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PERCEPTIONS OF TEACHERS ON THE USE OF HISTORY

IN TEACHING MATHEMATICS

Engr. Maria Cristina Agustin-Sicat Holy Angel University

Angeles City, Pampanga, Phils.

mcsicat@hau.edu.ph

Ms. Angela Faith B. Daguman Ateneo de Manila High School

Quezon City, Philippines

f8bd@yahoo.com

Ms. Ivy Gay O. Salvador

Pampanga State Agricultural University

Magalang, Pampanga, Phils.

Io_hea@yahoo.com.ph

ABSTRACT In this study, the researchers sought to investigate the perceptions of teachers on the use and the extent of utilization of mathematics history in teaching mathematics. A total of 72 teachers across the three levels-primary, secondary, and tertiary, from both public and private schools participated in the study. It was found out that there was no significant difference in the perceptions on the use of history of teachers across level but there was a significant difference in the perceptions of teachers depending on whether they came from a private or public school. In terms of the extent of use, teachers, regardless of the level and type of school in which they came from, sometimes use teaching methods which incorporate the history of mathematics.

Categories and Subject Descriptors: A.1 Introductory and Survey

General Terms: Documentation, Human Factors, Management

Keywords: History of mathematics, mathematics education, perceptions of teachers, teaching methods

1. INTRODUCTION History of mathematics has always been a special

branch of mathematics that actually all those concerned with the process of learning and teaching mathematics demonstrated their interest to. That interest was from primary school students to outstanding mathematicians, according to their level of understanding. The same situation remains nowadays. Lectures and seminars in

which mathematical discoveries, even local and insignificant, could be traced with analysis of historical information about them, provide for students better understanding different ideas and theories, motivation for further learning, and show brilliant richness of human activities in mathematics. It is therefore fitting on us, educators, to keep the narrative alive and never let the history of mathematics becomes just a myth of antiquity and, thereby, help perpetrate its fall into disuse.

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The role of using the history of mathematics in

the teaching and learning of mathematics is a major area of research which has made important contributions to the field of mathematics education (Fauvel & Maanen, 2000). For example, the use of the history of mathematics in instruction provides opportunities for students to deepen their mathematical understanding and can help students gain a better understanding of the meaning of mathematical concepts, methods, theories, and proofs (Tzanakis & Arcavi, 2000). In most institutions of higher education, mathematics is taught as an abstract science without much attention given to teaching what mathematics is about and how mathematical ideas developed. In order to bridge this gap, the history of mathematics can serve as a major pedagogical tool for the teaching of higher mathematics. Concerning the use of the history of mathematics as a pedagogical tool, there exists a plethora of classroom resources for teachers (Swetz, Fauvel, Bekken, Johansson, & Katz, 1995). However, there is currently a limited amount of research focused on how the historical development of mathematics contributes to students’ growth of mathematical understanding.

The virtues of incorporating history into mathematics education have received considerable attention and have been discussed for decades. Nevertheless, before taking as viewpoint that history must be integrated in mathematics, an obvious question is, “why should the history of mathematics have a place in mathematics education?” Addressing this question is difficult, since the answer is subject to one’s personal definition of teaching and is also bound up with one’s perspective of mathematics.

It is in this regard that the researchers embarked in a study aiming to find out the extent of utilization of the history of mathematics in teaching mathematics. Particularly, the research task attempted to pinpoint worthwhile considerations to help teachers from primary

to tertiary level, in both public and private schools, to think about what history can really do for the curriculum and for their teaching.

Statement of the Problem

This research was designed to determine the different perceptions of teachers on the use of history in mathematics education. Specifically, it focused on the viewpoint of mathematics teachers, from primary to tertiary levels, in both public and private schools regarding the extent of utilization of the history of mathematics in teaching mathematics.

Thus, the research aimed to look into the following questions: 1. How did teachers perceive the meaning of the

following: a. History b. Mathematics

2. To what extent did teachers make use of history in teaching mathematics?

3. How did teachers perceive the use of history in teaching mathematics?

4. Is there a significant difference on the perceptions of teachers in utilizing history in teaching mathematics across levels?

5. Is there a significant difference between the perceptions of teachers in the public and private schools regarding the use of history in teaching mathematics?

6. Is there an interaction effect between the type of school and the different educational levels?

Significance of the Study

The result of this study will be useful to the following:

The Curriculum Experts. This will provide empirical data which will be utilized in curriculum planning as well as in the development of lessons that match the desired teaching strategy to make teaching-learning more effective and meaningful. Results of the study can serve as bases for redesigning the curriculum and can be used in short and long term plans in education.

The School Administrators. The findings of the study may serve as the baseline empirical data for planning quality education that will satisfactorily meet the program of activities in mathematics and other

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developmental needs of students related to mathematics instruction and in recommending to evolve innovations for a mathematics curriculum, if necessary. In their capacity as administrators, they can promote the results of this study and encourage teachers from other subject areas to also test similar techniques in their fields of specialization.

The Teachers. This study can be utilized to help teachers modify their teaching practices not only to improve students’ mathematics achievement but also to facilitate the appreciation of history in teaching mathematics. This will also serve as a guide in developing other lessons with the integration of history in them. They can then attend to the broader spectrum of individual needs of each student, thereby enabling them to think of some other ways to improve their teaching skills.

The Students. The lessons will definitely arouse student’s motivation for further inquiry and investigation. This will challenge them to engage in meaningful learning that could be a transformative experience and will, somehow, enable them to improve their achievement in mathematics.

Scope and Delimitation of the Study

Research participants were teachers from primary to tertiary levels, in both public and private schools where the researchers are currently connected with. It cannot be interpreted as extending to other populations. This necessitates the researchers to make use of purposeful sampling technique in selecting their respondents.

.

2. REVIEW OF RELATED LITERATURE The history of mathematics and its implications in

mathematics education had been studied by different kinds of researchers (historians, mathematicians and educators) from different dimensions. The following are results from some of these studies.

Lahoylahoy (2003) looked into the relative effects of integrating history of mathematics in the teaching of algebra and trigonometry on the cognitive and affective learning. In the study both qualitative and quantitative method of collecting data were employed. The quantitative data gathered from the experimental method that was implemented indicated that integration of history had no effect on the cognitive learning of the students but it had a positive effect on their affective learning. On the

other hand, the qualitative data gathered from classroom observations, journals of students and interviews indicated effectiveness of the integration of mathematics history in both the cognitive and affective aspects.

Farmaki and Paschos (2007) conducted a study employing an experimental design on the use of genetic ‘moments’ in the history of mathematics in the classroom. They developed self-contained courses on the topic linear motion using an approach that takes into account the historical origins of the concept under consideration and administered them to fifteen year-old students. Although, the use of mathematics history was not the main flavor of the courses they developed, they concluded that history of mathematics can inspire a chain of teaching activities that will lead to the attainment of the goals of mathematics education.

Katz (2007) zoomed in on the history of algebra and reflected on the role of this history in the teaching of algebra in the secondary or university level. A widely accepted summary of the development of the history of algebra is its progress into three stages of expressing algebraic ideas: the rhetorical stage, the syncopated stage and the symbolic stage. Katz offered an alternative view of the development of algebra as a four-stage conceptual development: geometric stage, static equation-solving stage, dynamic function stage and abstract stage. He discussed important development in the history of algebra in the context of these four stages and their use in the teaching of algebra and concluded that attention to the history of algebra can be a valuable guide in the teaching and learning of algebra.

Otte (2007), believing in the important roles of mathematical history and philosophy of mathematics within the educational context, offered some methodological reflections on them. Case studies from nineteenth century history of arithmetic and integration theory were considered from which he concluded that some mathematical ideas that may first appear abstract can become comprehensible if viewed from their historical angle. Fried (2007) changed his original belief of the separation between mathematics and history of mathematics. He now maintains the position that the historian’s and the mathematician’s way of knowing are complementary and thus accepts the essential role of the history of mathematics in mathematics education. An important discussion in his article is a comparison between a historical and non-historical view of mathematics which

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he later exemplifies using a particular case of teaching and looking at the topic “Conics” in analytic geometry using these two points of view.

Some studies provided a survey of the myriad literatures on history of mathematics in mathematics education and proposed a way of categorizing these literatures. Examples are the papers by Jankvist (2009) and Gulikers and Blom(2001).

Jankvist proposed a way of organizing and structuring the discussion of the “whys” and the “hows” of using history of mathematics In particular, he suggested two sets of categories, one for the “whys” and another one for the “hows”. He proposed dividing the “whys” or the arguments for using history of mathematics into the two groups: history-as-a- tool and history-as-a-goal. On the other hand, he recommended categorizing the “hows” or the different techniques of using history of mathematics into the three groups: the illuminations, the modules and the history based. He then exemplifies these categorizations using the results from a number of study and papers on the use of history of mathematics in mathematics education. He also discussed the interrelationships between these categories and discussed criticism on the different “whys” and “hows” of using history of mathematics in the classroom in the context of these categorizations. Similarly, Gulikers and Blom presented a survey of literature on the use and value of the history of geometry in mathematics education and offered a way of categorizing the arguments they were able to collect as conceptual, cultural and motivational. They also provided details and contents of the article surveyed for further studies of those interested to pursue the topic history of geometry in mathematics education. Some studies looked into the history of mathematics in relation to the development of teacher education programs. One is Furinghetti (2007) who conducted a study to determine the affect of history in the construction of lesson plans by prospective teachers. He found out that history affected their output in two ways. Some of the outputs considered looking at the evolution of a given concept through the centuries. Other outputs considered recovering the cognitive roots of a given concept.

The study by Charalambos et. al. (2009) on the effects of using history of mathematics to influence the beliefs and attitudes towards mathematics of prospective teachers traced through questionnaires that were

administered four times, the beliefs and attitudes of preservice teachers over a period of two years. The analysis of the data collected indicated changes in some dimensions of the preservice teacher’s beliefs and attitudes. From their analysis, they offered implications for the design of teacher education programs that take into account history of mathematics. These are just a few of the results related to history of mathematics in mathematics education and most of them indicated agreement on the positive effect of history of mathematics. But this is not the real picture for there are also a number of criticisms on the use of history of mathematics in mathematics education. In fact, Jankvist (2009) discusses some of these criticisms. Unfortunately, we, the authors of this study, were not able to get hold of actual studies criticizing the use of history of mathematics in teaching for review. Nonetheless, these criticisms exist and are indications that the research of applying history of mathematics in teaching can still be enriched.

3. METHODOLOGY This chapter presents the research design,

respondents of the study, local of the study, research instruments, data gathering procedures, and the statistical tools employed.

Research Design

The descriptive survey method was used in this study in identifying the profile of the teacher-respondents as well as in the determining the extent of utilization of the history of mathematics in the mathematics teachings of primary, secondary, and tertiary teachers.

Respondents of the Study

Research participants were teachers from primary secondary and tertiary levels, in both public and private schools where the researchers were connected with at the time this study was conducted. Table 1 presents the distribution of the respondents according to level and type of school. As seen from the table, most of the respondents except in the secondary levels are from private schools. The secondary level also got the highest number of respondents.

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Table 1 Distribution of Respondents According to Level and Type

of School

Level

Type of School

Total Percentag

e Private Public

F % F %

Primary 11 100 0 0 11 15.3

Secondary

11 35.5

20 64.5

31 43.0

Tertiary 20 66.7

10 33.3

30 41.7

Total 42 58.3

30 41.7

72 100

Legend: F – Frequency % - Percentage

Research Instrument

The researchers utilized a self-made questionnaire to answer the objectives of the study. Part A in the questionnaire asked the respondents five words they can associate with the word “history” while part B asked them to write five words they can associate with the word “mathematics”. The questionnaire used a 3-point scale for part C to determine the extent of use of the teachers on teaching methods involving history of mathematics. The respondents rated the given 11 items as always, sometimes, or never used in their mathematics teachings. In part D, the researchers used a 4-point scale to measure if the respondents strongly disagree, disagree, agree, or strongly agree on the given 16 statements regarding the use of history in teaching mathematics. There were 8 positive (3, 5, 8, 10, 13, 14, 15, and 16) and 8 negative (1, 2, 4, 6, 7, 9, 11, and 12) statements.

Data Gathering Procedure and Analysis

The questionnaires were administered personally to the respondents. The data gathered were arranged, tabulated, and analyzed. To address the objectives of the study, frequency count, mean, rank and percentage were used.

To interpret the answers of the respondents on their extent of use on the given teaching methods in the

questionnaire, the following numerical ratings with their descriptive ratings were employed.

Numerical Rating Descriptive Rating

2 Always

1 Sometimes

0 Never

To interpret the mean scores, the following numerical ratings with their verbal interpretations were used.

Numerical Rating Verbal Interpretation

1.50 – 2.00 Always

0.50 – 1.49 Sometimes

0 – 0.49 Never

To interpret the answers of the respondents on their perceptions on the use of history in teaching mathematics, the following numerical ratings with their verbal interpretations were used for both positive and negative statements.

Numerical Rating Descriptive Rating 4 Strongly Agree 3 Agree 2 Disagree 1 Strongly Disagree

To interpret the mean scores, the following numerical ratings with their verbal interpretations were used.

Numerical Rating Verbal Interpretation

3.50 – 4.0 Strongly Agree

2.50 – 3.49 Agree

1.50 – 2.49 Disagree

1 – 1.49 Strongly Disagree

Factor analysis was employed to reduce the vast number of variables used in the instrument for determining the extent of use of history in teaching

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mathematics to a meaningful, interpretable, and manageable set of factors. This enabled the researchers to identify relevant constructs in the instrument based on the obtained information from the respondents. The analysis involved two stages: factor extraction and rotation. Moreover, the Multivariate Tests were run to determine if there exists a significant difference on the perceptions of the respondents on the use of history in teaching mathematics across levels, and between the perceptions of these teachers in the public and private schools.

SPSS 16.0 Statistical Software and Microsoft Excel were utilized in all the computations and processing of data.

4. RESULTS AND DISCUSSIONS

Perceptions of Teachers on the Meaning of History and Mathematics

When teachers were asked on what words they can associate with the meaning of history, most common words listed were “past”, “events”, “origin”, “dates”, “background”, and “record”. When asked on the words they associate with the meaning of mathematics, most of them wrote “numbers”, “problem solving”, “operation”, “symbols”, “analysis”, and “variables”.

Extent of Use of History in Teaching Mathematics

Teacher respondents rated the listed methods in the questionnaire as to “always”, “sometimes”, or “never” used in teaching mathematics. Their responses are summarized in tables 2 and 3.

As seen in tables 2 and 3, most of the methods which incorporate the use of history in teaching mathematics are “sometimes” used by teachers regardless of the level and type of school they are teaching. Among all methods, “internet resources” obtained the highest mean score, followed by “experimental mathematical activities”. “Role playing” and “worksheets involving history of concepts” got the lowest mean scores among the given methods.

Table 2 Extent of Use of History in Teaching Mathematics of

Teachers from Different Levels

Method

Level Grand

Mean

DR

R

Primary

Secondary

Tertiary

1. Historical snippets or anecdotes

0.82

S 0.84

S 1.03

S 0.92

S 5

2. Student’s research project based on history texts

0.36

N 0.87

S 0.90

S 0.81

S 7.5

3.Worksheets involving history of concepts

0.82

S 0.74

S 0.59

S 0.69

S 10.5

4. Historical packages on math

0.45

N 0.87

S 0.87

S 0.81

S 7.5

5. Taking advantage of errors or alternative concepts

1.09

S 0.93

S 1.23

S 1.08

S 3

6. Historical problems

1.27

S 0.90

S 0.90

S 0.96

S 4

7. Mechanical instruments or ancient instruments of calculation and measurement

0.91

S 0.90

S 0.83

S 0.88

S 6

8. Experimental mathematical activities

1.27

S 1.03

S 1.30

S 1.18

S 2

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9. Role playing

1.45

S 0.65

S 0.47

N 0.69

S 10.5

10. Films and other visual means showing the history of mathematics

0.82

S 0.71

S 0.70

S 0.72

S 9

11. Internet resources

1.27

S 1.19

S 1.47

S 1.32

S 1

Legend: A – Always N – Never R - rank S – Sometimes DR – Descriptive Rating

It is shown in table 2 that teachers in the primary level never used student’s research project based on history text and historical packages on mathematics in teaching. Meanwhile, in this level, “role playing” obtained the highest mean score among all the methods listed. However this method obtained the lowest mean score in the secondary and tertiary level. It can also be seen in the table that it is “never” used by teachers in the tertiary level. “Internet resources”, on the other hand obtained the highest mean score in both secondary and tertiary level.

Table 3

Extent of Use of History in Teaching Mathematics of Public and Private School Teachers

Method

Type of School Grand

Mean

DR R Public Private

Score DR Score

DR

1. Historical snippets or anecdotes

0.93 S 0.90

S 0.92 S 5

2. Student’s research project based on history texts

0.79 S 0.83

S 0.81 S 7.5

3.Worksheets involving history of concepts

0.79 S 0.55

S 0.69 S 10.5

4. Historical packages in math

0.76 S 0.87

S 0.81 S 7.5

5. Taking advantage of errors or alternative concepts

1.17 S 0.97

S 1.08 S 3

6. Historical problems

1.07 S 0.80

S 0.96 S 4

7. Mechanical instruments or ancient instruments of calculation and measurement

0.88 S 0.87

S 0.88 S 6

8. Experimental mathematical activities

1.24 S 1.10

S 1.18 S 2

9. Role playing

0.79 S 0.57

S 0.69 S 10.5

10. Films and other visual means showing the history of mathematics

0.81 S 0.60

S 0.72 S 9

11. Internet resources

1.26 S 1.40

S 1.32 S 1

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Legend:S A – Always N – Never R - rank S – Sometimes DR – Descriptive Rating

Table 3 also shows that “internet resources” obtained the highest mean score from teachers both in the private and public schools. “Historical packages in math” and “worksheets involving history of concepts” obtained the lowest mean scores from the teachers in the public and private schools respectively.

Perceptions of Teachers on the Use of History in Teaching Mathematics

Tables 4 and 5 show how teacher-respondents perceive the use of history in teaching mathematics. In table 4, teachers’ perceptions are compared according to the education level they are teaching while in table 5, comparison of perceptions was based on the type of school.

It can be seen in table 4 that teachers in different levels almost have the same perceptions on the use of history in teaching mathematics except in statement 3. Teachers in the primary and secondary levels believe that “teachers have sufficient time to include history in teaching mathematics”, while teachers in the tertiary level do not agree in this statement. In table 5, it can also be seen that it is only in statement 3 that teachers in the private and public schools differ in their perceptions. Teachers from private schools agree that “teachers have sufficient time to include history in teaching mathematics, while teachers from public schools disagree in this statement. Meanwhile, teachers in general agree on the positive effect of incorporating history in teaching and learning of mathematics and disagree on the negative statements. Statements which obtain the highest mean scores were “History in mathematics class can increase teachers’ and students’ appreciation of the evolution mathematics” and “History can help learning mathematics.” Statements which obtained the lowest mean score is “History is not mathematics” followed by the statement “History is tortuous and confusing rather than enlightening.”

However, despite the belief that incorporating history has a positive effect in teaching mathematics, teachers also believe that they “lack training and expertise in using history of mathematics as well as historical resources and appropriate assessment rubrics in mathematics involving history”. They all believe that “chief emphasis should be on equipping students with routine skills rather than on historical context of mathematics”. Some of the unedited comments of the teachers are the following:

History can be a helpful tool in injecting this “real life situations” but not the sole key in making pupils learn Math concepts. It may only be one of the various ingredients in making Math concepts tastier to children.

The utilization of the history of math in teaching math is not sufficient enough to improve Mathematics education.

This could be an avenue for other strategies like role playing, puppet show, among others. However, discussion of history is sometimes pretty boring especially when the class is used to problem solving.

Most students are not aware about the history of mathematics.

Sometimes, it would be better if the roots of a certain tree are being appreciated first before its fully grown leaves and fruits. History is more on appreciation.

DepEd should give teachers seminars/trainings on how to include Mathematics history in their teachings.

Mathematics has a very rich history. It is just waiting for us to learn from it.

For college students majoring in mathematics, a Mathematics history subject can be part of the curriculum but for high school students, the teacher should have a creative way of injecting it so that students would not find that boring.

Curriculum planners should include the subject “History of Mathematics” in the undergraduate course of BSE Math.

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Table 4 Perceptions of Teachers from Different Levels on the Use of History in Teaching Mathematics

Statement

Level Grand

Mean

DR

Primary Secondary

Tertiary

1. Teachers lack training and expertise in using history of mathematics. 2.73 A 2.97

A 2.93

A 2.92

A

2. Teachers lack historical resources. 3.00 A 2.74

A 2.87

A 2.83

A

3. Teachers have sufficient time to include history in teaching mathematics.

2.73 A 2.61

A 2.33

DA

2.51

A

4. History is not mathematics. 2.00 DA

1.94

DA

2.17

DA

2.04

DA

5. Using historical projects in mathematics class increase my knowledge of mathematics.

3.18 A 2.93

A 3.00

A 3.00

A

6. History is tortuous and confusing rather than enlightening. 2.09 DA

2.10

DA

2.00

DA

2.06

DA

7. It is hard to make any connection of history with the present day context and present topics in mathematics.

2.18 DA

2.47

DA

1.97

DA

2.21

DA

8. Historical projects in mathematics class increase teachers’ and students’ knowledge of different ways of thinking.

2.91 A 3.10

A 3.21

A 3.11

A

9. Involving history in mathematics is only time consuming and inappropriate for most topics in mathematics.

2.18 DA

2.29

DA

2.07

DA

2.18

DA

10. History in mathematics class can increase teachers’ and students’ appreciation of the evolution mathematics

3.18 A 3.17

A 3.21

A 3.19

A

11. Chief emphasis should be on equipping students with routine skills rather than on historical context of mathematics.

2.55 A 2.81

A 2.50

A 2.64

A

12. Teachers lack appropriate assessment rubrics in mathematics involving history.

2.91 A 3.00

A 2.76

A 2.89

A

13. Using history in mathematics can develop students’ creativity and critical thinking.

3.00 A 3.00

A 3.07

A 3.03

A

14. Using historical projects in mathematics class can make me a more versatile teacher.

3.18 A 2.90

A 3.07

A 3.01

A

15. History can help learning mathematics. 3.27 A 3.13

A 3.23

A 3.19

A

16. Using historical projects in mathematics class can make me a more effective teacher.

2.91 A 2.84

A 3.07

A 2.94

A

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Legend: SA – Strongly Agree D – Disagree DR – Descriptive Rating A - Agree SD – Strongly Disagree

Table 5

Perceptions of Public and Private School Teachers on the Use of History in Teaching Mathematics

Statement

Type of School Grand Mean

DR

Public Private

Score

DR Scor

e DR

1. Teachers lack training and expertise in using history of mathematics.

2.79

A 3.10 A 2.92

A

2. Teachers lack historical resources.

2.88

A 2.77 A 2.83

A

3. Teachers have sufficient time to include history in teaching mathematics.

2.62

A 2.37 DA

2.51

A

4. History is not mathematics.

2.17

DA

1.87 DA

2.04

DA

5. Using historical projects in mathematics class increase my knowledge of mathematics.

2.98

A 3.03 A 3.00

A

6. History is tortuous and confusing rather than enlightening.

2.10

DA

2.00 DA

2.06

DA

7. It is hard to make any connection of history with the present day context and present topics in mathematics.

2.12

DA

2.36 DA

2.21

DA

8. Historical projects in mathematics class increase teachers’ and students’ knowledge of different ways of thinking.

3.00

A 3.27 A 3.11

A

9. Involving history in mathematics is only time consuming and inappropriate for most topics in mathematics.

2.12

DA

2.27 DA

2.18

DA

10. History in mathematics class can increase teachers’ and students’ appreciation of the evolution mathematics.

3.12

A 3.29 A 3.19

A

11. Chief emphasis should be on equipping students with routine skills rather than on historical context of mathematics.

2.52

A 2.80 A 2.64

A

12. Teachers lack appropriate assessment rubrics in mathematics involving history.

2.88

A 2.90 A 2.89

A

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13. Using history in mathematics can develop students’ creativity and critical thinking.

3.00

A 3.07 A 3.03

A

14. Using historical projects in mathematics class can make me a more versatile teacher.

3.05

A 2.97 A 3.01

A

15. History can help learning mathematics.

3.12

A 3.30 A 3.19

A

16. Using historical projects in mathematics class can make me a more effective teacher.

3.00

A 2.87 A 2.94

A

Legend: SA – Strongly Agree D – Disagree DR – Descriptive Rating A - Agree SD – Strongly Disagree

The sixteen (16) items pertaining to the perceptions of the respondents on the use of history in teaching mathematics were then processed using exploratory factor analysis to identify four relevant constructs. These constructs were formed using an eigenvalue of 1. These four constructs have 53.58% variance explained. Five items (1, 10, 13. 14, 15) belong to the first factor; another five items (2, 4, 6, 7, 11) comprise the second factor, and three items each for the third (5, 9, 8) and fourth (3, 12, 16) factors. Table 6 shows these results of the rotated component matrix done under factor analysis.

Table 6

Rotated Component Matrix

Component

Perceptions

(Note: Only keywords are used)

1 2 3 4

14-VERSATILE TEACHER .77

9

15-HELP LEARNING MATH .71

8

1-TEACHERS LACK TRAINING

IHISTORY

.67

2

13-HISTORY CAN DEVELOP

CRITICAL THINKING

.65

8

10-INCREASE TEACHER

APPRECIATION OF MATH

.46

9

4-HISTORY IS NOT

MATHEMATICS

.406

6-HISTORY IS TORTUOUS

AND CONFUSING

.74

9

7-HARD TO CONNECT .60

6

11-EMPHASIZE ON ROUTINE

SKILLS

.59

2

2-TEACHERS LACK

HISTORICAL RESOURCES

.65

4.5

35

5-HISTORY INCREASES

KNOWLEDGE OMATH

.76

9

9-TIME CONSUMING .44

6

.71

2

8-HISTORY PROJECTS

INCREASE TEACHER AND

STUDENT KNOWLEDGE

.51

9

12-TEACHERS LACK

ASSESSMENT RUBRIC

.58

971

2

16-MAKE A MORE EFFECTIVE

TEACHER

.56

7 3-TEACHERS HAVE

SUFFICIENT TIME

.52

5

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.

a. Rotation converged in 7 iterations.

On the other hand, the outcome of the multivariate tests on Table 7 shows that the level effect on the perspectives of teachers on the use of history in teaching mathematics is not significant, Wilks’ Lambda (8, 118) = 1.201, p < .304. That is, there is no significant difference in the perception of teachers on the use of history on math teaching across all educational levels. On the contrary, the effect of the type of school on the perception of these teachers on utilizing history in teaching mathematics is significant (Wilk’s Lamba (4,59) =

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3.309, p = .016. Thus, in terms of public and private school teachers, the perceptions are significantly different. The tests also reveal that there is no interaction effect between the type of school and the different educational levels (Wilk’s Lamba (4,59) = .402, p < .806. This indicates that the perceptions of the teachers across all educational levels on the use of history in teaching mathematics do not depend on the type of school where these respondents are coming from.

Table 7

Multivariate Tests

Effect Value F Hypothes

is df

Error

df Sig.

Interce

pt

Pillai's

Trace

.996 4.134E

3a

4.000 59.000 .000

Wilks'

Lambda

.004 4.134E

3a

4.000 59.000 .000

Hotelling'

s Trace

280.2

43

4.134E

3a

4.000 59.000 .000

Roy's

Largest

Root

280.2

43

4.134E

3a

4.000 59.000 .000

ELEM1

HS2COL

3

Pillai's

Trace

.147 1.187 8.000 120.00

0

.312

Wilks'

Lambda

.855 1.201a 8.000 118.00

0

.304

Hotelling'

s Trace

.168 1.215 8.000 116.00

0

.297

Roy's

Largest

Root

.154 2.317b 4.000 60.000 .067

PUBLIC

2PRIVA

TE1

Pillai's

Trace

.183 3.309a 4.000 59.000 .016

Wilks'

Lambda

.817 3.309a 4.000 59.000 .016

Hotelling'

s Trace

.224 3.309a 4.000 59.000 .016

Roy's

Largest

Root

.224 3.309a 4.000 59.000 .016

ELEM1

HS2COL

3 *

PUBLIC

2PRIVA

TE1

Pillai's

Trace

.027 .402a 4.000 59.000 .806

Wilks'

Lambda

.973 .402a 4.000 59.000 .806

Hotelling'

s Trace

.027 .402a 4.000 59.000 .806

Roy's

Largest

Root

.027 .402a 4.000 59.000 .806

a. Exact

statistic

b. The statistic is an upper bound on F that yields a

lower bound on the significance level.

Multivariate Tests

Effect Value F Hypothes

is df

Error

df Sig.

Interce

pt

Pillai's

Trace

.996 4.134E

3a

4.000 59.000 .000

Wilks'

Lambda

.004 4.134E

3a

4.000 59.000 .000

Hotelling'

s Trace

280.2

43

4.134E

3a

4.000 59.000 .000

Roy's

Largest

Root

280.2

43

4.134E

3a

4.000 59.000 .000

ELEM1

HS2COL

3

Pillai's

Trace

.147 1.187 8.000 120.00

0

.312

Wilks'

Lambda

.855 1.201a 8.000 118.00

0

.304

Hotelling'

s Trace

.168 1.215 8.000 116.00

0

.297

Roy's

Largest

Root

.154 2.317b 4.000 60.000 .067

PUBLIC

2PRIVA

TE1

Pillai's

Trace

.183 3.309a 4.000 59.000 .016

Wilks'

Lambda

.817 3.309a 4.000 59.000 .016

Hotelling'

s Trace

.224 3.309a 4.000 59.000 .016

Roy's

Largest

Root

.224 3.309a 4.000 59.000 .016

ELEM1

HS2COL

3 *

PUBLIC

2PRIVA

TE1

Pillai's

Trace

.027 .402a 4.000 59.000 .806

Wilks'

Lambda

.973 .402a 4.000 59.000 .806

Hotelling'

s Trace

.027 .402a 4.000 59.000 .806

Roy's

Largest

Root

.027 .402a 4.000 59.000 .806

a. Exact

statistic

c. Design: Intercept + ELEM1HS2COL3 + PUBLIC2PRIVATE1

+ ELEM1HS2COL3 * PUBLIC2PRIVATE1

17. CONCLUSIONS

Based on the findings of this study, the following conclusions were drawn:

1. History as perceived by the respondents is a record of past events detailing the origin or background of things while mathematics is something that involves numbers, symbols,

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problem solving and analysis.

2. Methods that involve history of mathematics were not popular among all the respondents regardless of the level and type of school in which they came from. They sometimes use those methods but they prefer using internet resources and experimental mathematical activities. Teachers in the primary level that were asked never assigned research project based on history texts to their students and never used historical packages in teaching mathematics. Role playing was the method preferred by them. On the other hand, role playing was the least popular among the teachers from the secondary and tertiary level while the use of internet resources is the most popular among them.

3. In general, all the teachers have the same perceptions on the use of history in teaching mathematics. They agree on all the enumerated statements regarding the positive implication of using history in mathematics educations except for the item stating that teachers have sufficient time to include history in teaching mathematics. Those in the primary and secondary levels agree that they have sufficient time to include history while the teachers in the tertiary level disagree. Teachers from private schools maintain that they have sufficient time while teachers from the public schools say they do not. All the teachers are also in agreement with the statement that they lack training and expertise in using history of mathematics, historical resources and appropriate assessment rubrics in mathematics involving history. They all agree that the chief emphasis of teaching should be on equipping students with routine skills rather than on the historical context of mathematics.

4. There is no significant difference in the perception of teachers on the use of history on math teaching across all educational levels.

5. In terms of public and private school teachers, the perceptions are significantly different.

6. However, the perceptions of the teachers across all educational levels on the use of history in teaching mathematics do not depend on the type of school where these respondents are coming from.

The teachers agree on the positive effect of using history in teaching mathematics and yet they don’t usually employ methods that will incorporate history. This can be attributed to their perceived lack of time and their perceived lack of confidence to integrate history. The uniform stand of the teachers on the lack of training and expertise, historical resources and appropriate assessment rubrics indicates that they may not be ready to incorporate history in teaching mathematics and so they evade those methods that require the use of the history of mathematics education.

The general agreement on the positive effect of using history by the teacher respondents who had some experiences incorporating history in their teaching practices signifies that there is a merit in the pursuit of utilizing history in mathematics education. The responses of the teachers to the survey give us hints on where to focus our attention in this endeavor. We may look at history of mathematics in relation to the design of teacher education program, in relation to the design of our curriculums and in relation to the development of resource materials in mathematics.

In conclusion, the authors are keen to point out that history of mathematics is not to be regarded as a solution to all pedagogical issues in mathematics education, just as mathematics, though important, is not the only subject worth studying. It is the harmony of mathematics with other intellectual and cultural pursuits that makes the subject even more worth studying. In this wider context, the history of mathematics has yet a more important role to play in providing a fuller education of a person.

18. ACKNOWLEDGMENTS We would like to express our sincerest gratitude

to the faculty members of LPU, HAU, PSAU for sparing their time to answer the questionnaires for this study. We

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are also grateful to Dr. Amelia Punzalan, our faculty-in-charge, for validating the questionnaire. Her valuable corrections and inputs on the earlier version of the instrument inspired the authors to pursue this study. Above all, we praise and thank the Almighty God for His goodness, for the countless blessings that He has showered upon us and for having paved the way, using institutions and people, to enable us to finish this paper. Laus Deo Semper! Praise be to God always!

19. REFERENCES

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[2] Farmaki, V., Paschos, T. (2007). Employing genetic ‘moments’ in the history of mathematics in the classroom activities. Educational Studies in Mathematics, 66, 83-106.

[3] Fauvel, J. & van Maanen, J. (Eds.) (2000). History in Mathematics education. The ICMI Study. Dordrecht: Kluwer Academic

[4] Fried, Michael N. (2007). Didactics and History of Mathematics: Knowledge and Self-Knowledge. Educational Studies in Mathematics,66, 203-223.

[5] Furinghetti, F. (2007). Teacher Education through the history of mathematics. Educational Studies in Mathematics, 66, 131-143.

[6] Gulikers, I, Blom, K. (2001). ‘A Historical Angle’, A survey of recent literature on the use and value of history in geometrical education. Educational Studies in Mathematics, 47, 223-258.

[7] Jankvist, Uffe T.(2009). A Categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics , 71, 235-261.

[8] Katz, Victor J. (2007).Stages in the History of Algebra with Implications for Teaching. Educational Studies in Mathematics, 66, 185-201.

[9] Lahoylahoy, Myrna E. (2003). Effects of Integrating History in Mathematics on High Schools Cognitive and Affective Learnings. Ph.D. Dissertation, Univeristy of the Philippines Open University, Quezon City.

[10] Otte, Michael (2007).Mathematical history, philosophy and education. Educational Studies in Mathematics, 66, 243-255.

[11] Swetz, Fauvel, Bekken, Johansson, & Katz (eds.). Learn From the Masters. Washington D.C. Mathematical Association of America, 1995

[12] Tzanakis, C., & Arcavi, A. (2000). Integrating History of Mathematics in the Classroom: An Analytic Survey. Dordrecht: Kluwer Academic, pp. 201-240.