CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELF-EFFICACY IN

MATHEMATICS

A Dissertation

by

HILLARY P. CROISSANT

Submitted to the Office of Graduate Studies

of Texas A&M University-Commerce

in partial fulfillment of the requirements

for the degree of

DOCTOR OF EDUCATION

May 2014

CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELF-EFFICACY IN

MATHEMATICS

A Dissertation

by

HILLARY P. CROISSANT

Approved by:

Advisor: Gilbert Naizer

Committee: Tami Morton

Katy Denson

Head of Department: Martha Foote

Dean of the College: Gail Johnson

Dean of Graduate Studies: Arlene Horne

iii

Copyright 2014

Hillary P. Croissant

iv

ABSTRACT

CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELF-EFFICACY IN

MATHEMATICS

Hillary P. Croissant, EdD

Texas A&M University-Commerce, 2014

Advisor: Gilbert Naizer, PhD

This study aimed to find the characteristics of public school math classrooms and how

they influence self-efficacy of students. Data were collected on math students in grades 4

through 12 in a North Texas school district. Two surveys were administered to students in the

district. Within 10 days, the students completed a classroom environment survey, followed by a

self-efficacy survey. Both surveys were electronic and administered during the school day.

Student data were analyzed by conducting a simple linear regression in order to determine if a

relationship existed between classroom environment and student self-efficacy. A multiple

regression was used in order to determine which dimensions under classroom environment could

predict a high or low self-efficacy. Data analysis was unable to generalize low self-efficacy in

mathematics and classroom environment correlation due to a small effect size. High self-

efficacy in mathematics was found to increase as cohesion and satisfaction would increase and

high self-efficacy in mathematics would increase as friction and difficulty would decrease.

v

ACKNOWLEDGEMENTS

Teaching is a work of the heart is a sign I have up in my classroom that reminds me

that not only as a teacher can I make a difference, but I am impacted by all kinds of teachers

throughout my life. I want to thank the many mentors and supporters from whom I have had the

opportunity to be influenced by and taught. You have encouraged me, supported me, and given

me the strength to complete this journey.

I would like to thank my closest friends for supporting me throughout this journey. First,

to my friend Wendy Ulrich for encouraging me to continue on this path while being my work

spouse by ensuring me that I could be a teacher and student at the same time. Also, to Laura

Ahrens for reminding me how fortunate I am to be on this adventure and keeping me passionate

about the knowledge that I was gaining.

My inspiration comes from my teachers from the past. This great idea started with my

professors from Austin CollegeJane White, Julia Shahid, and Barbara Sylvesterand my goal

to be like them someday. I appreciate my mentors and support from administration and fellow

teachers in my school district for their extended support. A special thanks goes out to my

advisor Dr. Gilbert Naizer who has read and reread through my work, emailed and conferenced,

and helped me make sure that I am the best that I could be. Also thank you to Katy Denson and

Tami Morton for being a part of my dissertation committee and supporting my statistical and

literary efforts. Jane Braddock and Kelli Knight for bringing snacks to class and being the

perfect support system for this doctoral stage of life.

Lastly I would like to thank my family for their continued support. My mom and dad for

always being my number one fan as well as my parents-in-law who support any crazy idea I

come up with and ensure I have everything I need to be successful. Most of all I want to thank

vi

my husband Eric for putting up with the late nights, study sessions, and tears that come with the

crazy life of being a doctoral student. You are my greatest supporter and sounding board, and I

could not have done it without your continued love and motivation. Weston better be ready for a

wild ride as a part of this family.

This dissertation is dedicated to students who strongly dislike math in the hope that one

day they will be positively impacted by a classroom or a teacher who instills the love of math in

them so that it becomes a subject to be passionate about rather than despised.

vii

TABLE OF CONTENTS

LIST OF TABLES ...........................................................................................................................x

LIST OF FIGURES ....................................................................................................................... xi

CHAPTER

1. INTRODUCTION .........................................................................................................1

Statement of the Problem .........................................................................................1

Purpose of the Study ................................................................................................3

Research Questions ..................................................................................................3

Research Hypotheses ...............................................................................................4

Theoretical Framework ............................................................................................4

Significance of the Problem ...................................................................................10

Method of Procedure..............................................................................................11

Definitions of Terms ..............................................................................................13

Limitations .............................................................................................................14

Delimitations ..........................................................................................................15

Assumptions ...........................................................................................................15

Organization of the Study ......................................................................................16

2. REVIEW OF THE LITERATURE .............................................................................17

Math Anxiety .........................................................................................................17

Classroom Environment.........................................................................................20

Self-Efficacy and Classroom Environment ..........................................................25

Self-Efficacy and Math ..........................................................................................30

Self-Efficacy and Achievement .............................................................................32

viii

Student Attitudes and Achievement.......................................................................38

Anxiety and Achievement......................................................................................39

Teacher Attitudes ...................................................................................................42

Conclusions ............................................................................................................46

3. METHOD OF PROCEDURE......................................................................................48

Research Design.....................................................................................................49

Population and Sample ..........................................................................................50

Instrumentation ......................................................................................................51

Procedures ..............................................................................................................55

Data Gathering .......................................................................................................57

Treatment of Data ..................................................................................................58

Summary ................................................................................................................58

4. ANALYSIS OF DATA................................................................................................60

Results ....................................................................................................................60

Summary ................................................................................................................65

5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS,

IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ......66

Summary of the Study ...........................................................................................66

Summary of the Findings .......................................................................................66

Conclusions ............................................................................................................67

Implications............................................................................................................71

Recommendations for Further Research ................................................................74

Summary ................................................................................................................75

ix

REFERENCES ..............................................................................................................................76

APPENDICES .............................................................................................................................107

Appendix

A. My Classroom Inventory .....................................................................................108

B. Patterns of Adaptive Learning Survey .................................................................111

C. Parent Permission Form .......................................................................................115

D. Child/Minor Agreement to Be in a Research Study ............................................119

E. District Agreement ...............................................................................................122

F. Parent and Student Recruitment Letters ..............................................................125

G. Demographic Survey ...........................................................................................127

H. Video Script .........................................................................................................129

I. Spanish Translation of Parent Letter....................................................................132

J. Spanish Translation of Parent Permission Form ..................................................134

K. Signed Site Letter .................................................................................................138

L. Tables 1-4.............................................................................................................141

VITA ............................................................................................................................................144

x

LIST OF TABLES

TABLE

1. Means, Standard Deviations and Intercorrelations for High Self-Efficacy, Cohesiveness,

Friction, Satisfaction, Difficulty, and Competitiveness .....................................................62

2. Multiple Regression Analysis Summary for Variables Predicting High Math Self-

Efficacy ..............................................................................................................................63

3. Means, Standard Deviations and Intercorrelations for Low Self-Efficacy, Cohesiveness,

Friction, Satisfaction, Difficulty, and Competitiveness .....................................................64

4. Multiple Regression Analysis Summary for Variables Predicting Low Math Self-Efficacy

............................................................................................................................................65

xi

LIST OF FIGURES

FIGURE

1. Theoretical Framework ........................................................................................................5

1

Chapter 1

INTRODUCTION

Starting at a young age, people are very impressionable through interactions in their

environment including at home, at school, and with peers. These impressions can be reinforced

or changed throughout the students life. An impression that has been an epidemic in our society

is the negative attitude toward mathematics. Having a negative attitude in mathematics can lead

to lower achievement in mathematics and lack of interest in continuing to develop a knowledge

base of this topic. This study aimed to examine existing research and add to the body of

knowledge in order to create an environment for students that leads to an increase in

mathematics self-efficacy and ultimately improves attitudes and achievement in mathematics.

Statement of the Problem

A 2005 Associated Press poll found that nearly 40% of adults strongly disliked

mathematics in school, twice the percentage of adults who disliked other subjects (Philipp,

2007). The way individuals see mathematics can negatively or positively impact their attitude

toward the subject. While students learn mathematics, they acquire skills, understand maths

value, how it is learned, who should learn it, and what is needed for engagement in mathematics

understanding. Heller stated, Be careful how you interpret the world; it is like that (McFague,

2001, p. 39). This implies that the way that an individual makes sense of the world, not only

defines the person for the world, but also the world for that person.

The importance and need for math are emphasized in many areas of the world around us

and in our life and workplace. Math is a significant part of the scientific and technical

community our society has become, as well as our cultural heritage (National Council of

Teachers of Mathematics [NCTM], 2000). The increase in the complexity of our everyday life

2

has raised the importance and significance of mathematics and the role it has in our society.

Unfortunately, the level of difficulty and abstractness of math are a large reason why people have

developed a negative view, attitude, or affect toward mathematics (Adeyemi, 2012). This

negative view of educators can trickle down to students and lead to unsatisfactory achievement

and participation in mathematics (Malmivuori, 2008). Lack of intrinsic motivation can lead to

resistance toward mathematics and the learners self-perception will decline and difficulties in

mathematics will increase (Royer & Walles, 2007). Students who have difficulties in math often

have lower confidence in math and lower achievement in mathematics.

Self-efficacy is defined by Bandura (1986) as peoples judgments of their capabilities to

organize and execute courses of action required to attain designated types of performances (p.

391) and can be easily confused with attitudes. Attitudes toward math have been defined as a

liking or disliking of mathematics, a tendency to engage in or avoid mathematics activities, a

belief that one is good or bad at mathematics, and a belief that mathematics is useful or useless

(Neale, 1969, p. 623). While both strongly reflect an individuals feelings toward an area of

focus, in this case mathematics, they are different through the fact that self-efficacy has a greater

emphasis on the performance that is associated with the attitude rather than just the feeling.

It is crucial that educators create learning environments that build students into adults that

approach challenging math and science tasks with full force. Times where students shy away

from these tasks should be limited. Educators need to be sure that they present environments

where students are getting a positive feeling about how they do mathematics and want to do

more. When students feel successful in a school setting, they are more likely to want to explore

it further into their adult life. Classroom environment is a topic that needs to be explored so we

can not only prevent students from avoiding math, but also encourage them to take it further.

3

Purpose of the Study

The purpose of the study was to examine how a classroom and the environment created

by the teacher and classmates can impact how students feel about their ability to do and be

successful in mathematics. It focused on how students perceived their classroom environment

and measured student attitudes toward mathematics in order to determine relationships between

the two. The relationship between how the students perceived their classroom environment and

their attitudes toward math was analyzed.

The quantitative data collected gave insight into the classroom environment

characteristics that foster negative and/or positive students self-efficacy in mathematics

classrooms. This study determined how different characteristics of a classroom correlates to

student self-efficacy in mathematics. The researcher sought to find what characteristics in a

classroom environment are predictors of negative and/or positive attitudes toward mathematics.

Emphasis was placed on examining how students feel about the environment created in a

mathematics classroom and how their feelings toward mathematics were affected. Another

emphasis of this research was to examine which classroom environment dimensions impact

negative and positive student self-efficacy in mathematics.

Research Questions

This study addressed the following questions:

1. Which dimensions of classroom environment (cohesiveness, friction, satisfaction,

difficulty, or competitiveness) are the best predictors of high self-efficacy for students

in mathematics?

4

2. Which dimensions of classroom environment (cohesiveness, friction, satisfaction,

difficulty, or competitiveness) are the best predictors of low self-efficacy for students

in mathematics?

Research Hypotheses

The following null hypotheses reflect the research questions:

1. No relationship exists among the dimensions of classroom environment

(cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students high

self-efficacy in mathematics.

2. No relationship exists among the dimensions of classroom environment

(cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students low

self-efficacy in mathematics.

Theoretical Framework

Individuals behaviors and attitudes are caused by multiple variables including their

environment, peer interactions, feedback from authority figures, and their personal experiences

(Battistich, Solomon, Kim, Watson, & Schaps, 1995). In a classroom, all of these variables

impact students and their behavior as well as self-efficacy toward the subject being taught. The

following historical and current theories support these findings. These theories include the social

cognitive theory, attribution theory, self-efficacy theory, person environment fit theory, and the

expectancy-value theory.

Each theory supports different variables in this study. Figure 1 shows a visual

representation of how each theory is directly connected to the current study. Self-efficacy is

connected to the social cognitive theory, attribution theory, and expectancy-value theory.

Classroom environment is supported by the person-environment fit theory. The social cognitive

5

theory is thinking about and reflecting over your behavior. Self-efficacy is impacted by the

social cognitive theory because thinking leads to judgments created about oneself which impact

individual future performance. The attribution theory causes individuals to think about why they

succeed or fail and these ideas can lead to future behaviors and performance. Expectancy-value

theory involves individual motivation in an area based on its value according to that individual.

This can impact future performance from that individual, as well as self-efficacy. Person-

environment fit theory is based on how the environment impacts behavior. This directly

connects to how a classroom is conducted, and the culture created within it can impact the

students in it.

Social Cognitive Theory

Social cognitive learning theorists view human functioning as reciprocal interactions

among behaviors of individuals, environmental variables, cognition, and personal factors

(Bandura, 1986). When individuals perform a task, the perceived importance of the task is a

large part of the result of the outcome expectation the individual has for the task. Bandura

(1986) stated that beliefs determine expectations; therefore people generally value what they feel

6

capable of accomplishing and do not value the activities in which they have little confidence.

Through self-reflection, individuals evaluate their own experiences and thought processes, which

powerfully influences how they will behave in future tasks (Pajares, 1996).

Banduras (1997) social cognitive theory proposed that self-efficacy is strongly affected

by previous performance and influenced by observing others, verbal persuasion, and

interpretation of physiological states, with possibilities that student perceptions of their learning

environment also affect their efficacy. People are self-organizing, proactive, self-reflecting, self-

regulating, non-reactive beings easily influenced by their environmental or inner impulses.

People interpret their own behavior, which impacts their environment and personal impulses and

can therefore alter their subsequent behavior. Pajares (2002) supported the idea that teachers can

work to improve their students perception of school and students emotional state in order to

self-correct false self-beliefs and develop habits to improve their academic skill and self-

regulatory practices.

Additionally, society constructs values and standards that impact the ways students view

themselves, depending on their approach and success with given tasks in the education system

(Hickey & Granade, 2004). The social cognitive theory is based on the idea that people

purposefully engage in their own development and can make things happen through their actions.

Attribution Theory

The attribution theory emphasizes the thought that for individuals who believe success is

due to high ability and failure is due to lack of effort, motivation will remain constant. However,

students who believe success is luck and failure is expected are less likely to be motivated

(Diener & Dweck, 1978). Students or others who have always failed in the past in a specific

task, attribute that failure to themselves, especially if they see others succeeding (Weiner, 2004).

7

The attribution theory is based on causal attributions that people make about the success or

failure of their actions that will influence how they feel and how they expect to perform on future

tasks or activities of the same nature (Weiner, 1986). The effect of childrens own perceptions of

their ability to achieve success has a direct impact on their personal attitude toward math.

Attributions influence motivation and performance through the meditational role of self-efficacy

(Bandura, 1995; Schunk, 1991).

Self-Efficacy

Individuals self-efficacy influences how people feel, think, motivate themselves, and

behave. Bandura (1997) described four major processes that are impacted by self-efficacy

including cognitive, motivational, affective, and selection processes. Major focuses of cognition

included the impact of comparing, feedback, and amount of control over a

situation. Additionally, individuals that believe they will perform well will tend to perform well,

while those that feel inferior will perform poorly. Students with high self-efficacy seem to

participate more readily, work harder, persist longer, and achieve higher results.

Bandura (1986) defined self-efficacy as peoples judgments of their capabilities to

organize and execute courses of action required to attain designated types of performances (p.

391). Self-efficacy impacts almost every aspect of peoples lives and is the core of human

motivation, well-being, and personal accomplishment. It influences individual choices, goals,

emotional reactions, efforts, coping, and persistence (Gist, Mitchell, & Mitchell, 1992). When

individuals are faced with adversity, self-efficacy determines their behavior (Pajares, 2002).

Self-efficacy impacts motivation, affect, and actions based on the interaction of what the

individual believes rather than what is actually true (Bandura, 1997).

8

Self-efficacy influences the choices that people make and how much effort they put into

the tasks, their thought patterns, and their emotional reactions (Pajares, 2002). There are four

different sources through which self-efficacy can be developed including mastery experience,

vicarious experience, social persuasions, and somatic and emotional states. Mastery experience

is the most influential source and is the act of individuals engaging in the actual task or activity

and then interpreting the results of their actions. These interpretations are then used to develop a

personal belief about their capability to perform the task or activity and then act in line with the

beliefs they have created (Pajares, 2002). Researchers have shown that self-efficacy is related to

the career path and choices made by individuals along with other decisional behaviors (Betz &

Hackett, 1981, 1983; Lent, Brown, & Larkin, 1987). Also, self-efficacy can predict success and

persistence in certain academic majors and is strongly related to achievement status (Multon,

Brown, & Lent, 1991).

Person Environment Fit Theory

The person-environment fit theory (Lewin, 1935; Murray, 1938, 1951) emphasizes the

idea that behavior is a function of the person and the environment. There is a mutual relationship

between the environment and person such that the environment influences behavior. Hunt

(1975) emphasized the need for a match between the person and the environment in the course of

learning. Early adolescents have an increase in a need for higher quality interactions with adults,

sense of autonomy, and a sense of belonging (Eccles, et al., 1993; Kuperminc, Leadbeater, &

Blatt, 2001; Midgley, Feldlaufer, & Eccles, 1989; Osterman, 2000). There is dual emphasis on

the person and the environment and behavior, attitudes, and well-being are determined by both

the person and the environment. Within the research under person-environment fit theory, the

feeling gained by the individual arises not from the person or environment but rather by his or

9

her fit or congruence with one another (Edwards, Caplan, & Harrison, 1998). Classroom

environments have a culture of their own created by the people within and surrounding it. The

environment created has an impact on the individuals that are a part of it, which include the

students. This theory supports the concept that the environment created has an impact on the

behavior of those that are a part of the environment, in this case, with emphasis on the students.

Expectancy-value Theory

The expectancy value theory emphasizes how motivation is a primary result of an

individuals belief about the outcome of a specific activity and the importance placed on that

outcome (Atkinson, 1957; McClelland, 1985; Rotter, 1982). Individuals will be motivated to

participate in tasks if they find value in the outcome of that particular task and will not be

motivated to take part in a task if they do not find value in the outcome. Researchers have

agreed that competence in completing a task plays a crucial role if the task will be valued by the

individual (Eccles, 1983; Wigfield & Eccles, 1992). Bandura (1986) emphasized that outcome

expectation will have a stronger influence on the motivation and predicting behavior of the task

performed. Bandura stated that personal judgments of the individuals competence are different

than the individuals judgment of the likely outcome from the task. Those who expect success

will behave in such a way in order to achieve that goal. The opposite is also true; if individuals

expect failure, they will be more likely to fulfill that belief (Pajares, 1996).

According to Eccles (2009), achievement related behaviors like course selection and

occupational aspiration are most directly influenced by the individuals expectation for success.

Research has indicated that students who are most likely to take math courses and to aspire to

math focused careers place higher value and have greater confidence in their math abilities than

those who do not (Eccles, 2007).

10

The expectancy-value theory also shows that the feedback students receive on their

academic performance influences their motivational beliefs and academic choices (Eccles, 2009).

Wang (2012) concurred; he found that students who earned higher grades in math also reported

higher math expectancies and subjective task values, and were more likely to continue with

course work in math and have math-related jobs in the future.

Significance of the Problem

Students in our colleges are straying away from majoring in mathematics intensive fields

because of the lack of self-efficacy in this area (Committee on Science, Engineering, and Public

Policy, 2007). This shortage of math majors and graduates has put the United States behind in

mathematics, science, and technology development. The Industrial Revolution spawned a

multitude of engineering endeavors that spring boarded the economy in the United States

(Committee on Science, Engineering, and Public Policy, 2007). Many areas of our life including

transportation, communication, agriculture, education, health, defense, and employment

opportunities are available due to the investment in scientific research and engineering (Popper

& Wagner, 2002). The United States has been considered a leader in science and engineering

activities since the early 1900s with 30% of the worlds scientists and engineers as well as 17 of

the worlds top 20 universities (Freeman, 2005). With the reputation so high in the US, other

countries have stepped up and increased their competitiveness with the US over the past 20

years. This changing global market requires the US to produce not only more engineers, but

higher quality engineers that are needed to be worldwide leaders in this high-tech production

market. High school graduates pursuing engineering degrees are declining (Noeth, Cruce, &

Harmston, 2003), and less than half the freshmen who begin college with engineering as their

major finishing with an engineering degree (Besterfield-Sacre, Atman, & Shuman, 1997). One

11

attempt to solve this problem is to increase the number of students choosing to study engineering

(Fantz, Siller, & Demiranda, 2011). Mathematics is a crucial piece of many fields, including the

engineering field. Without mathematics, problem solving, process formation, and application

would find disconnect within this field of study.

This research study helps to determine what characteristics of classrooms can lead to a

low or high self-efficacy in mathematics. Using this information, educators will be able to

determine what they can do in their classroom to encourage high mathematics self-efficacy in

their students and eliminate characteristics that tend to form a lower self-efficacy. This will lead

to improved math interest and achievement as well as an increase in students in mathematic

career fields. This boost in mathematics in America could jump start the society with

improvement in areas like Science, Technology, Engineering, and Mathematics (STEM) fields.

Method of Procedure

This research study sought to determine what characteristics of the mathematic classroom

environment could predict high or low student self-efficacy in mathematics. Two surveys were

administered to participants in order to collect data. The data were then analyzed using multiple

regression.

Selection of Sample

Participants for this study included students in fourth through 12th grade in a small North

Texas school district. Only participants with parent permission and student assent were included

in the data analysis. The school district superintendent gave prior permission for the researcher

to collect the student data. Approximately 400 students participated in this study.

12

Instrumentation

The Patterns of Adaptive Learning Scale (PALS) (Midgley et al., 2000) instrument as a

whole is a tool used to measure a variety of learning aspects of the student. This study focused

solely on high and low self-efficacy, therefore, only parts of the PALS instrument were used in

data analysis to emphasize self-efficacy rather than the other student scales. The PALS

instrument was chosen because of its validity and reliability and there was no other appropriate

mathematics self-efficacy instrument.

Self-handicapping is associated with maladaptive behavior which leads to low self-

efficacy (Patrick, Kaplan, & Ryan, 2011), therefore low self-efficacy was measured using the

statements under academic self-handicapping strategies (p. 368). Self-efficacy also has been

found to be positively related to mastery goal structure, personal mastery goal orientation, effort,

not cheating, satisfaction with learning, school-related effort, and achievement (Ames & Archer,

1988; Anderman, 1999; Kaplan & Midgley, 1999; Murdock, Hale, & Weber, 2001). Therefore,

high self-efficacy was measured by analyzing the statements that fall under mastery goal

orientation and academic efficacy.

Students also took the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg,

1982) which measured students perception of the classroom environment in their mathematics

classroom. The MCI measures five dimensions of social climate, including cohesiveness,

friction, satisfaction, difficulty, and competitiveness.

Collection of Data

Students took the two separate surveys, in an electronic version, during the regular school

day in their computer lab, the MCI. My Classroom Inventory (MCI) and the selected items from

the Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) were used to collect and

13

analyze data from the students. Students entered some demographic information on both

surveys, including their ID number in order for their surveys to be matched by a district

employee for analysis. The ID number is a school district issued number that students are

familiar with and use on a daily basis. Student ID numbers were removed before data were given

to the researcher.

Treatment of the Data

The data were collected and analyzed using Statistical Program for Social Sciences

(SPSS) through conducting two multiple regressions to determine which dimensions of

classroom environment can predict a high or low math self-efficacy. Student demographics were

reported.

Definitions of Terms

The following terms are used in the present study:

Classroom environment. Classroom environment involves interpersonal relationships

with peers, relationships between students and their teacher, the relationship between students,

the subject studied and teaching methods, in addition to student perceptions of structural

characteristics of the class (Fraser et al., 1982). In this study, classroom environment was

measured by My Classroom Inventory (MCI) (Fraser et al., 1982). The five subscales under

classroom environment are listed below:

Cohesiveness- extent to which students, know, help and are friendly toward each other;

Friction- amount of tension and quarrelling among students;

Satisfaction- extent of enjoyment of class work;

Difficulty- the extent to which students find difficulty with the work of the class; and

Competitiveness- emphasis is placed on students competing with each other.

14

High self-efficacy. High self-efficacy is defined as mastery goal orientation and

academic efficacy. High self-efficacy was measured by Patterns of Adaptive Learning Survey

(PALS) (Midgley et al., 2000) using the mastery goal orientation and academic efficacy

scales.

Low self-efficacy. Low self-efficacy is defined as looking at student attribution through

academic self-handicapping strategies. Low self-efficacy was measured by Patterns of

Adaptive Learning Survey (PALS) (Midgley et al., 2000) using the academic self-handicapping

scale.

Mathematics self-efficacy. Self-efficacy of students specifically in the mathematics

classroom and academic area of math (Bagaka, 2011).

Mathematics classroom. Mathematics classrooms ranged from a self-contained

elementary classroom to a dual credit calculus classroom.

Self-efficacy. Self-efficacy was defined by Albert Bandura (1994) as the belief in ones

capabilities to organize and execute the courses of action required to manage prospective

situations (p. 72). It measures how people think, feel, and behave in certain situations and their

personal opinion of how they can succeed in that environment.

Students. Students are defined as children from fourth through 12th grades who were

approximately age 9 to 19.

Limitations

The limitations of this study were as follows:

1. The district selected has a small population and limited subgroups (ethnicity,

socioeconomic status, languages spoken).

2. The sampled participants were not an exact representation of the population of the

15

school district due to the requirements needed for students to participate.

3. Students completed the surveys on a computer-based survey system that could cause

students to make mistakes by incorrectly clicking an answer they do not want.

4. Previous experiences and events that occur prior to students taking the surveys were

not controlled by the researcher and could impact the results of the survey.

Delimitations

The delimitations of this study were as follows:

1. The data were collected from one school district.

2. The data were collected with limited student subgroups.

3. Only the student section of the PALS survey was used to measure students

perception of classroom environment in mathematics classrooms. No data were

collected using the teacher portion of the instrument.

4. The data were collected within a 10-day time period which could cause some

difference in data collection and change in attitudes of the participants.

5. Only grades four through 12 were analyzed.

6. The researcher chose the order in which the students completed the surveys.

Assumptions

This study is based on the following assumptions:

1. Students responded accurately and honestly.

2. Teachers administrating the surveys did not impact student responses.

3. Math teachers did not alter their teaching in order to gain specific results from the

data collected.

16

4. Both instruments are valid and reliable and the two surveys did not influence each

other.

Organization of the Study

This dissertation is organized into five chapters. Chapter 1 includes a statement of the

problem, purpose of the study, research questions, research hypotheses, theoretical framework,

significance of the study, definitions of terms, limitations, delimitations, and assumptions.

Chapter 2 includes related professional literature regarding self-efficacy and classroom

environment in mathematics. In Chapter 3 is a discussion of the research methodology. Chapter

4 includes the analysis of the data; Chapter 5 includes a discussion of the findings and

applications to education.

17

Chapter 2

LITERATURE REVIEW

This study aimed to determine what dimensions of classroom environment predict high

self-efficacy and low self-efficacy in mathematics. Students in a North Texas school district

participated in taking two surveys. One survey measured their perception of the classroom

environment of their math class while the other measured the high and low self-efficacy in

mathematics. Data were analyzed using a multiple regression in order to determine what

characteristics of the math class could predict high and low self-efficacy in mathematics.

Self-efficacy plays a major role in individuals everyday lives. Many different variables

can impact each individuals self-efficacy, especially in the area of mathematics (Hackett &

Betz, 1989). Students attitudes are influenced by many different things including parents, peers,

school, teacher, and classroom environment (Klassen & Usher, 2010). This literature review

examines the importance of a positive self-efficacy in students at all ages in the area of

mathematics and explains why classroom environment, in regard to self-efficacy, needs to be

studied further.

Math Anxiety

Mathematic anxiety is a worldwide concern. The root of the problem is in schools, where

students are developing negative attitudes toward mathematics at a very early age (Ashcraft,

2002). Math anxiety can be described as a feeling of tension that interferes with the

manipulations of numbers and the solving of mathematical problems in academic and ordinary

life situations (Sousa, 2008, p. 171). Math anxiety has been defined as the feeling of tension,

helplessness, mental disorganization and dread when one is required to work and manipulate

math problems (Ashcraft & Faust, 1994). Math anxiety can conjure up feelings of apprehension,

18

dislike, fear and dread (McLeod, 1994). It can prevent students from interacting with situations

that are math intensive and these students avoid upper level math courses (Akin & Kurbanoglu,

2011). Lazarus (1974) believed that mathematic anxiety developed in elementary and secondary

grades. Researchers have shown that negative math experiences can start around third or fourth

grade (Ashcraft & Ridley, 2005; Beilock, Gunderson, Ramirez, & Levine, 2010).

Math anxiety occurs in people from all different race, gender, and age group and can be a

product of the home, school, or society. Burns (1998) estimated that 60% of adults have a fear

of mathematics. Students develop a fear of mathematics (math anxiety) through negative

experiences in math classes or having a lack of self-confidence with numbers (Sousa, 2008).

These experiences and lack of confidence usually lead to fear of calculation, failure, and

difficulty in mathematics. The fear causes their minds to go blank and then causes frustration,

which leads to additional amnesia. Fear and anxiety is increased when time limits are added to

the mathematics activity. Students who have developed math anxiety need help to replace the

memory of failure with the possibility for success (Ashcraft, 2002).

The most obvious consequence of math anxiety is poor achievement and poor grades in

mathematics (Sousa, 2008). Poor performance can be caused by a chemical change happening in

the brain through the biology of the body. Any kind of anxiety causes the body to release

cortisol into the bloodstream. Cortisol is a hormone that refocuses the brain on the anxiety to

determine what action to take to relieve the stress. While this is happening, the frontal lobe is no

longer interested in learning or processing the mathematical operation while the brain is dealing

with a threat to the individuals safety. Therefore, the student cannot focus and has to cope with

the frustration of inattention. As well as their inability to manipulate and retain numbers and

expressions due to a disruption in the working memory (Ashcraft & Kirk, 2001).

19

Beilock, Gunderson, Ramirez, and Levine (2010) focused on how math anxiety can

impact students, specifically girls. This study looked at how female elementary teachers math

anxiety influences the female students achievement and how that compared to the male students.

Students were first and second grade students who were given math assessments throughout the

school year. Students were told two gender neutral stories about students who were good at

math and the other was good at reading and then the students drew a picture of what each looked

like. The pictures were coded and correlated with the math assessment finding that girls who

had confirmed gender ability roles (boys are good at math, and girls are good at reading)

performed worse on the math assessment than girls who did not. These girls also performed

worse than the boys with these differences related to the anxiety that the teacher had about math.

Harper and Daane (1998) studied the causes of math anxiety in preservice elementary

teachers and found that the cause usually stemmed from elementary school and included fear of

making mistakes, having the right answer, amount of time given for a task, word problems, and

problem solving. Philippous and Christou (2003) studied preservice teachers in Greece and

found that teachers with negative attitudes toward mathematics were slightly positively impacted

when they understood the usefulness of the skill while the deeply rooted anxieties about

mathematics did not seem to change.

Ma (1999) found that there is a significant relationship between math anxiety and math

achievement. Bretscher, Dwindell, Hey, and Higbee (1989) posited that students who learned

math because they wanted to, had higher math achievement, therefore the motivation toward

performing math increased the student achievement. Norwood (1994) found that the elements of

math anxiety included a mixture of truancy, poor self-image, poor coping skills, teacher attitude,

and the emphasis on learning math through drill practice rather than understanding. Zakaria and

20

Nordin (2008) found that students who had a high math anxiety also had a low math achievement

as well as the students with low math anxiety had high math achievement.

Classroom Environment

The term classroom environment refers to the social and psychological surroundings of

the classroom (Fraser, 1991). The teacher is a part of and contributes to the classroom

environment which influences choices and norms of the classroom (Shuell, 1996). Research has

shown that the quality of classroom environment is a significant determinant of student learning

(Fraser, 1994, 1998b). Early seminal work by Lewin (1935, 1936) and Murray (1938)

recognized that both the environment and its interaction with personal characteristics of the

individual are determinants of the human behavior. Students learn better when they perceive the

classroom environment positively (Dorman, 2003). Research on classroom environment has

been diverse and varied, but began with the work of Walberg (1979) and Moos (1974), who

spawned additional research programs all over the world. While questionnaires were used

greatly in the beginning of the classroom environment research, both quantitative and qualitative

methods are the more typical route of researchers. The majority of classroom environment

research has been done in science classrooms and very few have involved mathematics

classrooms (Spinner & Fraser, 2005).

Classroom environment has been shown to be the most significant factor in students

learning and attitudes in math and science (Fraser & Kahle, 2007). The classroom environment

is a critical context for promoting the development of students educational and career interests

(Simpkins, Davis-Kean, & Eccles, 2006). There is evidence to suggest that classroom

environment influences how well students achieve a range of desirable outcomes (Fraser, 2007).

Research has supported the fact that the social environment of classrooms can significantly

21

impact students motivated behavior, specifically the level of friendship students feel for each

other measured by students getting to know each other, helping each other, and working together

(Fraser & Fisher, 1983; Trickett & Moos, 1974). Students have been found to achieve better in

the types of classroom environments that they prefer (Fraser & Fisher, 1983).

Teacher techniques that include the focus on memorization rather than understanding the

concept are among the main sources of math anxiety. Math anxiety also stems from a classroom

culture that searches for one right answer with no recognition or appreciation for the thinking the

student goes through or their cognitive process. Flewelling and Higginson (2001) found that

students who have rewarding and successful learning experiences with math were able to

overcome their math anxiety. Math classrooms and teachers who focus on making sense of that

mathematical process and not memorizing or being correct cultivate students who avoid math

anxiety.

Having a positive classroom environment is a valuable goal of education (Fraser, 2001).

Describing the class through the actual participants, students are in a good position to make

judgments about classrooms because they have experienced many different learning

environments and have spent enough time in the class to form accurate opinions. While teachers

can be inconsistent in daily behavior, there is usually a consistent picture of the traditions and

features of the classroom environment. While observation is a strategy used to collect data on

classroom environments, it does not tell the whole story about the students perspective.

Classroom environment includes the relationships between students, teachers, and subject

material (Fraser et al., 1982). Five components of classroom environment will be emphasized in

this research including cohesiveness, friction, satisfaction, difficulty, and competitiveness.

22

Sinclair and Fraser (2002) conducted research that looked into three areas of classroom

environment. They worked on developing an instrument (Middle School Inventory of

Classroom Environments or ICE), collecting quantitative and qualitative data on typical

classroom environments, and used the information so teachers could positively impact their

classroom and students. Data were collected from about 745 students on their perceived and

preferred classroom environments, along with data collected from ten teachers on their perceived

and preferred classroom environments. Sinclair and Fraser also took part in classroom

observations of the participating teachers. Analysis of the data collected compared the teacher

and student preferred and perceptions of the classroom environment. A one-way analysis of

variance (ANOVA) was used in order to analyze the data for each scale within the instrument.

After initial scores were collected on the teachers and students, the researchers met with the

teachers to share the information and determine what areas that the teacher wanted to improve

upon in order to increase student perceived classroom environment. One teacher aimed to

improve her students perceptions of involvement and teacher empathy in her class. The teacher

worked on including students in the science lab preparation as well as assistance with class pet

maintenance.

Research done on classroom social climates has shown that classrooms characterized by

cohesiveness, satisfaction, and goal directions are preferred by students and are associated with

positive outcomes for students (Fraser, 1991). Students sense of autonomy and participation in

decision making has also been shown to have positive effects for children (Lewin, Lippitt, &

White, 1939). Having a caring environment conveys a set of values such as mutual respect,

valuing individual members contributions, and obligation of each member to meet the needs of

the community (Battistich, Solomon, Kim, Watson, & Schaps, 1995). Fraser (1998a), with

23

support from Goh, Young, and Fraser (1995) found associations between students perception of

the classroom environment in mathematical classes and established that students with greater

cohesiveness were linked to higher achievement for math and teacher support: task orientation

and equity were linked with more positive attitudes and self-esteem.

Cooperative classroom strategies are associated with improved peer relations and

supporting mutual respect (Anderson, 2004). Johnson and Johnson (1991) found that

cooperative learning environments lead to productive classrooms where students exert high

effort to achieve positive and supportive relationships and psychologically healthy and socially

competent students. In a teacher-centered mathematics classroom that is controlled by rules,

routines, and individual drilling, there is little room for student autonomy or social belonging

within the mathematic learning. Student-centered classrooms with teamwork and emphasis on

meaning making give students many opportunities to have students needs met through a variety

of approaches (Hannula, 2006).

The degree to which a classroom is challenging can also influence academic self-

efficacy. Challenging is defined as an environment where students are given progressively

difficult tasks as their proficiency increases. Some researchers have suggested that challenging

students can lead to a stronger belief in the students personal academic abilities (Battistich et al.,

1995; Pajares, 1996).

One of the essential ways to improve middle grade education is to establish a safe and

healthy school environment (Jackson & Davis, 2000). Students can be placed at academic risk

of failure because of the quality of their school and classroom learning environment

(Montgomery & Rossi, 1994). Ineffective and dysfunctional classrooms and instructional

learning environments have been uncovered in multiple middle schools (Midgley, Eccles, &

24

Feldlaufer, 1991; MacIver & Epstein, 1993; Waxman, Huang, & Padron, 1995). Middle schools

are usually structured, formal, and less personal than elementary schools and students frequently

become bored and alienated with an increase in teacher talk and lack of student involvement

(Waxman et al., 1995). Middle school classes tend to be more teacher-centered and discipline

focused where teacher student relations and student decision making are not a focus (Feldlaufer,

Midgley, & Eccles, 1988). Additionally, middle schools often do not encourage personal

relationships even though caring and supportive environments are critical for students (Baker,

1998; Roeser, Midgley, & Urdan, 1996). Classroom environment needs to be a focus in the

middle grades in order to increase student cognitive and affective outcomes (Fraser, 1998;

Haertel, Walberg, & Haertel, 1981). Researchers have shown that cohesiveness, student

satisfaction, and teacher support are positively related to student increase in academic

achievement (Waxman, Read, & Garcia, 2008).

Research has been devoted to comparing the perception students have of their classroom

as one which is performance based or encourages mastery (Patrick, Kaplan, & Ryan, 2011).

Classrooms structured around mastery goals focus on effort put into a task as well as the intrinsic

value of learning. This is compared to the performance-based classroom that focuses on

competition and natural ability. Previous research has found that classrooms based around the

mastery goal model have higher academic self-efficacy (Friedel, Cortina, Turner, & Midgley,

2007). The degree to which students perceive their classroom as a caring environment also has

an influence on self-efficacy. Teachers in these classrooms express personal interest in the

students, provide emotional support, and create a comfortable atmosphere. Murdock and Miller

(2003) suggested that students who perceive their teachers as caring are more likely to view

themselves as more academically capable, set higher goals for themselves, and have significantly

25

higher self-efficacy. The effect of emotional support on math achievement was larger than on

quantity of math instruction.

Roeser et al. (1996) found that a greater sense of school belonging, along with an

emphasis on effort, understanding, and beliefs that all students can learn, were associated with

academic self-efficacy. Cowen, Work, Hightower, Wyman, Parker, & Lotyczewski (1991)

found those students who perceive high levels of classroom competition, friction, and difficulty,

felt less efficacy when approached with an academic challenge.

McMahon, Wernsman, and Rose (2009) examined 149 fourth and fifth graders from

diverse backgrounds in California that completed two self-reports on their perceived classroom

environment. The MCI (My Classroom Inventory) was used to collect data from the students on

their perceived classroom environment, school belongingness was measured using the

Psychological Sense of School Membership Scale, and self-efficacy in language arts and math

was also measured using a The Academic Self-Efficacy Scale. They found that satisfaction,

cohesion, and school belonging were significantly and positively correlated along with difficulty,

competitiveness and friction. Additionally, classroom environment and school belonging predict

self-efficacy and lower difficulty predicted higher math and science self-efficacy. School

belonging and satisfaction and cohesion did not significantly predict math and science self-

efficacy.

Self-Efficacy and Classroom Environment

Consistent and convincing research gives evidence that the quality of the classroom

environment is a significant determinant of student learning (Fraser, 1994). A positive learning

environment can influence student academic achievement and attitudes (Fisher, Henderson, &

26

Fraser, 1995). Fraser (1994) indicated that student perceptions of learning environments are an

important factor in explaining their cognitive and affective outcomes.

In terms of self-efficacy and classroom climate, these factors play important roles in the

learning environment (Pitkaniemi & Vanninen, 2012). Students are more likely to have greater

expectancy values in math which can lead to students taking more math courses and pursuing a

career in mathematics. These students can then encourage, cooperate, interact, and help their

classmates and view the curriculum and teaching as meaningful and relevant to their lives when

they perceive their teacher as understanding and supportive while having high expectations for

their learning achievement (Wang, 2012). Teacher and school practices that promote students

mathematical self-efficacy may not only promote mathematic achievements, but also could

narrow the achievement gaps in mathematics as found by gender, socioeconomic status, and

minority status (Bagaka, 2011).

Self-efficacy predicts students math achievement, and there are reasons to suspect that

the relationship between teachers classroom behavior and students academic performance are

also positively correlated (Weinstein & McKown, 1998). Students carefully observe teachers

verbal and nonverbal behaviors while developing self-beliefs and academic behaviors based on

these observations (Weinstein & McKown, 1998). When educators demonstrate a direct interest

in student care and concern, as well as respect for their thoughts, opinions, and ideas, the

outcome supports a decrease in student depressive symptoms and an increase in self-esteem

(Reddy, Rhones, & Mulhall, 2003). Further et al. (1998) determined that affective teacher

behavior including listening, respect, recognition, and fair treatment significantly influenced

young adolescent motivation. Muller, Katz, and Dance (1999) established that students 8-18

years of age desire a personal connection with their teacher and yearn for the instructor to

27

maintain high academic expectations. Fairness is an additional characteristic that students retain

from their educator in the classroom. Students identify with different ways teachers treat

students associated with success and ability (Weinstein & McKown, 1998).

The powerful relationship that grows between the teacher and student in the classroom

plays a crucial role in developing the emotional, motivational, and academic behaviors of the

student. Teacher support correlates directly with youth adjustment, achievement, social, and

motivational development. While educators have a specialized focus of specific academic

content, there needs to be an equal focus on student affect and social-emotional needs (Osterman,

2000). Through self-recorded data, students show a decline in teacher support throughout school

years (Reddy et al., 2003) as well as a decline in a sense of belonging over time (Anderman,

2003). The data from the mathematics self-reports suggest that students feel less valuable and

see a lower persistence in middle school years.

A supportive teaching style has been positively linked to student achievement. It has

been found that if teachers academic support (the teacher cares about their learning, tries to help

them learn, and wants them to do their best), academic press (the teacher checks for

understanding and engagement), and mastery goal (the teacher emphasizes learning and

understanding, focuses on student development) are all implemented in the classroom, student

achievement improves (Goodenow, 1993; Kaplan & Midgley, 1999; Wentzel, 1994, 1997).

Students who perceive that their math teachers take into account student relatedness and

competence, and enforce positive demands on students academic work show more positive

motivational beliefs and achieve higher grades. Students who perceive their teacher as

responsive, helpful and recognizant of good work tend to perform better than their peers whose

teachers are perceived as less supportive (Ambrose, 2004). These results support Slovenes

28

findings of early adolescents perceptions of their teachers and motivational beliefs (self-efficacy

and intrinsic motivation) (Puklek, 2001; Puklek, 2004).

Self-efficacy beliefs are created through the individuals interpretation of information

from different internal and external sources (Bandura, 1997; Pajares, 2002). An external source

of self-efficacy beliefs is verbal judgments that others provide about their capabilities. Teachers

are a crucial element of the classroom environment. Students perception of affective teacher

support can influence their enjoyment in mathematics.

Math and science self-efficacy were significantly negatively correlated with difficulty,

and positively correlated with language arts self-efficacy (Pajares, 2002). Predictors of self-

efficacy include satisfaction and cohesiveness; difficulty, competitiveness, and friction, and

school belonging. In terms of math and science self-efficacy, difficulty was the sole predictor

when a self-efficacy test was given for the second time. Other variables that can impact self-

efficacy are parental influence, teacher-student and student-student interaction, teacher

instructional techniques, and appropriate teacher support. Kaplan, Gheen, and Midgley (2002)

suggested that students are more likely to have positive self-efficacy from mastering a subject

rather than from performing a standard. This could explain the finding that perceived difficulty

predicted math and science self-efficacy.

When students have a perceived high academic self-efficacy, they exhibit a positive

behavioral adjustment and social competence, greater self-concept, and stronger relationships

with peers and parents (Kuperminc, Blatt, & Leadbeater, 1997). Student academic self-efficacy

is a strong predictor of academic engagement, persistence, academic effort and performance

(Linenbrink & Pintrich, 1997). School environment significantly influences a students self-

efficacy.

29

The relationship between academic effort and academic achievement in middle school is

important because it has been found to predict math achievement in high school, which will

directly impact the student in college (Wang & Goldschmidt, 2003). Previous theory and

research suggested a positive relation between academic self-efficacy beliefs and academic

outcomes of students (Bandura, 1997; Pajares & Graham, 1999). Lorsbach and Jinks (1999)

suggested that student perceptions of their learning environment are influenced by student

academic self-efficacy and can lead to an appreciation of what is happening in classrooms.

As expected, students who reported a greater sense of belonging in their mathematics

classroom were likely to report higher academic enjoyment (Wang, 2012). Researchers did not

find any statistical significance between academic enjoyment and academic hopelessness, or

between academic enjoyment and academic self-efficacy. Academic enjoyment proved to be a

powerful connection with academic effort. Students who reported higher teacher affective

support were likely to report lower academic hopelessness, which was associated with greater

academic self-efficacy (Pekrun, Goetz, Frenzel, Barchfeld, & Perry, 2011). Academic

hopelessness did negatively predict academic effort through its detrimental effect on academic

self-efficacy. Students who reported high academic hopelessness were likely to report low

academic self-efficacy belief and related to lower academic effort. Students who report higher

academic self-efficacy tended to report greater academic success in mathematics.

There was a positive correlation between teacher academic press and student

motivational beliefs; students self-efficacy and mastery goal orientation in math were positively

related to their math grade. Results also showed that level of parental involvement would predict

student math grades, while the math teaching measures were the most powerful predictors of

student self-efficacy in math (Battistich et al., 1995). The students ratings of math teachers

30

academic support contributed to student mastery goal orientation and math achievement. The

perceptions of teacher academic press predicted student self-efficacy and mastery goal

orientation in math and their math grade (Anderson, Hamilton, & Hattie, 2004).

Overall, it was found that classroom environment does have an impact on student

academic self-efficacy and the many different variables that can impact these relate to students

and their experiences (Weinstein & McKown, 1998).

Self-Efficacy and Math

Self-efficacy in mathematics has been studied, but not in great detail. Math self-efficacy

is a strong predictor of math performance (Pajares & Miller 1994, 1995). The self-efficacy

theory states that perceived self-efficacy influences and is influenced by thought patterns,

affective arousal, and choice behavior as well as task performance (Bandura, 1977, 1986).

According to the social learning theory, self-efficacy expectations are an important factor in

influencing math attitudes and math anxiety (Bandura, 1977; Hackett & Betz, 1981). Bandura

(1986), Pajares (1996), and Schunk (1991) found that self-efficacy beliefs predict student

performance in mathematics. Self-efficacy can also influence math performance as strongly as

general mathematics ability (Pajares & Kranzler, 1995). Across ability levels, students who have

high self-efficacy are more accurate in their mathematical computation and are more persistent

when faced with a challenge when compared to students with low self-efficacy (Collins, 1985).

Lloyd, Walsh, and Yailagh (2005) analyzed fourth and seventh graders in order to

compare their math grades, math foundation skills, performance attributions, and self-efficacy

looking specifically at gender differences. They found that boys and girls equally attributed their

success to effort and fourth graders were more likely to attribute their success to effort when

compared to seventh graders. Ability was the attribution that the majority of students believed

31

lead to success. Fourth graders were also more likely than seventh graders to attribute their

success to help from their teachers than seventh graders. Fourth graders were more efficacious

than seventh graders and girls tended to be under-confident while boys were over-confident;

however, girls achievement met or exceeded boys achievement.

Akin and Kurbanoglu (2011) examined the relationship between math anxiety and self-

efficacy. Participants included 372 university students in Turkey who took the assessment R-

MARS (Revised Mathematics Anxiety Rating Scale) to measure anxiety, Mathematics Attitudes

Scale to measure mathematic attitudes, and Motivated Strategies for Learning Questionnaire

(MSLQ) to measure self-efficacy. They found that self-efficacy is a proximal determinant of

math attitudes and self-efficacy and that math anxiety was predicted by negative self-efficacy.

Overall, the stronger the self-efficacy, the more active are the individuals efforts and the longer

they will persist. Additionally, self-efficacy predicted negative attitudes and positive attitudes.

Pajares and Miller (1996) found that math self-efficacy has stronger direct effects on

mathematics problem solving than self-concept, perceived usefulness, or prior experience.

Judgments of individuals ability to solve math problems should be more strongly able to predict

their ability to solve those problems than their confidence in their ability on math related tasks.

Similarly, judgments of their ability to succeed in math related courses should predict their

choice to enroll in math courses than should their confidence in their ability to solve specific

problems or perform math tasks (Pajares, 1996). Schunk (1981) showed that teacher modeling

increased persistence and accuracy on division problems by arising student self-efficacy, which

had a direct effect on skill. Additionally, he found that student effort was attributed to feedback

of prior performance. This behavior raised student self-efficacy expectations in elementary

32

students. Later, he also discovered that ability feedback had a stronger effect on self-efficacy

and performance (Schunk & Gunn, 1986).

Self-Efficacy and Achievement

Self-efficacy contributes to personal goals individuals set for themselves, how much

effort they will exert in order to perform a task, how long an individual will persevere when

facing a challenge, and how resilient the individual is toward failures. Bandura (1982) found

that self-efficacy is more strongly related to future and actual task performance than past

performance. Self-efficacy is not concerned with specific skills an individual has but the

judgments and self-belief of what one can do with the skills they possess (Bandura, 1982).

Several studies have established the strong positive connection between student self-

efficacy and their academic performance (Pajares, 1996; Pajares & Graham, 1999). Self-efficacy

has been shown to predict achievement outcomes in a variety of content areas including

mathematics, science, and writing (Klassen & Usher, 2010; Pajares, 1996; Pajares & Urdan,

2006). Self-efficacy is also a powerful predictor of student achievement (Al-Harthy, Was, &

Isaacson, 2010; Andrew, 1998; Bandura, 1993; Barkly, 2006; Paulsen & Gentry, 1995; Schunk,

1989; Zimmerman, 2000).

Bandura (1977, 1997) and Pajares (1996) found that higher self-efficacy scores leads to

better performance and persistence in engineering courses. Self-efficacy is a task-specific

capability (Gist, Mitchell, & Mitchell, 1992) and a dynamic construct. The self-efficacy

judgment from the individual changes over time as new information and experiences are gained

(Bandura, 1989). Personal efficacy beliefs help individuals determine how much effort people

will spend on an activity, for how long they will persevere when faced with a challenge, and how

resilient they are when the odds are not in their favor (Pajares, 1996). Self-efficacy also

33

influences the thought patterns and emotional reactions of individuals. Self-efficacy beliefs are

powerful predictors of the choices that individuals make on a daily basis, the level of effort that

they put on the task, and their persistence toward facing challenges (Multon, Brown, & Lent,

1991). Individuals with low self-efficacy may view a challenge and think that it is more difficult

than it really is, impacting their stress level, depression, and ability to best solve the problem. In

contrast, high self-efficacy helps individuals create a feeling of confidence when approaching

difficult tasks and activities (Pajares, 1996). Pekrun et al. (2011) found that focusing on

academic enjoyment in a college classroom positively impacted self-efficacy, intrinsic and

extrinsic motivation, academic effort, self-regulation, and academic performance.

There are four factors that influence self-efficacy: mastery experience, vicarious

experience, social persuasions, and somatic emotional state. Mastery experience, interpreting

ones own performance, is the most potent source of self-efficacy (Bandura, 1986, 1997). Prior

experience will affect students initial belief in their personal capabilities. Those who perform

well on the activity believe they are capable of furthering their abilities in that area. Individuals

who experience challenge and difficulties may doubt their capabilities (Schunk, 1989). Actions

perceived by the individual as successful typically raise self-efficacy and perceived failure

lowers it. Positive feedback can enhance self-efficacy but can be short lived if efforts following

the feedback are poor as students are generally not motivated to behave in ways that they believe

will result in negative outcomes (Schunk, 1989). Research shows that mastery goal orientation is

linked to positive, adaptive pattern of attributions, whereas a performance goal orientation was

linked to a maladaptive, helpless pattern of attributions (Ames, 1992b; Dweck & Leggett, 1988).

Under mastery goal orientation, students are more likely to see a strong link between effort and

outcomes and make more effort attributions for success and failure (Schunk, Meece, & Pintrich,

34

2014). Students with performance goal orientation see effort and ability as inversely related, as

opposed to the positive relation under mastery goal (Schunk et al., 2014). Self-efficacy has been

found to be related to goal orientation and found that people with mastery goals have higher self-

efficacy and better task performance than people with performance goals (Locke, Frederick, Lee,

& Bobko, 1984; Locke & Latham, 1990; Wood, Bandura, & Bailey, 1990).

Researchers have found links between mastery goals and judgments of self-efficacy are

generally positive (Sakiz, 2011). As mastery goals were formed, Dweck and Leggett (1988)

performed laboratory research that showed that students oriented toward mastery and learning

maintained positive and adaptive self-efficacy beliefs and perceptions of competence in the face

of difficult tasks. Mastery goals related positively to self-efficacy in college students enrolled in

statistics courses (Bandalos, Finney, & Geske, 2003). Bong (2009), Kaplan and Midgley (1997),

Middleton and Midgley (1997), Sakiz (2011), and Thorkildsen and Nicholls (1998) have also

shown the same general pattern.

Vicarious experience, observing the actions of others, is also another way that individuals

obtain information about what they can do (Bandura, 1997; Schunk, 1987). Students who

observe similar peers perform a task may believe that they are capable as well. This source of

self-efficacy is not as strong as mastery experience, but when individuals are uncertain of their

abilities or have little prior experience, they become more sensitive to it (Pajares, 2002). Self-

efficacy can also be created through the result of social persuasions received from others in their

environment. Efficacy will increase when individuals are being told they are capable by a

trustworthy source. This can include verbal judgments from peers or adults and play an

important role in the development of an individuals self-beliefs. Individuals compare

themselves to others in their environment around them and evaluate themselves with those who

35

are similar in ability (Festinger, 1954). Lastly, anxiety, stress, arousal, and mood states fall

under that category of somatic and emotional states and can influence self-efficacy. Strong

emotional reactions to a task can foreshadow the anticipated success or failure of the outcome

(Pajares, 2002). Bandura (1997) found that people live in psychic environments that are of their

own making, so therefore, individuals have the capability to alter their own thinking and feeling

to enhance their self-efficacy beliefs. Self-efficacy can change as a result of learning,

experience, and feedback (Gist et al., 1992).

Self-efficacy can affect individuals psychological well-being and performance while

exerting some influence over their lives through the environments they select and environments

they create. Personal efficacy affects each individuals choices of activities to take part in.

Those who believe they are not capable of a task will avoid it, but the same individual will be

willing to take on an alternate activity they feel they are capable of completing or accomplishing

(Wood & Bandura, 1989). Perceived self-efficacy also has an impact on the choice of the

individuals career path with stronger self-efficacy connecting to more career options they

consider to be possible (Betz & Hackett, 1986; Lent & Hackett, 1987). Self-efficacy also

enhances students memory performance by enhancing persistence (Berry, 1987).

Academic self-efficacy can be seen as a part of student motivation and is defined as

students beliefs about their ability to learn or perform specific tasks (Bandura, 1986, 1997).

Students with high self-efficacy attempt difficult tasks and activities regularly and tend to

achieve higher than students with low self-efficacy (Pajares, 1996; Schunk, 1991). Students with

low self-efficacy generally give up on a learning activity when the results of success are not as

they preferred, which can lead to lower success, and a further reduced sense of academic self-

efficacy. High self-efficacy has been linked to higher grade point averages, standardized test

36

scores, persistence on a challenging task, and enrollment in upper-level math courses (Pajares,

1996; Pintrich & Schunk, 2002).

Students with high self-efficacy have a variety of characteristics that help them increase

their achievement and success in the classroom (Schunk, 1981). These students try harder, and

persevere longer than their lower self-efficacy counterparts (Bandura, 1982; Bandura, 1986;

Pajares, 2003; Pajares & Schunk, 2001) while having a strong sense of responsibility. They are

more concerned with the subject, deeply involved in the classroom activities, and try different

strategies when they meet difficulties, which lead to greater effort and success (Morgan & Jinks,

1999). Students with high self-efficacy set high expectations for themselves and produce

behaviors to perform well (Maxwell, 1998) along with being comfortable and confidently

approaching tasks (Schunk, 1991; Bandura, 1993). When these students are faced with a

challenge, they put forth greater effort to overcome obstacles (Bandura, 1986, 1997) and spend

more energy when encountering difficulties (Schunk, 1990) while being more relaxed and

efficient when faced with a challenge (Bandura, 1993; Schunk, 1991). Students with higher

math self-efficacy persist longer on difficult tasks and are more accurate in computations

compared to students with lower math self-efficacy (Collins, 1985; Hoffman & Schraw, 2009).

The students with low self-efficacy in writing were easily distracted from activities,

wandered around the room, avoided writing tasks, gave up easily, and took a lot of time to write

(Kim & Lorsbach, 2005). Other characteristics of low self-efficacy include a lack of strong

achievement (Schunk, 1981), giving up easily and that leads to lower success (Morgan & Jinks,

1999). These students also may avoid specific choices (Bandura, 1982) and experience stress

and ineffectiveness when faced with a challenge (Bandura, 1986, 1997).

37

Efficacy cues include performance outcomes where success in a task raises the self-

efficacy and failure will lower it. Individuals can perceive their success or failure using

attribution cues such as ability, effort, task difficulty, or luck (Frieze, 1980; Weiner, 1985).

Bodily symptoms like sweating and trembling can symbolize physiological cues for determining

efficacy.

Self-efficacy can also be assumed to be a motivating factor and is correlated with

characteristics of the learning environment such as goal orientation, high cohesion, satisfaction,

and a low level of disorder and conflict (Anderson et al., 2004). Bandura (1997), Nichols

(1996), and Pajares (1997) argued that student perceptions of self-efficacy have a positive impact

on student motivation and achievement. Self-efficacy determines individuals level of

motivation which is reflected in how much effort they will exert and how long they will

persevere. The stronger their self-efficacy, the more persistence, effort, and accomplishment

they have (Bandura & Cervone, 1983, 1986; Weinberg, Gould, & Jackson, 1979). Self-efficacy

can lead to self-aiding or self-hindering thought patterns, as well as personal goal setting. The

higher their self-efficacy, the higher goals are set and the firmer the commitments to those goals

(Locke et al., 1984; Taylor, Locke, Lee, & Gist, 1984).

Student perceived self-efficacy affects their academic interest and motivation as well as

management of stress (Bassi, Steca, Fave, & Caprara, 2007) while mediating the effect of skill,

previous experience, mental ability, or other self-beliefs on subsequent achievement (Pajares &

Schunk, 2001). Additionally, Eccles, Midgley, Wigfield, Buchanan, Reuman, Flanagan, and

MacIver (1993) suggested that achievement related activities selected by individuals are

influenced by social contexts of the individual, like the classroom and family.

38

Student Attitudes and Achievement

Student achievement in mathematics is impacted by environmental factors including the

emotional response to math (Sousa, 2008). Math and reading have been the standard in the

United States to determine the academic abilities of s