #3 #4 2 3 1/3%

Scientific

Notation

#5 1 1 2/3%

2ND

Algebraic

Expression

#7 #6 2 3 1/3%

First-degree

Equations

and

Inequalities in

One variable

#8 #9 2 3 1/3%

R

Y

A

L

G

E

B

R

A

3RD

Rational

Algebraic

Expressions

#10

#11

2 15 3 1/3%

Linear

Equations and

Inequalities in

Two Variables

#12 #13 2 3 1/3%

4TH

Systems of

Linear

Equations

and

Inequalities in

Two Variables

#15 #14 2 3 1/3%

I

N

T

E

1ST

Special

Products and

Factors

#16 #17 2

3 1/3%

Quadratic

Equations

#18 #19 2 3 1/3%

2ND Equations

Involving

Rational

#20 #21 2 3 1/3%

R

M

E

D

I

A

T

E

A

L

G

E

B

R

A

Expressions

15

Expressions

with Rational

Exponents

#22

#23

2 3 1/3%

3RD

Radical

Expressions

and Equations

#24 #25 2 3 1/3%

Variations #26 #27 2 3 1/3%

4TH

Sequences

and Series

#28 #29 #30 3 5 %

G

E

O

M

E

T

R

Y

1ST

Geometry of

Shape and

Size

#31 1

15

1 2/3%

Geometric

Relations

#32 1 1 2/3%

Writing Proofs #34 #33 2 3 1/3%

2ND

Perpendicular

Lines and

Parallel Lines

#35 1 1 2/3%

Triangle

Congruence

#36

#37 2 3 1/3%

Inequalities in

a Triangle

#38 1 1 2/3%

3RD

Quadrilaterals #39 1 1 2/3%

Similarity #40

#41

2 3 1/3%

4TH Circles #42 2 3 1/3%

#43

Plane

Coordinate

Geometry

#44

#45

2 3 1/3%

A

D

V

A

N

C

E

D

A

1ST

Relations and

Functions

#46 1

1 2/3%

Linear

Functions

#47 1 1 2/3%

Quadratic

Functions

#48 1 1 2/3%

2ND

Polynomial

Functions

#49

#50

2 3 1/3%

Exponential

and

Logarithmic

Functions

#51 #52 2 3 1/3%

3RD Circular #53 #54 2 3 1/3%

L

G

E

B

R

A

T

R

I

G

O

&

S

T

Functions

15 Trigonometric

Identities and

Equations

#55 #56 2 3 1/3%

4TH

Counting

Techniques

and Probability

#57

#58

2 3 1/3%

Measures of

Central

Tendency and

Variability

#59 #60 2 3 1/3%

A

T

TOTAL 14 16 16 14 60

PERCENTAGE 23 1/3 % 26 2/3 % 26 2/3% 23 1/3% 100%

Questionnaire

QUESTIONNAIRE FOR HEADS

(SAC/Dept. Head/Academic Coordinator/Principal)

SAINT LOUIS COLLEGE


GRADUATE SCHOOL

October 11, 2010

Highly Esteemed Educators,

The undersigned is a Master of Arts in Education Major in Mathematics

(MAEd-Math) student of Saint Louis College undertaking the study

entitled, ―Competence of Mathematics Teachers in the Private

Secondary Schools in San Fernando: Basis for a Two-Pronged

Training Program.‖ It is with this cause that your support is sincerely

solicited so that this study can be carried out and may greatly contribute

to the improvement of the teaching-learning process.

Please accomplish then this very objectively and accurately. It may

take much of your precious time but your responses will contribute

much to the success of this study. Please don‘t leave an item

unanswered. Rest assured that all information obtained herein will be

held strictly confidential. Your immediate attention to this request is

highly cherished.

Thank you so much!

Sincerely yours,

Mr. Feljone G. Ragma

Researcher

QUESTIONNAIRE FOR HEADS

COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN

SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED TRAINING PROGRAM

PART I. PROFILE OF THE HEADS

Directions: Please fill in the data needed by putting a check mark (√ ) in the option that corresponds to your

answers.

A. Name (Optional): _______________________________________________

B. Institution Connected with:

___BHC ___CICOSAT ___CKC ___DSHJ ___UCC

___FELKRIS ___GLC _ __ LUCI ___LUCNAS ___MBC

___NCST ___SLC ___SLSHS

PART II. LEVEL OF INSTRUCTIONAL COMPETENCY

Directions: Below are behaviors of an effective and efficient Mathematics Teacher. Please feel

free to rate your math teacher by checking the blank in the appropriate column using

the scale below:

Scale Equivalent Description

5 Outstanding (O) -refers to performance that is rarely equaled and with

numerical rating within 95-99

4 Very Satisfactory (VS) - refers to performance that clearly exceeds acceptable

standards and with numerical rating within 90-94

3 Satisfactory (S) - refers to performance that meets acceptable standards

and with numerical rating within 85-89

2 Fair (F) - refers to performance below acceptable standards and

with numerical rating within 80-84

1 Poor (P) - refers to performance that is unacceptable and with


D. Teaching / Facilitating Skills

5

4

3

2

1 7. Substantiality of Teaching

The teacher...

i. shows confidence and exhibits mastery of the subject matter

j. shows awareness of the developments of the subject matter as seen in the utilization of key concepts, relationships, and different perspectives related to the content area

k. aligns classroom instruction with national standards, school’s vision-mission and educational philosophy

l. focuses on and covers all important aspects of the subject matter

m. connects students’ prior knowledge, life experiences, and interests in the instructional process

n. provides values clarification and integration considering the applications of the subject area to the students’ practical life

o. engages students in in-depth and varied experiences that meet the diverse needs and promote holistic growth

p. relates ideas and information within and across content areas


The teacher …

e. makes abstract concepts clear for students’ understanding

f. asks students how they got a particular answer

g. encourages students to probe into reactions, answers and responses

h. uses knowledge of students’ development to make learning experiences meaningful and accessible for every student


The teacher …

d. leads students to ask or initiate thought-provoking questions

e. integrates and elaborates students’ questions and contributions into the class discussion

f. demonstrates flexibility and responsiveness in adjusting instruction to meet students’ needs, ideas and contributions


The teacher …

g. poses thought-provoking questions that promote high-order thinking skills

h. encourages students to explain ideas and ask questions about the content

i. provides time for student to think, ponder on and express response

j. poses follow-up questions to clarify initial question when a student is unable to respond effectively

k. emphasizes on essential ideas and problems

l. ensures that factual information and skills are applied to ideas and problems


The teacher uses teaching methods which are…

f. determined on behavioral objectives and appropriate to the content area

g. used in expressing ideas and problems (projects, themes, panel discussion, demonstration, etc)

h. emphasizing on and eliciting students’ inquiry

i. used to address individual differences and develop multiple intelligences

j. intended to engage students in learning and supportive of theories of collaborative and cooperative learning


The teacher uses…

f. computers for designing and printing instructional materials

g. the principles of computer-aided and computer-based instruction

h. multi-media resources, including technologies such as the internet, in the development and sequencing of instruction

i. computerized grading sheets (without received corrections)

j. overhead/LCD projector

E. Guidance Skills


The teacher …

f. arouses, maintains and sustains students’ interests

g. gives students recognition (praises and reinforcements)

h. regards students’ errors/mistakes as fruitful opportunities for learning

i. makes use of teaching as guide in helping students improve their work

j. communicates high and realistic expectations from students


The teacher ensures that…

f. activities are purposeful, relevant and experiential

g. students are developing increased self-reliance and responsibility

h. learning activities are appropriate for students’ developmental tasks

i. time allocation is flexible to allow continuity of productive activities

j. resources and facilities are appropriate for the learning activities

F. Management Skills

1. Atmosphere in the Classroom

The teacher …

i. creates and encourages positive social interaction, active engagement and self-regulation for every student

j. is enthusiastic and maintains a warm friendly atmosphere conducive to learning

k. establishes, communicates, models, and maintains standards of responsible student behavior

l. instills mutual respect, order and discipline

m. incorporates creative and constructive discipline techniques rather than coercive and restrictive discipline techniques

n. develops and implements classroom procedures and routines that support learning and enforce school policies among students

o. cultivates students’ deep sense of controlling for their direction

p. is organized, punctual and manages class time well ( accomplish the objectives and procedures set for the time period)


The teacher …

g. corrects test papers, quizzes, assignments/requirements carefully

h. returns corrected test papers, quizzes, requirements promptly

i. conducts efficiently quizzes/ examinations to avoid cheating

G. Evaluation Skills


The teacher is able to…

f. frame questions to find out students’ understanding

g. ask questions, integrated in varying techniques, that lead to the synthesis of the salient points of the lesson

h. prepare well-framed questions covering the subject matter taken in class

i. guide students in goal setting and assessing their own learning

j. provide students substantive, timely, and constructive feedback for specific area for improvement (write comments on paper/talk to students privately)


The teacher provides and considers…

f. varying authentic assessments to gauge the extent of authentic learning

g. assignment/ enrichment activities to supplement the day’s lesson and/or aligned to classroom instruction

h. subject requirements that are practical and challenging

i. adequate time for students to complete assignments/ requirements

j. availability of materials in giving assignments and subject requirements


The teacher …

e. observes the standard grading system of the school

f. grades/ scores students objectively and accurately

g. encourages students’ participation in creating rubrics

h. utilizes criteria/ rubrics in checking requirements

Questionnaire

QUESTIONNAIRE FOR MATHEMATICS TEACHERS

SAINT LOUIS COLLEGE


GRADUATE SCHOOL

October 11, 2010

Dear Fellow Math Teachers,













highly cherished.

Thank you so much!

Sincerely yours,


Researcher

QUESTIONNAIRE FOR MATHEMATICS TEACHERS



PART I. PROFILE OF THE TEACHER-RESPONDENTS


answers.

A. Name (Optional): _______________________________________________

B. Institution Connected with:


___FELKRIS ___GLC _ __LUCI ___LUCNAS ___MBC


C. Highest Educational Attainment

___ BSED/BSE/AB/BS graduate (Non-licensed)

___ BSED/BSE/AB/BS graduate (Licensed)

___ BSED/BSE/AB/BS graduate MS/MA units

___ MS/MA graduate

___ with EDd/PHd units

___ EDd/PHd graduate

D. Years of teaching mathematics

___0-5 years ___6-10 years ___11-15 years

___16-20 years ___21-25 years ___26 years and above

E. Mathematics seminars/trainings attended (last two years)

Name of Seminar School Local Regional National Internat’l

_____________________________ ___ ___ ___ ___ ___

_____________________________ ___ ___ ___ ___ ___

_____________________________ ___ ___ ___ ___ ___

_____________________________ ___ ___ ___ ___ ___



free to rate yourself by checking the blank in the appropriate column using the scale below:












A. Teaching / Facilitating Skills

5

4

3

2


I...










I…


b. ask students how they got a particular answer




I…





I…





e. emphasize on essential ideas and problems



I use teaching methods which are…



c. emphasizing on and eliciting students’ inquiry




I use…





e. overhead/LCD projector

B. Guidance Skills


I…

a. arouse, maintain and sustain students’ interests

b. give students recognition (praises and reinforcements)





I ensure that…


b. tudents are developing increased self-reliance and responsibility






I…




d. instill mutual respect, order and discipline






I…

a. correct test papers, quizzes, assignments/requirements carefully

b. return corrected test papers, quizzes, requirements promptly

c. conduct efficiently quizzes/ examinations to avoid cheating



I am able to…














I…


b. grade/ score students objectively and accurately


d. utilize criteria/ rubrics in checking requirements

Questionnaire

QUESTIONNAIRE FOR STUDENT-RESPONDENTS

SAINT LOUIS COLLEGE


GRADUATE SCHOOL

October 11, 2010

My Dearest students,













highly cherished.

Thank you so much!

Sincerely yours,


Researcher

QUESTIONNAIRE FOR STUDENT-RESPONDENTS



PART I. PROFILE OF THE STUDENT-RESPONDENTS


answers.

A. Name (Optional): _______________________________________________

B. School Connected with:


___FELKRIS ___GLC _ __LUCI ___LUCNAS ___MBC




free to rate your math teacher by checking the blank in the appropriate column using

the scale below:












A. Teaching / Facilitating Skills

5

4

3

2


The teacher...

a. knows very well his lesson

b. is updated with his subject

c. connects teaching to school’s vision-mission, philosophy and national goals

d. teaches all important areas of the subject matter

e. connects students’ knowledge, life experiences, and interests to the lesson

f. gives values integration practical to life

g. gives students different activities (puzzles, games, recitation)

h. connects the lesson to other lessons and subjects (ie. English, Science,AP)


The teacher …

a. makes math concepts clear

b. asks students how they got an answer

c. asks students to agree or disagree with presented answers

d. makes his teaching understandable to all (teacher simplifies lessons)


The teacher …

a. pushes students to raise very good questions

b. includes students’ questions into the discussion

c. fits lessons to students’ level


The teacher …

a. asks questions that make students think deeply

b. lets students explain answers

c. allows students to think and react

d. rewords questions when a student is unable to answer

e. emphasizes important ideas (formulas, techniques etc.)

f. makes sure that concepts and skills are learned


The teacher uses teaching methods which are…

a. applicable to the subject

b. used in explaining ideas and problems

c. allowing students to investigate and examine

d. appropriate to every student in the class (no one is left behind)

e. intended to keep students learning


The teacher uses…

a. computers for making and printing materials for teaching

b. computers in teaching

c. the internet in teaching

d. computerized grading sheets (without mistakes)

e. overhead/LCD projector

B. Guidance Skills


The teacher …

a. awakens, keeps and sustains students’ interests (students are not bored)

b. appreciates students’ correct response (says very good, thank you)

c. doesn’t get angry when a student commits mistakes

d. helps students improve their work

e. talks of high but practical expectations from students


The teacher ensures that…

a. activities are practical, focused and applicable

b. students are developing independence and responsibility

c. activities are appropriate for students (not too hard but not too easy)

d. time is flexible for students’ activities

e. materials and facilities are proper for learning


1. Atmosphere in the Classroom

The teacher …

a. leads students to correct their misbehavior

b. maintains a friendly classroom environment (students don’t fear the teacher)

c. shows good behavior

d. encourages respect, order and discipline

e. uses positive discipline procedures

f. implements school policies among students

g. develops students’ sense of control

h. is organized, punctual and manages class time well


The teacher …

a. checks test papers, quizzes, assignments/requirements carefully

b. returns corrected test papers, quizzes, requirements on time

c. conducts efficiently quizzes/ examinations to avoid cheating



The teacher is able to…

a. ask questions to find out students’ understanding

b. ask questions that lead to the important points of the lesson

c. prepare very good questions covering the lessons taken in class

d. guide students in evaluating their own learning (helps a student if he needs improvements or not)

e. provide feedback for specific area for improvement (write comments on paper/talk to students privately)


The teacher provides and considers…

a. different activities and ways to measure the amount of learning

b. assignment/ enrichment activities that support learning





The teacher …

a. uses the standard grading system of the school

b. grades/ scores students with accuracy and fairness

c. encourages students’ participation in creating rubrics

d. utilizes criteria/ rubrics in checking requirements

QUESTIONNAIRE FOR VALIDATION ON THE INSTRUCTIONAL COMPETENCE CHECKLIST

NAME:_____________________POSITION:___________________DATE:______

Purpose: To validate questionnaire on instructional competence for

Secondary Mathematics Teachers in the City Division of San Fernando

Direction: Please put a check (√) in the box that corresponds to your

judgment on validity of the instructional competence questionnaire for the secondary mathematics teachers.

1-poor 2-slight 3-moderate 4-high 5-very high

CRITERIA 5 4 3 2 1

Other comments:

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

1.Every sentence is easily understood

2.The sentences are grammatically correct

3.There are no errors in sentence construction

4.The directions are clear and easy to follow

5.The headings/titles of the different items are

Appropriate

6.The scales are suited to what they are supposed to

Measure

7.The questionnaires are representation of what they are

to measure

QUESTIONNAIRE TO ESTABLISH CONTENT VALIDITY

OF THE MATHEMATICS COMPETENCE TEST

NAME:________________________________POSITION:__________________

EDUCATIONAL ATTAINMENT:_____________________________________

YEARS IN TEACHING MATHEMATICS:_____________________________

DIRECTION: Please place a check (√) on the appropriate point value to

evaluate the extent of content validity of the test indicate by the factors

below:


Criteria 5 4 3 2 1

1. Are the items representative of the concepts being

measured?

2. Are the questions free from grammatical error?

3. Are the items perfectly clear and unambiguous? Is the

general frame and reference from which these are

asked, and from which the answers should be given

clear?

4. Are the test items stable, relatively deep-seated, well-

considered, non-superficial, non-ephemeral, but

something which is typical of the subject area?

5. Do the test item pull? That is, can these be responded

to by a large enough proportion of examinees to permit

validity? Are the test items engaging enough to get

response with some depth and reality?

6. Are the options of reasonable range of variations?

7. Are the test items sufficiently inclusive? Are full scope

and intent of the test items so clearly indicated that

the test takers will not omit parts of the options

through lack of certainty as to what the test items

desired.

Other Comments

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

Lifted from the study of Dr. Ramos (2009) on Mathematics Education.

QUESTIONNAIRE TO ESTABLISH THE VALIDITY

OF THE TWO-PRONGED TRAINING PROGRAM

NAME:________________________________POSITION:__________________

EDUCATIONAL ATTAINMENT:_____________________________________

DIRECTION: Please place a check (√) on the appropriate point value to

evaluate the extent of validity of the two-pronged training program as

indicated by the factors below:


Criteria 5 4 3 2 1

I. Face

II. Content a. Functionality

b. Acceptability

c. Appropriateness

d. Timeliness

e. Implementability

f. Sustainability

Other Comments

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

CURRICULUM VITAE

PERSONAL DATA

Name: Feljone Galima Ragma

Date of Birth: July 31, 1986

Place of Birth: San Isidro, Candon City, Ilocos Sur

Home Address: San Isidro, Candon City, Ilocos Sur

e-mail Address: [email protected]

Civil status: single

EDUCATIONAL ATTAINMENT

Pre-Elementary: UCCP Candon City, Ilocos Sur Graduated 1991

With honors Elementary: Candon South Central School

Candon City, Ilocos Sur Graduated 1997 With honors

Secondary: Santa Lucia Academy Santa Lucia, Ilocos Sur Graduated 2003

With honors Tertiary: Saint Louis College

San Fernando City, La Union Graduated 2007

Bachelor in Secondary Education Cum Laude Major in Mathematics

Recognition Award

Graduate Studies: Saint Louis College San Fernando City, La Union Graduated 2011

Master of Arts in Education Cum Laude Major in Mathematics Best in Research

mailto:[email protected]

BOARD EXAMINATION/ CIVIL SERVICE ELIGIBILITY

Licensure Examination for teachers (LET) 2007

P.D. 907 Civil Service Eligible

WORK EXPERIENCE. POSITIONS/SPECIAL ASSIGNMENTS

Saint Christopher Academy Bangar, La Union

Classroom Teacher, 2007-2008

Christ the King College San Fernando City, La Union

Classroom Teacher, 2008- present Subject Area Coordinator, 2010- present

TRAININGS/SEMINAR-WORKSHOPS FACILITATED

Problem-Solving Techniques in Secondary Mathematics Association of Private Schools

City of San Fernando, La Union July, 2010

Seminar-Workshop on Creating Gradebooks through MS EXCEL Christ the King College

City of San Fernando, La Union 2009

Seminar-Workshop on Creating Interactive Slides through MS PowerPoint

Christ the King College City of San Fernando, La Union 2009

Seminar-Workshop on Campus Journalism Saint Christopher Academy

Bangar, La Union 2008

How to Love and Like Math

Saint Louis College City of San Fernando, La Union

2007 CONFERENCES/ SEMINARS PARTICIPATED

Moving Forward with Backward Design: A Deeper look at UBD Saint Louis University Laboratory Elementary School

January, 2011

Understanding and Planning for the 2010 SEC for Mathematics Phoenix Hall, Quezon City November, 2010

Training Program for Mathematics Teachers

University of the Cordilleras September, 2010

Seminar on Yoga and Relaxation Christ the King College August, 2010

Critical Questions to Elicit Critical Thinking

Christ the King College July, 2010

Seminar-Workshop on Homeroom Guidance and Counseling Techniques Christ the King College June, 2010

Utilizing and Interpreting CEM Test Data

University of Baguio May, 2010

In-Service Training and Workshop on Curriculum Programs and Teaching Strategies

Christ the King College November, 2009

Seminar on Innovations in Teaching and Learning Approaches Christ the King College

July, 2009

Understanding and Planning for the SEC Phoenix Hall, Pangasinan

September, 2009 First Aid Program for Teachers

Christ the King College June, 2008

PROFESSIONAL ORGANIZATION/ GROUPS

Professional Teachers‘ Organization Mathematics Teachers‘ Association in Region I (MATARI)