INTRODUCTION Mathematics is fundamental

Mathematics is fundamental to our way of life and knowing how the world works.

Science, Technology, Engineering, and the advances in these fields on which a nation's

economic future hinges on mathematics. Hence, having a solid mathematics education is

vitally important for all students. Furthermore, having a solid command of mathematics

allows students to be creative problem-solvers, assertive, and skilled individuals in

demand in universities and industries (Ofsted, 2012).

Mathematics is a powerful tool for universal understanding and communication

(Appiah, 2006). Using mathematics, learners can navigate the world and answer

complicated, real-life problems. For students to do well in a global setting, their

mathematics content must be reliable. It involves understanding the world from different

perspectives and acknowledging that issues are interconnected globally (Appiah, 2006).

In today's world, numerical aptitudes are increasing in significance; and essential

numeracy and quantitative skills are becoming very important in all employments, life

skills, and financial planning and data management (Ofsted, 2012). The ever-changing

world economy means strong math knowledge and skills are needed more than in recent

history. Businesses utilizing Science, Technology, Engineering, and Mathematics are

becoming fundamental to development and economic prosperity and promise to be the

leading provider of jobs for future generations (Chitate, 2016).

The focus on mathematics success continues to receive much international

attention as researchers strive for a richer understanding of factors that contribute to

mathematics success, the influence on mathematics learning and teaching, and pupils'

beliefs and attitudes towards mathematics. Academic achievement in mathematics and

avoiding academic failure have become the concern of educational institutions

worldwide. Researchers investigating student difficulties with math (Fleischner &

Manheimer, 1997; Hembree, 1990; Maccini, Mulcahy, & Wilson, 2007; Miller & Mercer,

1997) have identified affective and motivational variables as notable predictors (Hall,

Davis, Bolen, & Chia, 1999; Pintrich 2002).

The first indications of mathematics difficulty appear at lower elementary grade

levels (Hunt, Valentine, Bryant, Pfannenstiel, & Bryant, 2016). Gaps in fundamental

knowledge may occur even before pupils enter kindergarten, linked with skill deficits in

number sense that increase the chance of achievement gaps widening as they get older

(Mulligan, 2011; Schacter & Jo, 2016). Students who struggle in mathematics in

elementary school have negative long-term mathematics results during their education

and adulthood (Powell, Fuchs, and Fuchs, 2013). Compared to peers who begin school

with established standard numeracy abilities, students behind at the very start are not as

likely to be encouraged and involved in learning, setting the platform for future

difficulties associated with mastering mathematical material (Rabiner, Godwin, & Dodge,

2016). The growth of counting, understanding sequences, and estimation skills affects

math achievement in later grade levels, demonstrating that mastery of kindergarten skills

impacts prospective mathematics proficiency (Peng et al., 2016). Low-level mathematics

proficiency could result from the hierarchy of math skills and concepts in education. If an

unsteady foundation is established, advanced content areas will be challenging for pupils

to master (Peng et al., 2016).

A variety of factors influence success in mathematics among students, including

mathematics self-concept (Wang, 2007; Kuyper et al., 2014); mathematics anxiety

(Ashcraft, 2002; Ma & Xu, 2004); attitude toward mathematics (Hannula, 2002);

mathematics self-efficacy (Pietsch, Walker, & Chapman, 2003; Williams & Williams,

2010); parental involvement (Museus, Palmer, & Davis, 2011; Rosa & Mensah, 2016);

teachers (Klem & Connell, 2004; Pape, & Hoy, 2012; Ryan & Patrick, 2001); peers

(Palmer, Maramba, & Dancy, 2011); and gender (Kenney-Benson, Pomerantz, Ryan, &

Patrick, 2006).

While student motivation and hard work are vital elements of student

achievement, low self-efficacy toward schooling could hinder students' ability to complete

the coursework successfully and finally graduate (Spence & Usher, 2007). Selfefficacy,

the potency of one's belief in one’s capacity to finish a task or goal, is a significant

predictor of math achievement and plays an essential role in developmental math courses

(Spence & Usher, 2007). The encounter of long-term negative emotions toward

mathematics and math anxiety brought on by various course failures should be addressed

to enhance pupils' achievement in mathematics courses (Taylor, 2008). To achieve success

in math classes, students need to have positive self-efficacy.

Investigations have demonstrated that students' mathematics self-efficacy is

closely associated with their mathematics achievement (Klassen, 2004; Pajares & Miller,

1994; Stevens, Wang, Olivarez, & Hamman, 2007). Research by Pajares (1996) revealed

that mathematics self-efficacy is the strongest predictor compared to other factors

associated with mathematics performance, such as cognitive ability and previous

mathematics achievement. Students with superior levels of mathematics self-efficacy also

show more interest in mathematics (Lent, Lopez, & Bieschke, 1993; Post, Stewart, &

Smith, 1991; Steven, Olivarez, & Hamman, 2006) and are inclined to be registered in

additional math- and science-related courses (Kemp, 2002; Lim, 2001; Tyler-Smith,

2006). So, do different cultures acquire self-efficacy beliefs in the same way? Is

mathematics self-efficacy also the most critical predictor of math achievement for

Trinidad students compared to American students? Therefore, self-efficacy may not be as

strong a predictor of academic performance in some cultures as in Western cultures.

Much of the studies on math self-efficacy and math achievement have been

focused on high school pupils; this creates a void in the literature on a significant subset

of underperforming math individuals -- primary school students. Further, studies about

math self-efficacy have not been mirrored locally (in Trinidad and Tobago); this functions

to further widen the gap in what is known about how mathematics self-efficacy affects

classroom performance. This study’s findings might enlighten policymakers and

individuals involved in program design, pedagogy, and training conditions for practicing

primary school teachers in Trinidad and Tobago.

The recognized importance of self-efficacy in academic success has triggered

widespread interest in specific elements that affect students' self-efficacy beliefs.

Bandura's (1997) social cognitive theory proposed that one's past performance strongly

influences self-efficacy, and studies broadly support this (Chen & Zimmerman, 2007).

Bandura (1997), in his theory, also indicates that self-efficacy is affected by observing

others (e.g., observing peers succeed in a job), verbal persuasion (e.g., encouragement

from parents and teachers), and interpretation of physiological conditions (e.g., lack of

stress may be a signal that a person possesses skills). In mathematics education, scholars

have demonstrated that students with high self-efficacy regulate their learning more

effectively and perform better than individuals with low self-efficacy (Pajares, 2006).

Stevens et al. (2006) stated that self-efficacy is a more reliable predictor of mathematics

achievement than general mental ability. Self-efficacy, like other psychological constructs,

is domain-specific (Pellegrino, 2014), inferring that students' self-efficacy in one subject

could be different from their self-efficacy in another.

Understanding the impact of self-efficacy beliefs on school motivation during

adolescence is essential because a decline in these beliefs often begins early. The decrease

in academic self-efficacy during middle school (i.e., grades 6-8) is associated with later

academic failure (Klassen, 2004). Adolescence is a trying period of transition for many.

Those who are more self-efficacious about coping with this developmental period are

expected to have a higher probability of succeeding (Zimmerman & Cleary, 2006). Self-

efficacy is strongly linked to the quality and quantity of effort in school and plays an

influential mediating role in academic attainment (Bandura, 1997). Adolescents with high

self-efficacy are more likely to use various cognitive and metacognitive learning

strategies (Linnenbrink & Pintrich, 2003). Yet skills alone are not enough, and abilities

can be overruled by doubts about one's abilities (Bandura, 1997). Self-efficacy becomes a

critical issue for students because, as children age, their beliefs become more related to

school achievement (Shell, Colvin, & Bruning, 1995). According to social cognitive

theory, those who perceive themselves as inefficacious when coping with potential threats

will be prone to anxiety and avoidant behavior (Bandura, 1997).

Four self-efficacy sources may influence mathematics performance: performance

mastery experiences, vicarious experiences, verbal persuasion, and emotional arousal

(Bandura, 1994). This study examined the relationship among the sources of mathematics

self-efficacy, mathematics self-efficacy, and mathematics achievement in a sample of

Trinidad primary school students.

Statement of the Problem

Improving math achievement is essential for long-term student achievement.

"Leading societies also have demanded mathematical abilities that have brought them

advantages in medicine and wellness, engineering and commerce, navigation and

exploration, defense and finance, and the capability to comprehend past failures and even

to predict future developments" (p. 1), (NMAP,2008). Knowledge of mathematics can

produce opportunities for a successful future livelihood. Reports from external evaluation

bodies such as the Ministry of Education and private and public agencies on math

achievement have concluded that most of our pupils and society aren't well served.

(Ministry of Education program document, 1998). In preceding years, the pass rate for

math in the

Caribbean Secondary Education Certificate (CSEC) has been 2015=61%, 2016=54%,

2017=53%, and 2018=53.5%. CSEC subjects are examined for certification at the General

and Technical Proficiency levels. The General and Technical Proficiencies provide

students with the foundation for further studies and entry into the workplace. The mean

score for mathematics in the Secondary Entrance Assessment (SEA) for Primary School

pupils are 2015= 60, 2016= 61, 2017=58, and 2018= 59. The SEA, administered by the

Caribbean Examination Council (CXC), is a marker of educational achievement for male

and female primary school students. After approximately seven years of primary school,

most students living in Trinidad and Tobago take the SEA; candidates are placed in

secondary schools based on their examination performance. The highest-scoring students

are placed in schools of their first choice. Students with lower scores are placed in schools

based on demand and space availability. Any student under thirteen, scoring below 30%,

is assigned to re-sit the SEA in their primary school.

Any pupil feature that favorably influences accomplishment in high-stakes testing

environments requires attention. The level to which the student thinks they can

accomplish particular tasks, known as self-efficacy, is especially germane since

selfefficacy strongly influences success behavior (Bandura, 1986). Those with higher

selfefficacy are suggested to have greater aspirations, more substantial commitments to

their objectives, and the capacity to recover quickly from obstacles than those with

reduced self-efficacy. Beliefs in your efficacy may vary across academic areas (e.g.,

reading, composing, etc.), with self-efficacy for math receiving close attention. Pupils

with higher mathematics self-efficacy continue longer on mathematics issues and are far

more precise in mathematics calculations than individuals with reduced mathematics self-

efficacy (Collins, 1982; Hoffman & Schraw, 2009).

The SEA results have shown that the mathematics achievement of Trinidadian

students varies greatly. There are many explanations for the vast disparity in mathematics

performance. Pupils may not always be able to complete the prescribed curriculum on

time; pupils, from an early age, may develop a psychological block against mathematics

caused by the myth that mathematics is complicated. Furthermore, some pupils may have

had a bad experience with mathematics. In many schools, there are, on average, 30 pupils

to one teacher, resulting in some pupils not receiving the individual devotion they may

require. There might also be a lack of motivation, or students may have difficulty

understanding the necessary mathematics level as they lack the essential prerequisites.

Hence, how active students believe they can be at a specific task will, in turn, impact how

well they will perform at that task.

Bandura 1996, defined self-efficacy as the confidence in one's abilities to organize

and execute the courses of action necessary to manage prospective situations; it performs

a crucial role in the learning process. Self-efficacy beliefs affect a person's choice of

activity, goal orientation, achievement in various fields, learning, effort, and perseverance.

As self-efficacy is a latent construct (i.e., not directly observable), a theoretical

framework must be chosen and consistently adhered to when studying and devising

instrumentation.

Self-efficacy is a personal construct about self. It is domain-specific in that you

can believe yourself to be efficacious in one area rather than another. Domain-specific

efficacy is also not automatically continuous as time passes. In education, there's overall

academic efficiency and topic-specific efficacy. Mathematics self-efficacy is the person's

confidence or judgment about their ability to solve mathematics problems correctly,

which means that there is a given degree of efficacy in every job at any given period, and

certain conditions can change it.

Rationale for the Study

This study focused on two problems in the literature. Firstly, while many research

results have emphasized the critical role of self-efficacy in students' achievement, further

research was required about the four sources hypothesized by Bandura that affect the

improvement of students' mathematics self-efficacy. Many studies on the sources of

selfefficacy were done with measures not directly tied to social cognitive theory and have

not exhibited adequate reliability. Using the Sources of Mathematics Self-Efficacy Scale,

Usher and Pajares (2009) addressed this problem. They proposed several suggestions for

future research (Usher & Pajares, 2009), including investigating the validity of their scale

in different contexts, investigating changes in students' self-efficacy across significant

transition stages, and explaining gender differences in the sources of self-efficacy. The

first part of my study addressed those recommendations. This scale was validated with

pupils in Standards 4 and 5 (Grades 5-6) because this context has gained less attention in

studying mathematics self-efficacy sources. Demographic differences in pupils' scores on

the sources of Middle School Mathematics Self-Efficacy Scale were evaluated, and the

independent impact of each source on predicting mathematics self-efficacy. Finally, pupils

face a critical transition from primary to secondary school. By collecting data from

standards 4 and 5 (fifth and sixth-grade students), we can discover how math self-efficacy

influences those students when they transition to secondary school.

Purpose of the Study

The study investigates whether mathematics self-efficacy is a predictor of

mathematics achievement and whether mathematics self-efficacy mediates the

relationship between the sources of mathematics self-efficacy and mathematics

achievement in a Trinidad sample. Trinidad and Tobago is a twin island state, and

the sample used in the study was taken from primary schools in Trinidad.

Research Questions

The questions guiding the investigation are as follows:

1. What are the levels of mathematics self-efficacy among primary school students?

2. What are the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago?

a. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by school type?

b. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by age?

c. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by gender?

d. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by ethnicity?

3. To what extent do mathematics self-efficacy and mathematics self-efficacy

sources explain mathematics performance among primary school students?

Conceptual Framework

Empirical research has supported the long-held assumption that individual

variations exist in students' learning. Recent methodological advancements have allowed

academic analysis to look at not solely what students learn; however, conjointly how they

learn. According to Bandura's Social Cognitive Theory (1997), self-efficacy is essential

to students' achievement. Proposing the Social Cognitive Theory in 1986, Bandura

introduced variables in learning psychology that explained numerous learning

phenomena. The psychological feature alignment in Bandura's theory and his special

attention to the idea of 'self' served as a basis for introducing many variables. One of

the variables that received Bandura's special attention because of its outstanding role in

learning was the idea of 'self-efficacy.' This variable strongly influences people's behavior

by changing individuals' assessments of their capabilities. Self-efficacy beliefs affect the

choice, the number of efforts pupils make, the level of apprehension they experience,

their tenacity when facing adversity, and whether failures are demoralizing or informative

for remedial action. According to Bandura (1997), selfefficacy judgments depend on a

particular domain. In other words, they are domainspecific, meaning high self-efficacy

judgments in a specific area are not necessarily indicative of high self-efficacy in

different fields.

Numerous studies have investigated the sources of students' self-efficacy in

different academic domains (Klassen, 2004; Pajares, Johnson, & Usher, 2007; Usher &

Pajares, 2006b). The sources of self-efficacy among students have been compared by

academic levels (Pajares et al.,2007), gender (Hamption & Mason, 2003; Pajares et

al.,2007; Usher & Pajares, 2006b), and ethnic groupings (Usher & Pajares 2006b). Most

researchers have discovered that the four sources were correlated with self-efficacy (Lent

et al., 1991; Usher & Pajares, 2006b). The results, however, were not consistent with the

effects of the sources of self-efficacy on efficacy beliefs. Klassen (2004) found that

vicarious experience predicted self-efficacy beliefs, but other studies found no such

conclusion (Anderson & Betz, 2001; Lent et al., 1991). Some studies indicated that social

persuasion was a predictor of self-efficacy (Klassen, 2004; Pajares et al., 2007), while

others did not (Lent et al., 1991). Anderson and Betz unearthed evidence that emotional

and physiological states were significant predictors of self-efficacy, while Lent et al.

(1991) found no significance. However, many analyses of the sources of self-efficacy

have discovered that mastery experience accounted for the most substantial proportion of

variance in self-efficacy (Pajares et al.,2007). These results supported Bandura's claim

that mastery experience is the most valuable source of self-efficacy (Bandura, 1997).

From a theoretical standpoint, establishing and expanding self-efficacy beliefs in

elementary school children has been limited to a few research studies (Britner & Pajares,

2006; Pajares et al., 2007). The primary school years are critical, particularly for children

with limited cognitive maturity, to choose, evaluate, and integrate various information

sources to form their self-efficacy beliefs. We do not know, for example, whether mastery

experiences take priority in the selection and evaluation process. Limited learning

practices in elementary schools may, for example, prevent students from employing

successes/failures as a source of information. Likewise, we do not know the other three

sources' functioning patterns.

From the brief synthesis of self-efficacy, I have developed a conceptual model that

depicts two significant strands of research (i) the sources of mathematics selfefficacy and

mathematics self-efficacy and (ii) mathematics self-efficacy and mathematics academic

achievement. While differing from previous studies, the present research entails

examining structural relations between the sources of mathematics selfefficacy,

mathematics self-efficacy, and mathematics academic achievement. The conceptualization

also underlines the essential role of self-efficacy in teaching and learning. The alignment

of self-efficacy, in this case, specifies a possible mediating mechanism of self-efficacy

between sources of self-efficacy and academic attainment. For example, studies using

path analytical procedures have described evidence demonstrating the mediating role of

self-efficacy in academic learning (Pajares, 1996a, 1996b; Pajares & Miller, 1994; Pajares

& Valiante, 1997).

Figure 1: The sources of Mathematics Self-Efficacy, Mathematics Self-Efficacy, and

Mathematics Achievement.

Figure 1 displays the hypothesized model with mathematics self-efficacy as

the mediator of mathematics self-efficacy sources and mathematics achievement.

This model relates one exogenous latent variable, the sources of mathematics

selfefficacy, to two endogenous latent variables: mathematics self-efficacy and

mathematics achievement. Several studies report that the sources of mathematics

self-efficacy are predictive of mathematics achievement (Klassen, 2004; Usher &

Pajares, 2009; Zeldin and Pajares, 2000), and mathematics self-efficacy is predictive

of math achievement (Usher and Pajares, 2009; Klassen, 2004; Skaalvik & Skaalvik,

2011). Studies also suggest that self-efficacy may be a mediating variable (Canpolat,

2012, & Peters, 2013).

The latent exogenous variable, sources of math self-efficacy, is measured by

mastery experience, vicarious experiences, social persuasion, and physiological

states. Bandura (1994) hypothesized that four self-efficacy sources might predict

mathematics achievement: performance mastery experiences, vicarious experiences,

verbal persuasion, and emotional arousal. The latent endogenous variable mathematics

self-efficacy is measured by the observed variables, operation, and application,

derived from the Trinidad Mathematics Skill Self-Efficacy Scale (TMSSES). Number,

Measurement, Geometry, and Statistics are the observed variables for the second

endogenous latent variable, mathematics achievement. Number, Measurement,

Geometry, and Statistics are the strands that make up the Trinidad Primary Math

Curriculum.

As displayed in Figure 1, a direct path links the latent endogenous variable,

sources of mathematics self-efficacy, to the latent endogenous variable, mathematics

achievement. A second path connects the latent endogenous variables, sources of

mathematics self-efficacy and mathematics self-efficacy, to mathematics

achievement, with mathematics self-efficacy as a mediator.

Significance of the Study

Results from this study could help further enhance and extend research in social

cognitive theory in several important ways. First, the reliability and validity of the

SMMSE scale would be verified so that it could be used with more confidence in primary

schools. Increased emphasis on primary school readiness in preparation for the Secondary

Entrance Assessment (SEA) has put more importance on mastering mathematics concepts.

An instrument measuring the sources of mathematics efficacy for primary school students

enables researchers to collect reliable quantitative data on how selfefficacy beliefs are

formed as students learn these concepts. This study further validates the factor structure of

Bandura’s (1997) hypothesized sources of self-efficacy beliefs, assisting researchers in

better understanding possible differences in how self-efficacy beliefs are formed in

underrepresented populations among primary school mathematics students.

Second, this mediational role of self-efficacy makes it a predictor of subsequent

achievement. The findings of this study could promote a greater understanding of various

contributing factors influencing mathematics achievement. The exploration of these

factors involved the analysis of the association among multiple variables. These variables

included primary school students’ mathematics self-efficacy, the sources of mathematics

self-efficacy, and mathematics achievement.

Finally, with a better understanding of how mathematics self-efficacy mediates the

relationship between the sources of mathematics self-efficacy and mathematics

achievement, educators, school administrators, and education policymakers can work

toward creating curricula and programs that support or build primary students’

mathematics self-efficacy and enhance mathematics achievement.

Limitations

Limited demographic data was accessible about the participating students because

of restricted access to their parents. One more limitation is that self-report surveys fail to

consider the full context of a respondent's experiences, mainly when qualitative data do

not accompany them. Additional possible limitations of using self-report data involve

participants' inability to remember past events and their unwillingness to divulge personal

information (e.g., their private beliefs).

Delimitations

The study was delimited to selected standard five students from government and

denominational schools in the North Eastern Education District, which limited the

sample. I would have liked to sample students in all eight education districts. It bears

noting that a purposeful sample such as this one defines the inferences available to the

researcher. For this reason, conclusions drawn about students in other settings must be

made with caution. These delimitations prevented the generalizations of the results to

other populations.

Definition of Terms

A list of definitions of terms pertinent to the literature and the research questions is

presented here. Terms have been defined in ways most consistent with how they have

been operationalized in the literature and this study.

Mathematics achievement is the ability to manipulate mathematical concepts and

accurately perform mathematical calculations.

Mathematics self-efficacy is the belief in one’s capability to solve a

mathematical problem or complete a mathematical task (Hackett & Betz, 1989).

Mastery Experiences are the perception of past performances.

Physiological and Affective State includes somatic and emotional events,

including stress, fatigue, anxiety, and mood.

Self-Efficacy is the belief in one's capabilities to organize and execute the courses

of action required to produce given attainments" (Bandura, 1997, p. 3).

Social Cognitive Theory: A psychological theory in which individuals'

behaviors, environment, and personal factors interact in triadic reciprocity.

Social Persuasion: Evaluative messages that convey capability-related

information.

Sources of Self-Efficacy: Antecedents of capability-related beliefs.

Vicarious Experiences: Encounters in which individuals witness the successes or

failures of others executing a task

Organization of the Remainder of the Study

Chapter 2 includes a review of related literature and research, including the

following areas: social cognitive theory, mathematics self-efficacy, and self-efficacy

towards mathematics achievement. Chapter 3 will describe the research methodology,

including information on the participants and procedures for collecting and analyzing

data. Chapter 4 presents the data analysis and results, and Chapter 5 includes the

summary, discussion, and recommendations for instructional improvement and further

study.

CHAPTER 2

LITERATURE REVIEW

Introduction

This chapter offers a review of the literature appropriate to this investigation. The

chapter begins with an explanation of what is meant by Trinidad and Tobago’s academic

achievement specific to the primary school context and how it is measured. The chief

tenets of Albert Bandura’s (1986) social cognitive theory, which serves as the study’s

conceptual framework, were summarised. Next, a review of studies focused on

selfefficacy sources, emphasizing mathematics self-efficacy and its correlations, was

presented. The review described an evaluation of instruments measuring constructs

related to the sources of self-efficacy, including the development of the Sources of

Middle School Mathematics self-efficacy (SMMSE) scale (Usher & Pajares, 2009),

which was used in this study, followed by the theory that has guided research on

mathematics self-efficacy sources. This section follows a review and critique of empirical

findings on the hypothesized sources. The segment on the inter-relationship among math

self-efficacy, sources of mathematics self-efficacy, and mathematics achievement looked

at cultural attitudes towards mathematics, sources of mathematics self-efficacy, and

mathematics achievement and self-efficacy and mathematics performance—the chapter

closed with a summary.

Literature Search Strategies

The search for relevant literature for research regarding this quantitative

correlational study was conducted through Andrews University’s library databases. The

literature reviewed for this study was obtained from EBSCOhost, ERIC, ProQuest,

Dissertations and Theses @ Andrews University, and Google Scholar databases. The

gathered literature was found through a search of scholarly, peer-reviewed research

articles, books, theoretical articles, etc., on self-efficacy, self-efficacy, and academic

achievement, mathematics self-efficacy, mathematics achievement, the sources of

selfefficacy, self-efficacy as a mediator variable, and the Social Cognitive Theory.

When searching for articles to support this research study and to learn about the

previous foundations of the topic, the following terms were used: (self-efficacy in

mathematics) (self-efficacy in elementary education) (the sources of self-efficacy)

(measuring the sources of self-efficacy) (student mathematics achievement) (self-efficacy

scales) (gender and mathematics achievement). From these search terms, the following

topics were organized for this literature review: : (a) Mathematics Achievement, (b)

Factors that Influence Mathematics achievement, (c) Social Cognitive Theory, (d) Self-

Efficacy, (e)Mathematics Self-Efficacy, (f) Sources of Mathematics Self-Efficacy (g)

Self-Efficacy studies (h) Assessing Self-Efficacy (i) The Sources of Middle School

Mathematics Self-Efficacy Scale (j) Likert Scales (k) The relationship among the Sources

of Mathematics Self-Efficacy, Mathematics Self-Efficacy, and Mathematics Achievement.

Social Cognitive Theory: A Conceptual Overview

The publication. Social Foundations of Thought and Action: A Social Cognitive

Theory (1986) served to introduce Bandura’s Social Cognitive Theory. In it, he stated that

individuals are not shaped and controlled by environmental forces but are driven by their

inner impulses. Bandura contended that people were self-organizing, self-regulating,

proactive and self-reflecting (Pajares, 2006). Bandura put forward a model of reciprocal

determinism in which cognitive and other personal factors, behavior and environmental

influences interact with each other. The product of this triadic reciprocality is human

thought and action (Figure 2).

People interpret the effects of their behaviors differently, dependent on their

unique factors in cognition, affect, and biological events (Pajares, 2006). Different

perceptions cause other subsequent behaviors, which, in turn, affect and inform the

external environment—additionally, environmental feedback influences individuals’

behaviors and personal cognitive and affective factors. The interaction of this triadic

reciprocality has considerable consequences for education. To change students’ behaviors,

teachers should concentrate on how students explain personal behaviors and focus on the

environment that can influence and be influenced by students.

Figure 2: Triadic Reciprocal Determinism.

Bandura identified this theoretical model as Social Cognitive Theory to emphasize

the critical function of cognition in this theory. According to the Social Cognitive Theory,

cognition plays an integral part in individuals’ abilities, such as symbolizing, forethought,

and vicarious and self-reflective capabilities to create reality and self-regulate, encode

information, and perform behaviors (Bandura, 1986). Instead, an individual’s cognitive

depiction of the future significantly impacts their present action (Bandura, 1986). In

educational situations, teachers can introduce foreseeable outcomes to their students, such

as an incentive for good grades, which can transform future results into present

motivators. The students might recognise the importance of the consequences of having

better grades and consequently regulate themselves to work more diligently. Hence,

cognized expectations are the antecedent to actions (Bandura, 1986). So, cognition is a

mediator between individuals and their behaviors.

Social Cognitive Theory is founded on a triadic reciprocal causation model with

environmental factors, human behaviors, and personal factors. The self-system is one of

the cognitive factors in which students apply control over their thoughts, feelings, and

actions (Bandura, 2001). Bandura (1986) contended that self-efficacy beliefs are a crucial

factor influencing human behaviors. People with comparable abilities might perform

badly, satisfactorily, or exceptionally, dependent on the perception of their efficacy. Also,

the same people might accomplish differently depending on their self-efficacy levels at

other times.

Self-efficacy is one of the personal factors in Social Cognitive Theory, one of the

three components of Bandura’s concept of reciprocal determinism. Empirically, a

significant body of research on self-efficacy beliefs has validated Bandura’s Social

Cognitive Theory and shown the pivotal role of self-efficacy in human behavior.

Mathematics Achievement in Trinidad and Tobago: An Overview

In Trinidad and Tobago, the Secondary Entrance Assessment (SEA) is a national

high-stakes test for primary school students at the Standard Five level. This level is

equivalent to Grade 6 in the United States. Initially, the intent was that this assessment

would be used to select students admitted to secondary schools and, among those chosen

students, determine to which tier of secondary education the selected students would be

assigned. The SEA comprises three papers, Creative Writing, Mathematics, and Language

Arts. It covers the national curriculum for primary-level education, focusing on content

from Standards Three to Five (grades 4 to 6). Before implementing the assessment, the

Ministry of Education offered universal secondary education (USE). Therefore, the

purpose of the examination is to place students in secondary schools based on their level

of achievement.

The score on the mathematics component of the SEA determines Mathematics

Achievement at the primary school level. The mathematics component of the SEA

requires students to respond correctly to a stimulus in which the mathematical problem

might expect a single numerical response involving either one of the four rules (addition,

subtraction, multiplication, and division). Replies may require other related mathematical

concepts or knowledge, as in the Standard Five curriculum. There are also

problemsolving items in word format. These word problems might involve a single rule

or a combination of any of the four rules or might similarly require any other

mathematical concept, law, or knowledge as appears in the curriculum. Students must

respond to these word problems by showing their work or explaining how they solved

each. Word problems allow students to express their thinking methods and explain the

processes by which they obtained their answers rather than focusing solely on the final

solution as the object of assessment.

Mathematics Achievement among Primary School Students

Competency in mathematics has become a rather important skill for every

individual today. Learning basic mathematics in primary school is the foundation for

understanding higher-level mathematics concepts. Failure to master the essential

mathematics concepts will affect the ability to acquire mathematics skills at a higher

level. In addition, the inability to understand and learn mathematics concepts early also

affects students’ interest and confidence in learning new mathematics knowledge.

Students are exposed to basic mathematics knowledge at the primary-school level. This

stage plays a vital role in learning mathematics up to a higher level. A strong mathematics

foundation will ensure smooth learning of mathematics. Competency in basic numbers is

formed at an early age (Jordan & Levine, 2009). Children with mathematics difficulties

will have a problem with symbolic number knowledge, which is influenced by experience

and teaching. The absence of concept formation added to the difficulty in remembering

basic facts, resulting in students being unable to solve problems.

Fluency in basic arithmetic combinations is a challenge for students with

difficulties in basic mathematics skills and concepts (Bryant et al., 2008). Generally, most

children with mathematics difficulties show weaknesses in memory and the application of

arithmetic facts. This weakness shows that difficulty in remembering number facts is the

most common component of arithmetic difficulty. However, it does not mean that each

student with arithmetic difficulty faces problems remembering number facts (Dowker,

2005). Dowker (2005) discussed a few situations or types of arithmetic difficulties shown

by students. Some students do not have a problem remembering number facts but lack a

strategy to solve counting problems. Some students can solve single-digit arithmetic but

face difficulty understanding and mastering concepts of ones, tens and place value.

Factors that Influence Achievement in Mathematics

Researchers have studied variables that may influence students’ achievement in

mathematics (Cotton, 2003; Fennema, 2000). Researchers have also focused on variables

inside and outside of school that affect students’ achievement, such as school factors, self-

concept, self-efficacy, attitude, attribution, motivation, peer variables, and gender (Trends

in International Mathematics and Science Study [TIMSS], 2015). TIMSS is the most

extensive, comprehensive international study to analyze students’ mathematics

achievement.

Researchers have also studied the variables that may influence students’ low

achievement in mathematics: exogenous variables such as socioeconomic status, family

dynamics, and gender have been shown to impact student progress (Campbell, 1994;

Campbell & Beaudrey, 1998; Campbell & Uto, 1994; Campbell & Wu; 1996; Fenemma,

2000). Teacher and peer influences also influence students’ academic progress (Dweck,

2000; Feng, Campbell, & Verna, 2002; Fennema, 2000; Gaving & Reis, 2003; Reis, 2005;

Zvoch & Stevens, 2006). The influences of endogenous variables, including prior ability,

effort, perceived usefulness of mathematics, motivation, and math self-concept, have

been shown to produce gender differences in students’ attitudes and attribution toward

mathematics and their ultimate academic success (Dweck, 2000; Fennema, 2000; Martin,

2002). Variables that impact pupil achievement in mathematics are numerous and

confounding. Further, some variables are profoundly entrenched and stable, so speedy or

easy modification is unlikely in many cases. This study focuses on self-efficacy’s

influence on mathematics achievement, as research has shown that self-efficacy

positively influences mathematics achievement.

The role of self-efficacy and student academic achievement has been considered

numerous times through various research studies. After examining factors related to

academic achievement, even in the content area of mathematics, researchers have found

self-efficacy to be an essential construct when understanding student academic

achievement. According to Bong (2001), self-efficacy involves describing and evaluating

an individual’s perceived intellectual abilities, often based on prior experiences or

achievements in a particular content area. Several studies show that self-efficacy beliefs

are significant predictors of academic achievement (Bong, 1998; Bong, 2001; Multon,

Brown, & Lent, 1991; Robbins et al., 2004). Also, several meta-analyses reveal a high

effect size of self-efficacy on academic achievement (Multon et al., 1991; Robbins et al.,

2004). High self-efficacy beliefs factor into higher academic achievement since students

with higher self-efficacy hold stronger beliefs about mastery of content (Bong, 2001).

In addition to factoring into higher academic achievement, self-efficacy is related

to positive outcomes and student persistence (Bandura et al., 2001; Komarraju & Nadler,

2013). Moreover, students who perform poorly on math tests tend to have higher math

anxiety, which results in less confidence and overall self-efficacy (Artemenka, Daroczy,

& Nurek, 2015). Thus, students with confidence try harder and often attempt to engage in

various tasks (Komarraju & Nadler, 2013). The body of research shows that several

researchers have studied the relationships between student self-efficacy beliefs and

academic outcomes (Bandura et al., 2001; Heggestad & Kanfer, 2005; Vancouver,

Thompson, & Wiliams, 2001). These studies are significant because it has been

determined student self-efficacy influences academic motivation and achievement (Bong,

1998; Bong, 2001; Multon et al., 1991; Robbins et al., 2004).

Regarding the relationship between student self-efficacy beliefs and academic

outcomes, two patterns have emerged concerning significant correlations between (1)

student self-efficacy and future academic achievement and (2) student self-efficacy and

past achievement. Hence, considerable research demonstrates the relationship between

student self-efficacy, goal setting, and academic achievement. For example, Brown et al.

(2008) found that educational goals, self-efficacy, and academic skills predict college

retention. In addition to a positive relationship between student self-efficacy and

academic achievement, research has shown a positive correlation between past

achievement and student self-efficacy.

Four sources develop an individual’s self-efficacy. Prior mastery experiences,

vicarious experiences, social persuasion, and physiological state responses help establish

self-efficacy (Bandura, 2001). The research supports the significant influence of past

achievement on student self-efficacy. Therefore, it is vital to understand the link between

self-efficacy and past achievement when studying the correlation between self-efficacy

and academic achievement and past achievement and self-efficacy. Self-efficacy directly

reflects an individual’s ability to control motivation and behaviors (Bandura, 1977, 1986,

1990, 1997). Thus, these influence human experience and the achievement that results

from an individual’s abilities.

Self-Efficacy: A Brief Historical Overview

The concept of self-efficacy was advanced out of the social cognitive theory from

the work of Bandura (Allan, McKenna, & Dominey, 2014; Bandura, 1977). Judge, Erez,

Bono, & Thoresen (2002) describe self-efficacy as self-perceptions of our ability to

complete various tasks. Bong and Skaalvik (2011) described self-efficacy as a

multidimensional task and domain-specific construct but argue that self-efficacy lacks

some stability and hierarchy of academic self-concept. Furthermore, self-efficacy is

considered to impact a person’s choice, and pursuit of tasks since persons with high levels

of self-efficacy are more likely to take on and complete complex tasks than those with

low levels (David et al., 2009).

According to the skill-development model, self-efficacy can be affected by the

person’s level of task-related capability (Marsh & O’Mara, 2010). On the other hand, the

self-enhancement model claims that self-efficacy can affect ability. It can also affect their

academic achievement level (e.g., test scores and class grades; Khan, 2013). Moreover,

academic self-efficacy affects motivational constructs, such as ambition type, willpower,

goal setting, and assignment choices during learning processes (Khan, 2013). A study by

Schunk and Zimmerman (2009) found that persons with high self-efficacy regarded

problems as challenges or puzzles to master and habitually selected complex tasks for

completion. Maffini and Kim-Ju (2018) also observed that persons with high self-efficacy

tend to display a sense of calmness during complex problem-solving activities. The

research also shows that persons low in self-efficacy are more willing to think they lack

the essential skills to solve complex problems (Maffini & Kim-Ju, 2018). Consequently,

self-efficacy is directly associated with our sense of accomplishment and mastery

experiences (Trautwein & Möller, 2016).

Self-efficacy constructs are built on data gathered from four primary sources of a

person’s life experience: (a) mastery experiences, that is, a person’s achievement

accomplishments. For example, suppose pupils are asked to guess their prospect of

effectively writing an essay. In that case, the past pupils’ essay experiences will be the

foremost determining factor in pupil responses (Usher & Pajares, 2009). Research studies

show that mastery experiences influence pupils’ academic self-efficacy and that

social/dimensional evaluations are secondary influences (Pajares, 1996; Usher & Pajares,

2009). Scientists view mastery experiences, which happen whenever a person

successfully undertakes the completion of a task or achievement of a goal, as the most

prominent source of self-efficacy for individuals (Kiang et al., 2017), (b) vicarious

experiences, that is, a person’s observation of the performance accomplishments of

others. Vicarious experiences happen when people cannot draw on experience to achieve

a given task, so people turn to observation to solve the problem. Observation of persons

performing a task that needs accomplishment helps deduce whether the observer will do

so (e.g., If you can do it, so can I; Kiang et al., 2017). (c) social persuasion is the

reassurance or discouragement persons receive from other people while engaged in

specific activities, and (d) physiological and affective state, that is, a person’s response to

anxiety and stress, both physical and emotional, when confronted with a task. We also

know that persons “learn to interpret their physiological arousal as a measure of personal

competence by appraising their performances under differing conditions” (Usher &

Pajares, 2009, p. 90).

Usher and Pajares (2009) highlighted that “mastery experiences prove particularly

influential when persons overcome difficulties or succeed on challenging tasks” (p. 89).

Hence, it is suggested that pupils take on challenging tasks more regularly to increase

their opportunities to experience mastery. Additionally, pupils should be provided with

inquiry-based interactive learning settings since interactive learning may offer more

mastery opportunities than the traditional, less dynamic teacher-led model due to pupil

expectations for active involvement and collaborative learning (Usher & Pajares, 2009).

To that end, Bandura (1993) defined the general features of high self-efficacy

individuals: (1) persons view complex tasks as challenges to master instead of threats to

evade, (2) persons set goals that test current abilities and preserve a solid commitment to

achieving them, and (3) persons do not quit when confronted with obstacles for success.

Caprara et al. (2008) noted that such persons quickly recover their sense of self-efficacy

after being unsuccessful at a particular task. This recovery happens because they attribute

a lack of success to either inadequate drive or a deficit of knowledge and skills, which

persons regard as remediable. In academic learning, Madonna and Philpot (2013) found

that pupils can display wide-ranging levels of self-efficacy, particularly during the first

days of school (Caprara et al., 2008). The instructor’s guidance and rewards can affect

pupils’ self-efficacy because direction and incentives give them feedback on how well

they might be learning. Pupils can use this information to better evaluate their academic

self-efficacy in the future (Caprara et al., 2008).

Sources of Self-Efficacy

Studies on the sources of self-efficacy have been performed in various domains

(e.g., science, engineering, writing and mathematics). Nearly all these studies on the

sources of self-efficacy have been conducted with high school and college students.

Usher and Pajares (2008b) reviewed the empirical research investigating the four sources

of self-efficacy in academic settings. They found that mastery experience had been

consistently shown to predict self-efficacy, confirming Bandura’s (1997) theory. In all of

the examined studies, there were significant positive correlations between mastery

experience and self-efficacy (median r = .58), with mastery experience being a significant

predictor of self-efficacy in all but one study. Inferences involving the other three sources

are less consistent, often due to defective scales not aligned with Bandura’s hypotheses.

Researchers have also demonstrated that the four hypothesized sources affect the

development of students’ self-efficacy.

Many scholars have investigated gender differences in the sources of selfefficacy.

Most have found no gender differences in the strength of the correlation between the

sources of self-efficacy and self-efficacy measures (Britner & Pajares, 2006; Lent, Lopez,

et al., 1996; Pajares, Johnson, & Usher, 2007). However, investigators’ outcomes are

varied concerning gender differences in the comparative strength of the four sources.

Some researchers have identified no gender differences (Klassen, 2004; Stevens, Wang,

Olivárez, & Hamman, 2007). However, others have found that girls and boys weigh the

sources differently (Britner & Pajares, 2006; Joët et al., 2011). The nature of gender

differences in the four sources’ comparative strength may be contingent on context, such

as the domain in which the sources are assessed. In a study investigating the self-efficacy

of 295 undergraduate students, Lent, Lopez, et al. (1996) determined that men report

more mastery experiences and are less affected by physiological states than women in

mathematics. Britner and Pajares (2006) got comparable outcomes with boys and girls in

Grades 5 through 8 in science.

However, other researchers have disclosed that girls in elementary, middle, and

high school report more mastery experiences and decrease anxiety than boys in writing

(Pajares et al., 2007). Gender variations have also been observed in social persuasion and

vicarious experiences. High school girls have been shown to have more favorable social

persuasion and vicarious experiences than boys in mathematics (Lopez et al., 1997).

Similar results were obtained for elementary, middle, and high school students in writing

(Pajares et al., 2007). Other scholars have found that social persuasion was a robust

predictor of academic self-efficacy for middle school girls but not boys; however,

vicarious experience was only a significant predictor for boys (Usher & Pajares, 2006a,

2006b).

In one of the few studies exploring the sources of mathematics self-efficacy

among primary school students, Joët et al. (2011) examined the impact of the sources on

395 French third-grade students’ mathematics self-efficacy. The results of hierarchical

linear modeling showed that mastery experiences and social persuasion predicted

mathematics self-efficacy. Boys showed higher mastery experience and social persuasion

than girls, and girls revealed more elevated physiological arousal levels. The validity of

the scale employed in this study to investigate the sources has not been satisfactorily

demonstrated with a third-grade sample.

Some researchers have investigated ethnic differences in the significance of the

sources of self-efficacy. African American middle school students indicated significantly

higher physiological arousal for their academic work than White students (Usher &

Pajares, 2006b). Even though all four sources predicted academic self-efficacy for White

students, only social persuasion, physiological states and mastery experience were strong

predictors for African American students (Usher & Pajares, 2006a). In 1998, Gainor and

Lent explored the predictive power of the sources of mathematics self-efficacy among

African American college students. They stated that social persuasion, mathematics

ability, and physiological states were predictive of self-efficacy. These findings imply that

vicarious experience may not be as crucial a source of self-efficacy for African American

students.

However, both studies used questionable vicarious experience subscales not

aligned with Bandura’s recommendations, which may have prejudiced this source’s

predictive ability. No assessments have yet investigated ethnic differences in the sources

among primary school students. Few researchers have involved children younger than

middle school students in their self-efficacy sources assessments. Of the 31 studies

evaluated, four included primary school children and only two examined mathematics.

Stevens et al. (2006) investigated the sources of mathematics self-efficacy in 666 Grade 4

through 10 students. They used an SEM and found that all four sources of self-efficacy

predicted mathematics self-efficacy. Stevens et al. (2006) included mastery experience,

social persuasion and vicarious experience as one joint latent variable in the model, so no

data about these three sources’ relative predictive power could be obtained. Physiological

states were incorporated as an “emotional feedback” latent variable (Stevens et al., 2006).

The researchers did not conduct any separate analyses of data from primary school

students, so this study could not determine if there are variances in the sources of

selfefficacy for primary school students versus older students. Only third-grade students

were included in Joët et al. (2011) sample, so they could not report grade-level

comparisons in the sources of self-efficacy.

Only one longitudinal study investigated adjustments in the sources of selfefficacy

over time. Phan (2012) employed a latent growth modeling approach to examine

adjustments in mathematics and English self-efficacy sources among third- and

fourthgrade Australian students over one year. Phan used a modified version of the

Matsui (1990) Sources of Information Questionnaire to measure the self-efficacy sources.

He employed a task-specific self-efficacy scale. Results showed that mastery experience

and social persuasion were positively related to students’ initial mathematics and English

self-efficacy. Mastery experience was positively correlated with the shift in self-efficacy

over time for mathematics and English, while physiological states were negatively related

to a change in mathematics self-efficacy.

Mathematics Self-Efficacy

Tait-McCutcheon, (2008) described mathematics self-efficacy as a belief in how

well students can learn mathematics. The amount of self-efficacy controls how the

students deal with mathematics tasks. Students with high self-efficacy perceive difficult

mathematics tasks as achievable and maximize their efforts to solve them (Pajares, 1997).

Such pupils tend to be highly interested in mathematics problems and motivated to solve

them (Pajares, 2005). Investigations discovered a positive correlation between

mathematics self-efficacy and problem-solving capability (Pajares & Miller, 1994;

Pajares & Krenzler, 1995). Notably, high levels of self-efficacy do not ensure

problemsolving capacity when pupils face demanding mathematics tasks. As an

alternative, high self-efficacy urges pupils to solve problems and gives them fortitude and

determination until the problem is effectively solved (Pajares, 2005). Self-efficacy also

impacts pupils’ use of appropriate cognitive strategies, which help them work out

mathematics problems (Pintrich & DeGroot, 1990).

Many countries’ mathematics achievement levels were not at the anticipated level

(Mullis, Martin, Robitaille & Foy, 2009). Investigators conducted many studies to explain

this situation and discovered many variables affecting attainment. Anxiety about

mathematics and self-efficacy are the variables that have gotten the most attention

(Walsh, 2008). The findings of many of these studies revealed that self-efficacy is the best

predictor of mathematics achievement and attainment (Fast et al.., 2010; Lindley &

Borgen, 2002; Pajares & Kranzler, 1995; Ferrari & Parker, 1992; Pajares & Miller, 1994;

Pajares, 1996; Siegel, Galassi & Ware, 1985; Schunk, 1989, 1991; Stevens et al., 2004).

A few studies found a positive correlation between self-efficacy and achievement

(Pajares, 1996; Hackett & Betz, 1989; Pajares & Graham, 1999; Randhawa, Beamer &

Lundberg, 1993; Peitsch, Walker & Chapman, 2003; Stevens et al., 2004). It is important

to note that there is a reciprocal association between self-efficacy and achievement.

Consequently, self-efficacy increases achievement and achievement, in turn, positively

influences self-efficacy. Many researchers studied the combined effect of self-efficacy

with other variables to predict mathematics achievement (Dumais, 2009; Pajares &

Miller, 1995; Pajares & Kranzler, 1995; Stevens et al., 2004). One research study by

Pajares & Miller (1995) found a negative correlation between self-efficacy and

mathematics anxiety; they stated that self-efficacy was more predictive of achievement

than anxiety. Bryan, Glynn & Kittlesson (2011) found that mathematics achievement was

correlated with self-efficacy, intrinsic motivation, and self-regulated decision-making, of

which self-efficacy was the best predictor of achievement. Numerous studies examined

the association between sources of self-efficacy and mathematics self-efficacy in the U.S.

(Lent, Lopez & Bieschke, 1991; Lopez & Lent, 1992). Lent Lopez and Bieschke (1991)

found that all self-efficacy sources correlate significantly with each other and with total

mathematics self-efficacy scores. They also investigated the association between sources

of self-efficacy and mathematics achievement, which revealed that (mastery experiences

(r = 0.54), social persuasion (r = .44), and physiological states (r = -.38) have

significantly correlated with achievement. Lopez and Lent (1992) had similar

conclusions. Both studies found that mastery experiences and social persuasion correlated

with self-efficacy. Studies in France and Turkey analyzed the association between

selfefficacy and the sources of mathematics self-efficacy (Arslan, 2012; Joët, Usher &

Bressoux, 2011). Arslan (2012) used a sample of 1049 Turkish students to study the

sources of self-efficacy for learning mathematics and achievement. He learned that only

social persuasion and mastery experiences were meaningfully correlated with selfefficacy

for learning mathematics and achievement, with mastery experiences having a higher

correlation with these two outcome variables.

Sources of Mathematics Self-Efficacy

Bandura (1997) hypothesized four sources of self-efficacy. These sources are

mastery experiences, vicarious experiences, social persuasion, and physiological states.

One must ground the investigation on the self-efficacy theory to explore self-efficacy in

any setting. Usher and Pajares (2006) studied 6th grades and stated that all self-efficacy

sources were predictive of self-efficacy; however, not all the sources were equally

weighted. This analysis revealed that mastery experience and social persuasion correlated

significantly with self-efficacy.

Mastery experiences can be developed by teachers through the problems they

formulate for the students. Teachers should provide opportunities for students to

demonstrate their mastery level; this should be done while still maintaining a challenge to

students (Usher, 2009). Usher and Pajares’ study of self-efficacy in middle schoolers

(2006) revealed that mastery experiences accounted for the most significant variance.

Similar results were found in a survey of college students (Lent, Brown, Gover, & Nijer,

1996), with the researchers suggesting that recent success, or mastery experiences, may

be of most significance later in life. One relies on past performance to determine

selfefficacy when encountering a previous topic. Males rely more on mastery experiences

to evaluate their mathematics self-efficacy, as they are more likely to evaluate themselves

by their achievements and failures (Usher & Pajares, 2006).

Students witnessing a classmate succeed at a mathematics problem can develop

the perception that they can be successful (Usher & Pajares, 2008). Modeling is a source

of vicarious learning (Usher, 2009). Students judge their abilities by likening themselves

to their classmates. Teachers should provide opportunities for peers to model their

problem-solving in class. Witnessing a peer as a model has a more significant impact on

self-efficacy than observing the adult as a model (Schunk, 1991).

Social persuasion has been shown to play a more critical role than mastery

experiences in informing mathematics self-efficacy for females (Usher & Pajares, 2006).

Social persuasion can provide encouragement and discouragement; in some cases,

students can be dissuaded from following certain academic paths. Classmates and parents

are also sources of social persuasion. Classroom culture can influence attitudes towards

mathematics (Sullivan, Tobias, & McDonough, 2006). Antagonistic classrooms can affect

students of all self-efficacy levels. Similarly, antagonistic households and parents’

comments can affect self-efficacy.

Physiological states also impact self-efficacy (Bandura, 1997). The experience of

a heightened state of excitement in the classroom can positively and negatively affect

pupils (Usher, 2009). Students with a high sense of self-efficacy would be encouraged by

this heightened state of excitement, while those with low self-efficacy would feel

depressed or discouraged. These sensitive states have magnified feelings of uncertainty,

anxiety, or apprehension. This apprehension is predominantly real for pupils placed into

low-attainment groups. A student placed in a low-attainment group has little to no

mastery experiences, has fewer chances to observe others succeeding, and is dissuaded by

social persuasion. For these students, physiological arousal will be the dominant source of

self-efficacy (Usher & Pajares, 2006). Students in below-level ability groups are inclined

to be more anxious. Consequently, their physiological states intensify negatively, leading

to low self-efficacy for the subject matter.

Assessing the Sources of Self-Efficacy in Mathematics

Scholars have used qualitative and quantitative methods to explore the sources of

self-efficacy. Usher and Pajares (2009) reviewed measures of the sources of self-efficacy

in various areas. Although comparatively little qualitative research has been done,

investigators have used interviews and open-ended measures to learn more about the

factors that lead to the development of self-efficacy (Lent, Brown, et al., 1996; Zeldin &

Pajares, 2000). Qualitative research can give a unique insight into how the sources impact

students’ self-efficacy and could even reveal new sources of self-efficacy. Qualitative

research, however, can be time-consuming and sacrifices the generalizability of results

because of the small sample sizes.

Most researchers have used rating scales and self-report measures to assess the

sources of self-efficacy. The Sources of Mathematics Self-Efficacy Scale (SMES),

developed by Lent et al. in 1999, is used by many researchers to investigate efficacy

sources in mathematics. This SMES is a 40-item scale with 10-item for each of the four

self-efficacy sources. The SMES was designed to assess the self-efficacy of college

students. The scale has been modified by researchers for different people and contexts

(Anderson & Betz, 2001; Britner & Pajares, 2006; Lopez & Lent, 1992; Smith, 2001).

The SMES is limited in tangible ways, namely the design of the physiological states

subscale. The physiological states subscale was measured using a modified version of the

Mathematics Anxiety scale from the Fennema-Sherman Mathematics Attitudes Scales

(Betz, 1978), which utilizes only one facet of this source of self-efficacy as hypothesized

by Bandura. The physiological states subscale overlooks other factors, such as mood,

stress, fatigue, and physical strength, which may not afford a complete picture of this

source. The vicarious experience subscale of the SMES has also demonstrated low

internal consistency (Gainor & Lent, 1998; Lent et al., 1991).

A revised 24-item version of the SMES was used to evaluate the sources of

mathematics self-efficacy of 395 third-grade French Joet et al. (2011). The alpha

coefficients for the revised scale were appropriate for mastery experience, social

persuasion, and physiological states (ranging from .83 to .89). Still, the internal

consistency for vicarious experience in this scale was still below acceptable values (α =

.61). No factor analysis was conducted on the scale to provide evidence for this measure’s

validity, demographic factors, such as age, can influence the factor structure (Lent, Lopez,

Brown, & Gore, 1996). Using a measure designed for older students with a different

sample without first checking its validity with the new sample can lead to false findings.

Several investigators have used other scales or constructed their own items to assess the

sources (Bates & Khasawneh, 2007; Hampton, 1998; Matsui et al., 1990).

Several of these items align poorly with Bandura’s Social Cognitive Theory.

Usher and Pajares (2009) developed a new measure closely aligned with

Bandura’s (1997) thinking to examine the sources of mathematics self-efficacy in middle

school students. They examined internal consistency, content validity, convergent and

divergent validity, and construct validity in a three-phase process. The psychometric

properties of the items were good, including measurement invariance across gender,

ethnicity, and mathematics capability. The alpha coefficients for four subscales were good

(mastery experience: α = .88; social persuasion: α = .88; vicarious experience: α = .84 and

physiological states: α =.87 The fit indices for the confirmatory factor analysis

measurement model were acceptable, and the factor loadings ranged from .61 to .83.

Development of the Sources of Middle School Mathematics Self-Efficacy Scale

The Sources of Middle School Mathematics self-efficacy (SMMSE) scale (Usher

& Pajares, 2009) was developed in three phases guided by Spector (1992) Spector’s

(1992) authentication protocol. The initial step was to construct items to measure each

source; this included having suitable stakeholders (e.g., students and teachers) review

items for clarity. The survey was then administered with a more significant sample of

middle school students for the first assessment of psychometric fitness leading to a

revision of the first instrument. The next phase focused on conducting an exploratory

factor analysis (EFA) using a new set of students, with the outcome of this analysis

leading to additional refinement of the questionnaire. The third stage included having

leading scholars in self-efficacy, including Albert Bandura, evaluate and further improve

the instrument’s wording. This final development stage also included performing a

confirmatory factor analysis (CFA) using different students. The findings in the three

steps led to the SMMSE scale (Usher & Pajares, 2009) used in this study. These stages

are described in the following segments and will identify the participants, data sources,

conducted analyses, and the results for every phase.

Phase 1.

Participants.

The first phase in developing the SMMSE scale focused on creating items and conducting

an initial analysis of the psychometric fitness of the scale (Usher & Pajares, 2009, p. 92).

A focus group comprising 23 sixth-grade students, a sixth-grade teacher, an eighth-grade

teacher, a principal, and a parent provided feedback on the instrument’s wording and

clarity. A few weeks later, a revised survey was administered to 1111 (552 boys, 225 girls)

registered in Grades 6 and 7(n = 373). Many participants were of uppermiddle

socioeconomic status, and 67% (n = 677) identified themselves as White.

Data sources.

Items were constructed as first-person declarations, which asked students to rate how

false or true a given declaration was to them on a scale of 1 (definitely false) to 6

(definitely true). Phase one of this survey consisted of 84 items, including 21 mastery

experience items, 20 social persuasion items, 23 vicarious experience items, and 20

physiological-affective items. Students answered each self-efficacy measure on a Likert

scale from 1 (not in any way confident) to 6 (completely optimistic).

Analysis.

Initial analysis of this Phase 1 data contained a descriptive exploratory examination

before fitting their data to some statistical model (Usher & Pajares, 2009, p. 92). This

phase assessed each data set’s means, standard deviations, frequency distributions,

skewness, and kurtosis. Construct validity was assessed using the bivariate correlation

with the subscale total with each of the four self-efficacy measures. Items were expected

to possess moderate correlations with the self-efficacy outcomes (|r| > .30); those with

smaller correlations were flagged for removal. Internal consistency was assessed using

Cronbach’s alpha coefficients. Items with poor item-to-item scale total correlations (r <

.40) were flagged for removal. The last stage of data screening was supposed to find

consistency across measures. Items flagged based on two criteria (e.g., high skewness,

kurtosis, or weak correlations) were deleted or revised.

Results.

Of the first 84 items, 23 were identified as performing poorly, and 13 were found inside

the vicarious experience subscale alone. This finding separated the vicarious experience

subscale into three sub-factors (peers, adults, and self), resulting in 10 problematic

products. These problems reflect previous difficulties in producing internally consistent

items to measure this specific source, particularly mathematics (Usher & Pajares, 2009, p.

9-3). Correlational analyses demonstrated that roughly 45% of the correlations were

below |.30|. New items were generated from poorly performing issues identified from

removed Phase 1 items.

Phase 2.

Participants.

The next phase of the SMMSE scale development centered on running an exploratory

factor analysis (EFA) to ascertain the nature of Bandura’s hypothesized sources of

efficacy influences on a set of responses (Usher & Pajares, 2009, p. 92). The revised

questionnaire was administered to 824 students (389 boys, 435 girls) registered in Grade

6 (n = 248), Grade 7 (n = 259) and Grade 8 (n = 317). Many participants were of

uppermiddle socioeconomic status; 66% (n = 546) identified themselves as White, and

21% (n = 172) were registered to get free or reduced-price lunches.

Data sources.

Items that revealed some psychometric weakness from the SMMSE scale were altered,

and items were added to reinforce the defects in the scales. In particular, items were

added to better assess vicarious experiences and social persuasion factors. The Phase 2

survey contained 86 items: 12 assessing mastery experiences, 28 assessing social

persuasion, 30 assessing vicarious experiences, and 16 assessing physiological states. The

same self-efficacy instrument from Stage 1 was used in Stage 2. Internal consistency of

self-efficacy measures ranged from .89 to .94.

Analysis.

The exact cutoff criteria for psychometric fitness for Phase 1 were employed for the

phase two study, which included the skewness (-2.0 to 2.0) and kurtosis (-7.0 to 7.0)

cutoff amounts recommended by Kline (2005). Phase 2 analysis’s primary purpose was

to conduct an exploratory factor analysis (EFA) to ascertain if four distinct factors could

be identified using the remaining student items that demonstrated good psychometric

fitness. This analysis comprised squared multiple correlations to gauge every item’s

communality and analyze the eigenvalues linked with each factor. An oblique Promax

rotation was employed because the proposed items were theorized to be correlated.

Variables that loaded onto more than one factor and variables with factor loading less

than |.35|. were omitted.

Results.

The cutoff criteria for descriptive data for Stage 2 were identical to those used in Phase 1

of this scale development. Thirty-five low-quality items were removed, which left 51

items for the EFA analysis; factor 1 described 70% of the variance, factor 2, 11%, factor

3, 7 %, factor 4, 4%, and factors 5-7 each reported 3% or less of the variance. The scree

plot proposed that a four-factor model best described the variance. The factor analysis

was performed again using a four-factor model with items with a factor loading over |.35|,

which caused a 39-item final version for Stage 2. Factor 1 comprised of thirteen items

(loadings ranged from .36 to .84), factor 2, 10 items (loading from .53 to .90), factor 3, 10

items (loadings from .40 to .75), along with six items loaded onto factor 4 (loadings in .44

to .66). These factors were subsequently categorized as (1) social persuasion; (2)

physiological states; (3) vicarious experience; and (4) mastery experience. Together, these

four variables reported 98 % of the variance. Inter-factor correlations ranged from .29

(mastery & vicarious experiences) to .60 (mastery experiences & social persuasion).

Items within each factor also exhibited good internal consistency (α range from .85 to

.92).

Phase 3.

Participants.

The third stage in developing the SMMSE scale centered on further optimizing the

instrument using a confirmatory factor analysis (CFA) to ascertain the ability of

Bandura’s four sources of self-efficacy factor model to fit the observed data set (Usher &

Pajares, 2009, p. 92). This stage also included asking three reputable authorities in the

self-efficacy theory (Bandura, Zimmerman, and Schunk) for their comments on the final

items. The revised survey was administered to 803 students (395 boys, 408 girls)

registered in Grade 6 (n = 282), Grade 7 (n = 255) and Grade 8 (n = 266). Most

participants were of upper-middle socioeconomic standing, 67% (n = 541) identified

themselves as White, and 19 % (n= 153) were registered to receive free or reduced-price

lunch.

Data Sources.

The Stage 3 instrument comprised 73 items, including the 39 objects from Stage 2 and

modified items excluded from the Stage 2 evaluation. For convergent and discriminant

validity, several motivational items were included as part of Stage 3. Additional factors

were selected because they have been proven to correlate with self-efficacy; thus, they

ought to correlate with the four sources.

Analysis.

For Stage 3, a confirmatory factor analysis helped determine the best model that

characterized self-efficacy sources’ straightforward structure. The identical cutoff criteria

for descriptive statistics were employed in Stage 1, although more rigorous standards

eliminated items demonstrating excessive skewness and kurtosis. Item-total correlations

were analyzed next, where items using subscale correlations less than or equal to |.55|

were identified, and items under |.30| to other subscales were also recognized for removal.

This removal led to a tight final sources scale, which was practical, conceptually, and

psychometrically strong. The next phase of this instrument development was a

confirmatory factor analysis to test their remaining measurement model. The authors

relied on four commonly-used indices to ascertain the fit of each CFA version: the

Satorra-Bentler (S-B) χ2 test statistics, used when data are nonnormally distributed,

which had been the case with information from this research; the comparative fit index

(CFI); the root mean square error of approximation (RMSEA); and the standardized root

mean square residual (SRMR) (Usher & Pajares, 2009). The authors also analyzed

significance tests for variable loadings, values, remaining and normalized residual

matrices, and modification indices such as Lagrange Multiplier (L.M.) when analyzing

each model.

Results.

Of the 73 Stage 3 items, 34 were removed from descriptive statistics, and five similarly

worded items were eliminated, leaving 34 items. Twenty-four items were chosen from

this collection of items based on psychometric and theoretical considerations (Usher &

Pajares, 2009). The model’s standardized- factor loadings were significant at the same .05

level and ranged in magnitude from .61 to .83. The four source factors demonstrated

intercorrelations varying in size from -.45 (between vicarious experience and

physiological states) to .83 (between social persuasion and mastery experience).

Evidence of Construct Validity

Several data sources supported the construct validity of this SMMSE scale,

including convergent validity with all self-efficacy measures and other related constructs

and discriminate validity with unrelated constructs (Usher & Pajares, 2009). Correlations

between sources and four self-efficacy scales utilized (mathematics grade self-efficacy,

mathematics courses self-efficacy, math skills self-efficacy, and self-efficacy of

regulatory learning) were significant (p < .001). Strong correlations were observed

between self-efficacy sources and relevant motivation constructs, such as self-concepts

and invitations. The self-efficacy sources also revealed strong correlations to pupil

achievement measures. The instrument demonstrated discriminating validity to unrelated

concepts such as self-efficacy and performance-approach goals. The authors also sought

to ascertain all four hypothesized sources’ contributions to predicting middle school

students’ math self-efficacy. They ran four distinct regression analyses of self-efficacy

sources to the four self-efficacy outcome variables - grade self-efficacy, math skills

selfefficacy, course self-efficacy, and self-efficacy for self-regulated learning. Mastery

experiences were the strongest predictor of three out of four outcome measures. Vicarious

experience has been the most potent predictor of self-efficacy in self-regulated learning,

with mastery experiences being the second most decisive factor.

Overall, the findings support Bandura’s (1997) claim that mastery experience is

the strongest predictor of all self-efficacy beliefs. The results also support Bandura’s

contention that weights individuals assign to several sources are not identical across

contexts. The predictive ability of each source can vary with various subjects. For

example, the predictive power of each source may vary with different content areas. Thus,

it is necessary to establish reliable self-efficacy measures for use in particular settings.

The SMMSE scale is a carefully designed and validated instrument to measure middle

school students’ self-efficacy in mathematics.

Assessing Self-Efficacy

Bandura (1997) proposed that strict adherence to content and context specificity in

self-efficacy studies is compulsory to yield valid results. According to Pajares (1996),

such compliance to uniqueness in self-efficacy measurement is often ignored in

educational research. The specificity of content relates to how precisely an efficacy

measure relates to the criteria tasks on which achievement is assessed. Pajares proposed

that self-efficacy beliefs should be measured at the specificity level that matches the

requirements task. This specificity might mean measuring self-efficacy for individual

statistics problems, particular geometry problems, etc. There are two direct concerns with

measurement correspondence at this level. First, it seems questionable that a student with

high self-efficacy for one statistics problem would have low self-efficacy for another

statistics problem. Second, self-efficacy measurement at such a specific level may mean

that every self-efficacy investigation requires a tailored instrument.

A more likely situation concerning mathematics self-efficacy patterns might be

that pupils with high self-efficacy for statistics per se could have either low or high

selfefficacy for, say, geometry or another mathematics area. On the other hand, a pupil

might have either high or low self-efficacy across the mathematics field. Thus,

mathematics self-efficacy might best be evaluated by adherence to domain

correspondence rather than specific task correspondence. Scores on such a scale might

show a unifactorial structure for mathematics or disclose a structure that discerns

statistics from geometry or fractions and decimals from geometry. Establishing what

specificity prevails to advise effective treatments (e.g., teaching, counseling) and future

investigation applications are crucial.

Likert Scale

The literature on self-efficacy scales has led to inconsistent recommendations for

measurement. This variation is partly due to contextual (e.g., domain, population)

differences across studies and the specific measurement approach used (e.g., classical test

theory, factor analysis, and generalizability theory). In research by Toland and Usher

(2016), a Rasch modeling method was used to assess the utility of two response scale

presentations to measure middle school students’ mathematics skills self-efficacy. The

results show that early adolescents’ responses to two scales—a 100-point scale suggested

by Bandura (2006) in his Guide for Constructing Self-Efficacy Scales and a 6-point

response scale regularly used in educational psychology research—are condensed into

four categories. After adjustments, the optimal number of response scale points was not

equal to the number of rating scale points presented to early adolescents on the original

version of the two self-efficacy forms. This finding suggests that more than four

categories are not ideal for this age group. Toland and Usher’s results are consistent with

Smith et al. (2003). The latter found that upper elementary pupils used four categories

despite being given a 0 to 100 response scale in 10-unit increments to measure their

writing self-efficacy. Furthermore, self-efficacy data from two independent samples

condensed into four categories offers preliminary evidence of stability and

generalizability.

One plausible explanation for this discovery is that when pupils judge what they

can do, their judgment boils down to four uncomplicated categories: I cannot do this, I’m

not sure that I can do this, I am pretty sure I can do this, I can definitely do this. Perhaps

children’s efficacy judgments are not more nuanced than that. Another explanation is that

early adolescents’ working memory capacity is restricted to three to five categories, and

offering more response choices induces an unnecessary cognitive burden (Cowan, 2010).

As noted, it could be that the better one’s level of expertise, the greater one’s capability to

make more fine-tuned self-judgments. Older pupils (e.g., undergraduates and graduates)

who are more acquainted with the demands of a given academic domain, such as

mathematics, might be better prepared to make more nuanced judgments about their

abilities to handle those demands (Weil et al., 2013). On the other hand, domain expertise

is not the only feature that explains whether persons think of their efficacy in more

complex terms. Individuals who enjoy a heightened awareness of themselves and their

capacities may make more nuanced appraisals of what they can do.

Persons might ask whether there is a practical benefit to a 4-point scale over a

6point range. I believe there is a benefit. Most noticeably, providing early adolescents

with fewer response categories reduces their cognitive load and thus increases the

possibility of completing surveys. Additionally, findings suggest that scholars may not

gain, and may indeed lose, in their understanding of self-efficacy and its correlates when

using response scales that comprise too many categories (Toland & Usher,2016).

Including more than four categories or too many categories on a self-efficacy response

scale might lead to unsystematic measurement error or less data (Smith et al., 2003) and

possibly correlations and effect sizes that may be misleading. Given these results and the

findings of Embretson (1996) and Kang and Waller (2005), we might speculate that

results would be misleading in inflated correlations and effect sizes.

Toland and Usher (2016) recommend that investigators studying self-efficacy and

related motivation paradigms with early adolescents use the approach they used in

Assessing Mathematics Self-Efficacy: How Many Categories Do We Really Need?, and

by Smith et al. (2003) for enhancing the number of rating categories of instruments. This

method increases the reliability and validity of group and individual-level inferences. A

secondary finding from Toland and Usher’s study was that categories in the middle of the

response scale tend to collapse more often than those near the anchor labels. This finding

suggests that labeling each response selection, not just the endpoints, might help escape

ambiguity in the meaning of response categories. Leaving unlabeled categories may

present error, “as the meanings of these unlabeled intermediate categories must be

formed by each individual, leading to undesirable response sets” (Smith et al., 2003, p.

387).

Furthermore, findings suggest that while fewer categories could increase the

validity of early adolescents’ responses, collapsing too many categories results in a loss of

separation and reliability and is not optimal. Likewise, too many categories can present

an avoidable measurement error (Smith et al., 2003). Whatever their analytical choice,

researchers should remember that the inferences drawn about a construct such as

selfefficacy are only as reasonable as the measurement instrument used to reflect that

construct. Therefore, it is recommended that researchers provide empirical evidence for

the response scale used to improve statistical conclusions and construct validity.

Interrelationships among Mathematics Self-Efficacy, Sources of Mathematics

SelfEfficacy, and Academic Achievement

Students come across misconceptions about mathematics in everyday life. I have

often listened to students and parents making unfavorable claims about their math

abilities in my thirty-six years of teaching primary school students. The ease with which

persons make statements about their inability to do math makes it socially acceptable to

not be good at math and delivers the message to students that its ok to be bad at math

(Provasnik, Kastberg, Ferraro, Lemanski, Roey, & Jenkins, 2012). The contrasting

perception of math is seen in countries like China and Taiwan, which outscore the United

States and other western countries on international benchmarking assessments (Provasnik

et al., 2012). Wei and Eisenhart (2011) found a considerable difference in the opinion of

mothers towards their child’s mathematics abilities in a study of 15-year-olds conducted

in the United States and Taiwan. They detected a substantial difference in mothers’

opinions about their child’s mathematics abilities. Asian mothers considered that

mathematics academic achievement resulted from effort, while American mothers

presumed it resulted from intelligence or innate ability. The opinion of U.S. mothers

influences their children, who also believe they require a natural ability to be good at

math (Provasnik et al., 2012). The Trends in International Mathematics and Science Study

(TIMSS) results of 2011 show that Taiwan ranked 3rd, with a score of 609, while the

United States ranked 9th, with 509 for the 8th-grade mathematics assessment (Provasnik

et al., 2012). There are also differences in how the students in both countries are

educated. Asian students spend many more hours at school receiving tutoring, especially

math, than American students (Wei & Eisenhart, 2011).

There is a common belief that some students cannot do math and that math is not

essential (Schmidt, 2012). Fredricks & Eccles, 2002 reported a decline in the perception

of one’s capabilities to do math as early as first grade persisting through grade twelve.

Students may believe they were not born to do math or were too stupid to learn it.

(Adelson & McCoach, 2011).

But, by fifth and sixth grade, students begin to think that everyone can learn math

and that low achievers result from an absence of effort—the significance of students’

relationship with mathematics changes over time. Student perceptions of the significance

of mathematics decrease from grades three through nine but rise again from classes ten

through twelve as they consider their future educational and employment paths (Fredricks

& Eccles, 2002).

There is a bit of tension in the literature concerning attitude and attainment in

mathematics. Lipnevich, MacCann, Krumm, Burrus, and Roberts (2011) show

that cognitive and attitudinal factors are crucial for mathematics success. They

state that attitudes towards mathematics explain 25-32% of mathematics grade

variance and perceived behavior control. They found that the more favorable a

student’s perception, the more likely they will do well. Subjective norms refer to

the social burdens existing in the learning environment. Perceived behavioral

control denotes the degree to which a person has confidence that they can perform

a specific behavior.

In contrast, Ma and Kishor (1997) discovered a weak positive association between

mathematics attitude and mathematics achievement. Their meta-analysis indicates a “not

significant” or “significant to not strong” effect size. Their overall stated effect size was

0.12, which according to Hattie (2009), is produced if the student did not attend school, in

which case the progress or maturation of the student alone would account for this

outcome. Ma and Kishor’s (1997) analyzed the cause-and-effect correlation between

attitude and mathematics achievement. Attitude toward math produced an effect size of

0.08 in mathematics achievement, while the reverse relationship showed an insignificant

impact.

Sullivan, Tobias, and McDonough (2006) claimed that attainment does not predict

a student’s orientation toward learning math. They wrote that even students who are

successful in mathematics choose not to engage; they proposed that this is caused by the

social pressures in the classroom, which shows how the school’s culture contributes to

students’ persistence and effort. Iben (1991) discovered that the intrinsic motivation to

study math is established in the early middle school years. Nevertheless, she went on to

say that internal drive was a substantial predictor of mathematics achievement for boys

aged 13 and 14; it was not for girls of that age range. However, Ma and Kishor (1997)

correlate drive to attitude and achievement at several ages or grade levels. The association

was not stable at the elementary level. Still, at the secondary level, the effect was robust

enough for practical consideration, with the junior high period being the most important.

Mathematics self-efficacy and mathematics achievement are correlated (Ayotola

& Adedeji, 2009; Bandura, 1993; Bouffard, Boileau, & Vezeau, 2001; Hackett & Betz,

1989; Khezri azar, Lavasani, Malahmadi, & Amani, 2010; Liu, 2009; Pajares & Graham,

1999; Pajares & Miller, 1994; Puklek Levpuscek, Zupancic, & Socan, 2013; Stevens,

Olivarez, Jr., Lan, & Tallent-Runnels, 2004; Usher & Parajes, 2008; Zimmerman, 2000).

Mathematics self-efficacy is an essential predictor of future mathematics achievement

(Hackett & Betz, 1989; Chen, 2003; Stevens, Olivarez, Jr., Lan & Tallent-Runnels, 2004).

Students with high mathematics self-efficacy care about more profound learning styles

and avoid surface learning (Khezri azar, Lavasani, Malahmadi, & Amani, 2010; Ayotola

& Adedeji, 2009). This more profound learning or “learning for understanding” allows

for transfer between learning situations and, subsequently, more excellent mathematics

academic achievement.

Bandura (1993) noted that students with high self-efficacy would have a higher

proportion of accurate math solutions when compared to students with low self-efficacy

at all ability levels. In comparing 15-year-old students from the United States and Hong

Kong, Liu (2009) discovered that mathematics self-efficacy was the most significant

predictor of mathematics achievement in both countries, according to the 2003

Programme for International Student Assessment (PISA) results. Mathematics

selfefficacy was also positively correlated with the final grades earned in a mathematics

assessment, as Puklek Levpuscek, Zapancic, and Socan (2013) determined.

An investigation has also revealed no significant difference in males’ and females’

mathematics attainment or mathematics self-efficacy (Ayotola & Adedeji, 2009). Females

display a weakness in mathematics self-efficacy and mathematics in general, but they do

not show weakness in specific and contextual mathematics. Students who self-regulate

their mathematics learning will nurture their mathematics self-efficacy beliefs (Usher,

2009). The correlation between mathematics self-efficacy and mathematics achievement

is evident.

If self-efficacy in mathematics drops, so too can attainment in mathematics.

Teachers play a crucial role in promoting student self-efficacy in mathematics,

influencing students’ mathematics achievement (Kitsantas, Cheema, & Ware, 2011;

Puklek Levpuscek, Zupancic, & Socan, 2013). By emphasizing mastery, being insistent

on understanding, and permitting time for students to explore thoughtful and meaningful

problems, teachers provide the opportunity to augment student self-efficacy (Puklek

Levpuscek, Zupancic, & Socan, 2013). When teachers regulate homework according to

the available resources, they improve individual students’ self-efficacy (Kitsantas,

Cheema, & Ware, 2011). Parents also promote self-efficacy by providing as many

homework resources as feasible and enabling the homework process. Teachers and

parents can positively impact mathematics academic achievement by consciously

attending to mathematics self-efficacy.

While many factors impact students’ success, low academic achievement is often

linked to self-efficacy by many contemporary education researchers (Gushue, Clarke,

Pantzer, & Scanlan, 2006; Witherspoon, Speight, & Thomas, 1997). The four

hypothesized self-efficacy antecedents have revealed that self-efficacy is a robust

predictor of pupils’ mathematics success (Luzzo, Hasper, Albert, Bibby, & Martinelli,

1999). Self-efficacy and the consequent outcome expectations impact motivation and

persistence in facing challenges and adversity (Pajares, 1997). These views regulate how

people think, feel, motivate, and behave (Pajares, 1997). Persons with low self-efficacy

tend to shy away from demanding tasks beyond their capabilities (Bandura, 1986).

Likewise, persons with high self-efficacy enthusiastically take part in these challenges

because they are confident they can get the better of them (Bandura, 1986). The pupils’

self-efficacy plays a crucial role in their choices (Chen & Zimmerman, 2007; Pajares &

Miller, 1997) in that pupils will be drawn toward and have a positive attitude toward

events in which they have the self-confidence to do well.

Summary

The purpose of this chapter was to review the literature applicable to the research

question of this study. Mathematics Achievement at the primary school level in Trinidad

and Tobago is determined by the Secondary Entrance Assessment (SEA) mathematics

component. Researchers have studied the many variables that may influence students’

low achievement in mathematics, both exogenous and endogenous variables. This study

focuses on the role of self-efficacy in mathematics achievement.

Several studies disclosed that self-efficacy is the best predictor of mathematics

achievement and attainment (Fast et al.., 2010; Ferrari & Parker, 1992; Lindley &

Borgen, 2002; Pajares & Kranzler, 1995; Pajares & Miller, 1994; Pajares, 1996; Schunk, 1989,

1991; Siegel, Galassi & Ware, 1985; Stevens, Olivare, Lan & Tallent-Runnels, 2004). A few studies

observed a positive correlation between self-efficacy and achievement (Pajares & Graham, 1999;

Randhawa, Beamer & Lundberg, 1993; Pajares, 1996; Peitsch, Walker & Chapman, 2003; Stevens

et al., 2004).

Considerable research has been undertaken over the last twenty years to support

Bandura’s (1997) self-efficacy theory. The concepts of self-efficacy and its four sources,

derived from social cognitive theory, provided the foundation for the research and were

discussed in this section. The first concept discussed was self-efficacy, whose main idea

was how this self-evaluation of one’s abilities motivates behaviour, initiation, and

persistence (Bandura, 1977). It is a context-specific construct, varies across domains, and

is shaped by experience and environment (Bandura, 1978). This emphasis on selfefficacy

is relevant as secondary and tertiary institutions are concerned about students persisting in

their academic programs.

The second and associated concept was the four self-efficacy sources: mastery

experiences, verbal persuasion, vicarious experiences, and physiological states. Each

source provides individuals with information for their self-appraisal, with a unique level

of influence per source and circumstance (Bandura, 1977). Bandura (1986,1997)

theorized that mastery experience is a reliable predictor of students’ self-efficacy across

academic domains and levels. Undoubtedly, students who interpret their past

achievements as successful will likely reinforce their self-efficacy beliefs. Less consistent

results have been reported for the other three sources. These inconsistent results are often

due to methodological complications such as low reliability of items on a particular scale,

combined scores that mask information from one source, or multicollinearity between the

sources. What seems clear is that the contextual features at work across studies partly

determine how the sources have operated in diverse academic settings. Variances in the

sources’ predictive value depend on the domain in which the constructs are measured.

Their size and relationship with self-efficacy influence students’ group membership(s) or

academic ability indexes. It is yet too early to make general observations about the part

played by these contextual influences. Still, initial findings make evident the need for

future investigators to identify the various forces students contend with when forming

their self-efficacy beliefs.

The predictive power of each source may vary with different subjects. Thus, it is

essential to establish reliable self-efficacy measures in specific settings. The SMMSE

scale is a carefully designed and validated instrument to measure sources of self-efficacy

beliefs in mathematics with middle school students. A detailed outline of the development

of the SMMSE was included in this literature review. A look at the research relevant to

adolescents’ use of the Likert scale was also included. Toland and Usher (2016) found a

practical benefit to a 4-point scale over a 6-point range for an adolescent sample. I believe

there is a benefit. Most noticeably, providing early adolescents with fewer response

categories reduces their cognitive load and thus increases the possibility of completing

surveys.

CHAPTER 3

METHODOLOGY

Introduction

The purpose of the study is to determine if and to what extent relationships exist

among mathematics self-efficacy, its four antecedent sources (mastery experiences, social

persuasion, vicarious experiences, physiological states), and mathematics achievement in

standard five primary school students in the North-Eastern Education District in Trinidad.

Mathematics self-efficacy and the four antecedent sources (mastery experiences, social

persuasion, vicarious experiences, physiological states) have been examined in

connection to mathematics achievement in traditional learning settings in the United

States. Still, they have not been directly discussed in the context of primary school

students in Trinidad. Chapter 3 presents this study's educational problem and the research

questions to examine that problem. Previous investigations have advised future studies

into self-efficacy and academic learning to focus on epistemology (Aktürk, 2014), of

which self-efficacy is an essential part (Johnson, 2011), and to study several

characteristics of self-efficacy rather than concentrating on a particular element (Shen et

al., 2013), which will be fulfilled in the current study by exploring all of the antecedent

sources of self-efficacy, which has not yet been done for a Trinidad primary school

sample.

This study's methodology and design describe the population, sample, and

instrumentation. This chapter also discusses the methods for data collection and data

analysis. Finally, the chapter will close with a summary explaining what the final two

chapters will cover.

Research Questions

The questions guiding the investigation are as follows:

1. What are the levels of mathematics self-efficacy among primary school students?

2. What are the sources of mathematics self-efficacy among primary school students

in Trinidad and Tobago?

a. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by school type?

b. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by age?

c. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by gender?

d. Do the sources of mathematics self-efficacy among primary school

students in Trinidad and Tobago vary by ethnicity?

3. To what extent do mathematics self-efficacy and mathematics self-efficacy

sources explain mathematics performance among primary school students?

Research Design

This study employs a correlational design to test the null hypothesis associated

with the research questions. A correlational research design is suitable for analyses to

determine the significance of the association between explanatory and response variables

(Creswell, 2014). Additionally, Fraenkel et al. (2012) noted that correlational studies are

suitable for determining the associations among variables. This research examines the

association among the four antecedent sources of mathematics self-efficacy, mathematics

self-efficacy (i.e., the explanatory variables), and mathematics achievement (i.e., the

response variable). Creswell (2014) indicated that this distinctive study design had given

rise to well-defined analysis methods and precise methods for categorizing correlations. A

correlational research design is suitable for evaluating how two or more values change,

measured at a particular time. Scholars who use this kind of correlational design are not

concerned about persons' past or future achievements in the study (Creswell, 2014).

Additionally, a correlational research design is suitable when examining the

amount of association among variables instead of any causal extrapolation (Creswell,

2014). As this investigation does not intend to describe the cause-and-effect association

between the explanatory and response variables, but the amount of association that the

four antecedent sources of mathematics self-efficacy had with primary students'

mathematics self-efficacy and achievement on the math component of the SEA, a

correlational design was the best option. Additionally, this study's research design used

cross-sectional surveys, allowing the researcher to gather data at one point to investigate

recent primary school students' existing thoughts, opinions, attitudes, or procedures

regarding mathematics (Creswell, 2014).

This research study employed two survey instruments for information collection,

which go with a correlational research design (Edmonds & Kennedy, 2016). The

instruments that made up the surveys to be administered to the sample were similar to

those used in comparable studies (D'Lima et al., 2014; Fong & Krause, 2014; Honicke &

Broadbent, 2016; Joet et al., 2011; Lin, 2016; Zelenak, 2015). Mathematics self-efficacy

was measured using a content-specific instrument designed to reflect the content of the

SEA curriculum. The four antecedent sources of mathematics self-efficacy were

evaluated with a modified form of the Sources of Self-Efficacy in Mathematics Scale

(SSEMS); the Likert scale was changed from 6 to 4. Finally, the survey collected the

score on a Secondary Entrance Assessment to measure mathematics assessment. This

study examined the possible influence of students' mathematics self-efficacy sources on

mathematics self-efficacy and mathematics achievement.

Population and Sample

This study's general population was primary school students in the North Eastern

Education District in Trinidad and Tobago since that is the context in which mathematics

self-efficacy and its four sources have not yet been studied. Data were collected from

standard five (sixth grade) primary school students in four primary schools, two

government primary schools, and two denominational primary schools; these schools are

located in the North-Eastern Education District in Trinidad. The research sample included

only regular education students; special-education students were excluded. This

convenience sample of standard five students served as data to answer the research

questions. All standard five students from selected schools in this district were invited

and encouraged to participate. Before data collection, a consent form was sent to all

parents, briefly describing the study and seeking consent for the students to participate.

An attempt was made to secure the participation of at least 200 students of the said

population. Sampling is limited only by parental consent.

Since this research investigates an association among the variables and not a

causal declaration, a convenience sampling procedure was used to enlist participants for

the study (Etikan, Musa, & Alkassim, 2016. Convenient sampling gathers data from

available members and those wishing to respond. Convenience sampling, however, is

regarded as a weak method of sampling because the chosen students in this study will be

different from students in schools in other Education Districts, thereby limiting the

application of the results (Gravetter & Forzano, 2018).

Instrumentation

This correlational study's instrumentation included the Sources of Middle School

Mathematics Self-Efficacy Scale (SMMSE), a content-specific Self-Efficacy Scale, and

the Secondary Entrance Assessment (SEA) mathematics component to measure

mathematics attainment. The survey measuring the sources of mathematics self-efficacy

used for this study has been adapted from the Sources of Middle School Mathematics

Self-Efficacy Scale (SMMSE). Usher and Pajares (2009) initially developed and used the

survey to measure middle school students' mathematics self-efficacy sources. The

SMMSE scale focuses on the four sources of mathematics self-efficacy hypothesized by

Bandura; the questions concentrate on mastery experiences, vicarious experiences, social

persuasion, and physiological states. The Likert Scale for the SMMSE scale was modified

from a six-point scale to a four-point scale which is more appropriate for primary school

students. Studies (Smith et al., 2003; Toland & Usher, 2016) offered tentative evidence

that middle school students only use four scale points. The items on the scales are best

matched with adolescents with average to below-average mathematics self-efficacy.

Mathematics self-efficacy was assessed using a content-specific self-efficacy

scale. Usher and Pajares (2009) designed a scale to assess mathematics skills selfefficacy

for middle school students centered on the National Council of Teachers of Mathematics

(NCTM, 2000) guidelines. This scale was used effectively with middle school students

and demonstrated acceptable content validity and reliability (α = .95) (Usher & Pajares,

2009). The researcher modified Usher and Pajares scale to incorporate skills pursued in

Standard 5 (Grade 6) to make the scale suitable for all participants in the sample. The

Assessment Framework for the Secondary Entrance Assessment 2021-2023 was used to

select items in the existing scale and create new items based on what is required for the

Secondary Entrance Assessment.

A team of content experts in primary school mathematics evaluated the items to

confirm they would be comprehensible for standard four students (i.e., students younger

than participants in this study). They also confirmed that it contained the critical math

skills in the focused grade level, providing further content validity for this scale. The

Trinidad Mathematics Skill Self-Efficacy Scale (TMSSES) scale follows strict adherence

to both content and specificity, as Bandura (1997) proposed.

Sources of Middle School Mathematics Self-Efficacy Scale (SMMSE)

The instrument selected for this research is the Sources of Middle School

Mathematics Self-Efficacy Scale designed by Usher & Pajares (2009). Items are

composed as first-person declarations, and pupils are asked to rate each statement on a

scale from 1 (clearly untrue) to 4 (clearly true).

Mastery experiences come from accomplishing, for example, mastering a task or

controlling an environment, which will build self-belief in that area. In contrast, a failure

will weaken that efficacy belief. A robust sense of self-efficacy requires experience in

overcoming obstacles through effort and perseverance. Sample mastery items include: "I

make excellent grades on mathematics tests."

Vicarious experiences come from observing people around us, especially those we

consider role models. Seeing persons like ourselves succeed through sustained effort

raises our belief that we possess the competencies to master the activities needed for

success in that area. Sample vicarious items include: "Seeing children do better than me

in math compels me to perform better."

Social Persuasion comes from influential persons in our lives, such as parents,

teachers, managers, or coaches, who can reinforce the beliefs that we have what it takes

to do well. Being persuaded that we have the competencies to master certain activities

means that we are more likely to put in the effort and endure when problems arise.

Sample social persuasion items include: "People have told me I have an aptitude for

mathematics."

Your physiological states will influence how you judge your self-efficacy.

Depression, for example, can dampen confidence in our capabilities. Stressful reactions

or tension are interpreted as signs of vulnerability to poor performances, whereas positive

emotions can boost our confidence in our skills. Sample physiological states items

include: "I'm getting depressed when I think of studying mathematics."

Each subscale contained six items. This scale was preferred for the current study

as it reflects Bandura's hypothesized four antecedent sources of self-efficacy and

demonstrates strong psychometric properties. Usher and Pajares (2009) reported

Cronbach's alpha coefficients as .88 for mastery experiences, .84 for vicarious

experience, .88 for social persuasion, also .87 for physiological states, demonstrating

satisfactory internal consistency. Usher and Pajares contended that the scale could be

reliably utilized to evaluate math self-efficacy antecedents with pupils in grades six to

eight.

Trinidad Mathematics Skills Self-Efficacy Scale – (TMSSE)

Bandura (1997) proposed that strict adherence to content and context specificity in

self-efficacy studies is compulsory to yield valid results. The specificity of content relates

to how precisely an efficacy measure relates to the criteria tasks on which achievement is

assessed. Pajares (2006) proposed that self-efficacy beliefs should be measured at the

specificity level that precisely matches the criteria task. This specificity might mean

measuring self-efficacy for individual statistics problems, particular geometry problems,

etc. There are two direct concerns with measurement correspondence at this level. First, it

seems questionable that a student with high self-efficacy for one statistics problem would

have low self-efficacy for another statistics problem. Second, self-efficacy measurement

at such a specific level may mean that every self-efficacy investigation requires a tailored

instrument.