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Vol. 3, No. 1, Dec 2014, pp. 21-32   
 
 
 
 
Motivations for Learning: Mastery Experiences in a Low Socio-economic Middle School 
Corey McKenna 
Whitworth University 
 
 
 
 
 

Abstract 
 

The purpose of this multi-case study was to discover the causes of low self-efficacy for math for 

a group of historically low-performing 7th grade students at a high-poverty urban middle school 

based upon Bandura’s (1986) Social Cognitive Theory, specifically the concept of self-efficacy. 

Qualitative methods were used to collect data, including structured one-on-one interviews and 

classroom observations. In addition, a student survey provided data on student self-efficacy and 

offered further insight into individual student perceptions. The cross-case analysis surfaced 

evidence for each of the four sources of self-efficacy. The findings of this study can provide 

educators with insights into the causes of low self-efficacy for students at the middle grade level 

and allow researchers to theorize about a broader set of cases related to learning math. 

 
Keywords: middle school mathematics, self-efficacy, urban middle school, high-poverty  



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Introduction 
 

The topic of mathematics achievement in the United States is a sum of many parts. Of 
special concern within this issue is that of minority students from high-poverty urban schools. A 
crucial juncture in the K-12 experience rests in the middle school years where the success or 
failure in mathematics courses often proves a substantial gatekeeper to higher-level mathematics 
content and the prospect of achieving a high school diploma (Balfanz & Byrnes, 2006). For some 
students at the middle school level, previous deficiencies in arithmetic skills accrued over the 
years of elementary school exacerbate the complexity of introducing algebra at this stage. 

A focus on national math achievement recurs in both research studies and policy 
recommendations (National Mathematics Advisory Panel, 2008; Provasnik, Gonzales, & Miller, 
2009). Results from NAEP in recent years demonstrate some growth in math achievement in 
both 4th and 8th grade, yet only 40% of 4th grade students and 35% of 8th grade students scored 
proficient or above in math in 2011 (NCES, 2011a). For urban districts, results on NAEP reveal 
even lower levels of achievement in math  (NCES, 2011b) while other measures of math 
achievement in urban schools show consistently alarming results (Rowan, Hall, & Haycock, 
2010; Ysseldyke, Spicuzza, Kosciolek, Teelucksingh, Boyes & Lemkuil, 2003). 

The preponderance of minority students who have achievement gaps upon entering high-
poverty middle schools typically see their achievement gap widen by the end of their middle 
school experience (Balfanz & Byrnes, 2006). It is during these critical middle school years that 
students will formulate judgments about their own interest in math and their ability to learn math, 
and once entrenched, these judgments will shape the life-long opportunities available to these 
students (NCTM, 2000). A student’s lack of confidence in their ability to succeed in math can 
contribute to a discouraging attitude toward math in the middle grades when the study of math 
transitions from a focus on concrete sequential procedures to abstract algebraic reasoning 
(McNeil, Grandau, Knuth, Alibali, Stephens, Hattikudur, & Krill, 2006). A history of low 
performance can promote low self-efficacy for math. Identifying the causes of low self-efficacy 
for math may provide educators with strategic means of supporting students at the middle-grade 
level. 

Self-efficacy, according to Bandura, “refers to beliefs in one’s capabilities to organize 
and execute the courses of action required to produce given attainments (1997, p. 3). Bandura 
theorized that what is foundational in forming one’s level of motivation, as well as their 
emotional status and what they act upon is based more on their beliefs about themselves rather 
than what is objectively true. “Unless people believe they can produce desired efforts by their 
actions, they have little incentive to act. Efficacy belief, therefore, is a major basis of action. 
People guide their lives by their beliefs of personal efficacy” (Bandura, 1997, p. 3). These beliefs 
play a powerful decision-making role in the lives of students. A latent hazard of low self-efficacy 
beliefs for mathematics formed early during the middle school years may cause students to avoid 
taking challenging academic courses in the future if they doubt their abilities. The more 
immediate hazards of low self-efficacy for math can be seen in how these beliefs impede their 
day-to-day interaction with the math instruction and curriculum. 

With increased attention on math achievement and the stubborn resistance to 
improvement represented in substantial numbers of students, knowing what is happening with 
students who lack the inner belief that they can succeed in math could produce helpful insight. 
Employing the lens of Bandura’s (1986) Social Cognitive Theory as a theoretical framework can 
discern the sources of low self-efficacy for students. By recognizing the four sources of self-



 Motivations for Learning    23 
 

efficacy 1) mastery experience, 2) vicarious experience, 3) social persuasion, and 4) 
physiological states, exploring the causes of low self-efficacy can identify means of responding 
to these students that influences increases in self-efficacy for learning math.   
 A history of low performance contributes to low self-efficacy and educators who serve 
these students encounter the conundrum of responding to students’ academic deficiencies while 
attempting to meet grade level standards. The contributing factor of poverty and the urban 
context of the school provide a distinguishing perspective for this study. Resilience in challenge, 
an outcome desired in math instruction and a vulnerable attribute for children living in poverty 
(Downey, 2008; Spencer, Cole, DuPree, Glymph, & Pierre, 1993) illuminates aspects of this 
study. Identifying the causes of low self-efficacy for math may provide educators with strategic 
means of supporting students at the middle-grade level.  

The purpose of this multi-case study was to discover the causes of low self-efficacy for 
math for a group of historically low-performing 7th grade students at a high-poverty urban 
middle school. At this school, 85% of the students lived in poverty. By selecting four students 
for cross-case analysis, this study sought to gain a richer understanding of how students judge 
their ability to engage in learning math within a context of poverty. From this analysis we can 
hold a better position for offering remedy to students at this level who struggle to learn math. 
The following research question guided the study: 

What are the causes of low self-efficacy in math mastery experiences for historically low-
performing students at a high-poverty urban middle school? 
 

Review of Literature 
 

This review of literature builds upon the complementary notions of self-efficacy by 
exploring the understanding of the concept of self-efficacy, then a presenting a discussion of 
self-efficacy beliefs among cross-cultural contexts. A concise examination of motivation for 
learning provides a broader consideration for our study. The context of middle school and the 
influence of poverty further inform the review of literature as these factors frame the context and 
design of our study.    

 
Self-efficacy 

A key component of the social cognitive theory is the concept of self-efficacy 
(Zimmerman, 2000). Self-efficacy has received considerable attention from educational 
researchers as relating to how students approach learning and the construct of classroom 
experiences. Others have drawn distinction to how students encounter learning mathematics 
(Usher & Pajares, 2009; Williams & Williams, 2010). Usher and Pajares’ (2008) review of 
literature on self-efficacy in schools confirmed self-efficacy beliefs as, “the critical determinants 
of human motivation and behavior” (p. 791). When considering learning experiences for 
students, recognizing these elements of motivation and behavior provides an elaborate backdrop 
for discerning the influences upon the teaching and learning processes.   

Bandura identified four types of behaviors or processes regulated by self-efficacy beliefs.  
The processes, which include cognitive, motivational, emotional, and choice, are critical to 
achievement in academic settings, namely a school classroom (Pajares, 1996). Variability of self-
efficacy exists among students establishing criteria of high and low self-efficacy. Students with 
high self-efficacy are more likely to: engage in higher order thinking; show greater effort and 
persistence; demonstrate an affect of curiosity and eagerness; and broaden their consideration of 



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what goals to set for themselves and what activities to participate in (Snowman, McCown & 
Biehler, 2012).  Contrastingly, students with low self-efficacy are likely to disengage from 
learning experiences or avoid the academic demands in an attempt to relieve themselves from the 
recurrence of failure or emotional distress (Zimmerman, 2000).  

 
Self-efficacy Beliefs 
 Beliefs about one’s abilities reveal differentials that can introduce inaccuracies between 
beliefs and actual abilities. Williams and Williams (2010) used the 2003 PISA to explore the 
cross-cultural effect of self-efficacy and math performance. Their findings affirmed that self-
efficacy is a concept that applies to students in many cultures. Their model was a “good fit to the 
data in 30 nations and was supportive of reciprocal determinism in 24 of these, suggesting a 
fundamental psychological process that transcends national and cultural boundaries (p. 453).” 
Interestingly, their study also identified that the influence of external agency (the expectation of 
significant others) influences the self-efficacy of girls across cultures. Girls everywhere, it 
seems, underrate their capabilities in mathematics relative to boys with the same degree of 
mastery. In a similar way, girls evidence lower levels of self efficacy with respect to 
mathematics, along with higher levels of anxiety, helplessness, and stress” (Williams & 
Williams, 2010, p. 463-464).  
 The accuracy of student self-efficacy can contribute to their beliefs about their 
prospective outcomes. This applies to performance in math as noted in studies by Chen (2003) 
and Chen and Zimmerman (2007). Such impact on math can influence middle school students’ 
perspective on their performance and their effort judgment with implications for both students 
and teachers. From Chen’s study, the direct effect of self-efficacy on math performance 
influenced the amount of efforts students invested in learning math. Recommendation from this 
study for math teachers suggested: 

Teachers should recognize that calibration accuracy is an important dimension of their 
students’ math self-efficacy beliefs. As a group, seventh-grade students overestimated 
their math capabilities, but their inaccuracies did not relate to the strength of their self-
efficacy beliefs. Both high and low self-efficacy students were overly optimistic about 
their performance. Although such over-optimism may enhance their motivation to 
improve future performance, students’ underlying math skill also significantly factored 
into their academic success (Chen, 2003, p. 90). 

Chen and Zimmerman (2007) found this incongruity between self-efficacy beliefs and 
performance in math when considering students from cross-cultural contexts. When comparing 
middle school students from Taiwan and the United States, they found that students from Taiwan 
demonstrated a higher degree of accuracy than the American students. This inaccuracy presents a 
challenge for teachers to contemplate and to determine the need for alignment between beliefs 
and performance. Bringing students’ self-efficacy into congruity with performance is suggested 
by other researchers (Campillo, Zimmerman, & Hudesman, 1999; Zimmerman, Bonner, & 
Kovach, 1996). Thus consideration of the accuracy of students’ self-efficacy needs to interface 
with the measured levels of particular students, such as psychometric test scores. When 
supporting students who have a history of low-performance in math, as our study endorses, 
addressing the discrepancy of self-efficacy and performance introduces another contingency for 
re-engaging students in learning math. 
 
 



 Motivations for Learning    25 
 

Motivation for Learning 
 When supporting students who have a history of low-performance in math, the matter of 
motivation for learning surfaces as a critical factor in overcoming the barriers to academic 
success in math. Zimmerman (2000) suggests that self-efficacy serves as indicator of motivation. 
“Self-efficacy beliefs have also shown convergent validity in influencing such key indices of 
academic motivation as choice of activities, level of effort, persistence, and emotional reactions” 
(p. 84). For students such as those in this study, effort, persistence and emotional reactions can 
contribute to revealing respective levels of self-efficacy. Zimmerman highlighted to notions of 
effort—rate of performance and expenditure of energy (2000). Although these illustrate 
indicators of self-efficacy, it is important to remember that these are merely predictors of 
motivation.  
 Considering the placement of motivation for learning as intrinsic through curiosity or 
interest, middle school students at-risk of school failure represent an intersection of influences in 
schools (Anderman & Maehr, 1994; Dweck & Leggett, 1988). At-risk indicators, such as 
delayed academic skill development, poverty, concentration of poverty within an assigned 
school, and race highlight gaps in the development of intrinsic motivation associated with 
school-structured activity. Niehaus, Rudasill, and Adelson (2012) drew connection between self-
efficacy and academic outcomes for Latino middle school students concluding consistent 
findings with prior studies “suggesting that academic self-efficacy is an important contributor to 
positive academic outcomes for Latino students” (p. 129). These researchers found that students 
possessing intrinsic motivation for learning directly correlated to their academic achievement as 
measured by grade point average. Recognition of the role of motivation for student learning can 
expose a related factor to self-efficacy, assuredly beyond the scope of this study yet in 
accordance with this line of inquiry.  
 

Method 
 

 This study utilized a multi-case study design to discover the causes of low self-efficacy 
for math. Yin (2005) endorses the use of case study to descriptions that enhance awareness and 
analytical insight that promotes knowledge. Each selected student represents a separate bounded 
case. By bounding the cases to individual students, gaining understanding of their distinct 
conditions will provide opportunity for analysis (Stake, 2000).  Qualitative methods were used to 
collect data, including structured one-on-one interviews and classroom observations. In addition, 
a student survey provided data on student self-efficacy and offered further insight into individual 
student perceptions.  

This study utilized a cross-case analysis of four students who demonstrated varying 
degrees of self-efficacy. The four students selected for case study were participants in a larger 
year-long study involving 24 students conducted at an urban middle school in a Western state. 
The research design represented a convergence of practitioner research and empirical study in 
which participants enrolled in a math class for 90 minutes each day. Three researchers 
contributed in distinct ways: one researcher served as the classroom teacher and collected 
assessment data, a second researcher served as the Principle Investigator and provided daily 
instructional support within the classroom and documented observational data, and the third 
researcher administered the surveys and conducted the one-on-one structured interviews with 
students.  

 



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Data Sources 

The students participating in this study attended a historically underperforming middle 
school (grades 6-8) where over 85% of the students lived in poverty. All participating students 
had demonstrated a history of low-performance in math and over 50% were English Learners. 
Therefore, the context of this study provides a valuable perspective for exploring the roots of low 
self-efficacy for math.  

Sample selection. The larger, year-long study included 24 students purposefully selected 
to match the demographics of the school. The selected students represented 80% Latino, 10% 
African-American, and 10% Caucasian with equal number of male and female students. 
Although all 24 students were historically low-performing in math, the four students selected for 
analysis in this study represent a contrast within the larger group. Two of the students (one male 
and one female) demonstrated higher levels of achievement while the other two students (one 
male and one female) demonstrated lower levels of achievement. The four students revealed 
varying degrees of self-efficacy for math and responsiveness to efforts to change.  

Data collected. Data was collected from four sources involving all three researchers. One 
researcher conducted one-on-one interviews with participating students and administered a 
survey to help determine their level of self-efficacy for math. The structured interviews utilized a 
protocol to ensure consistency in data collection among participants. The survey instrument was 
developed based upon a study conducted by Usher (2009) to determine sources of self-efficacy 
for math among middle school students. The instrument asked questions to mine responses 
revealing the four sources of self-efficacy discussed in the theoretical framework.  

The interviews and survey administration were conducted early in the school year. 
Assessment data were collected by the researcher serving as the classroom teacher. Such data 
included in-class and homework assignments, formative and summative assessments, and 
district-sanctioned benchmark exams. The researcher providing instructional support gathered 
daily classroom observations, including individual and small-group interactions.  

 
Data Analysis 
 A narrative was constructed for each case to incorporate the data collected into a story to 
depict illustration of the cogent concepts aligned with the theoretical framework guiding the 
study. Establishing validity within each case marked the first step in building trustworthiness in 
the study. The multiple data sources provided for triangulation within each case, which involved 
a “process of using multiple perceptions to clarify meaning, verifying the repeatability of an 
observation or interpretation” (Stake, 2000, p. 443). 
 
Participants 
 The cases of the four selected students are portrayed in concise format. More extensive 
cases of each student were constructed for analysis purposes. These cases emerged from a 
compilation of classroom observations, review of assessment data, interviews, and student 
responses to the survey instrument. The presentation of the four cases—Maria, Manuel, Missy, 
and Bobby—provides descriptive data for analysis. Pseudonyms have been used to mask the 
identity of the students. The first two students portrayed, Maria and Manuel, demonstrated higher 
levels of achievement and revealed fluctuating levels of self-efficacy (i.e., selectively low one 
time and malleable the next time). Missy and Bobby demonstrated lower levels of achievement 



 Motivations for Learning    27 
 

and persistently low levels of self-efficacy. Each case provides evidence of the causes of self-
efficacy analyzed through the theoretical framework of this study.      
 

Findings 
 

Bandura’s (1986) Social Cognitive Theory and component self-efficacy provided a lens 
for determining the causes of low self-efficacy for the students in this study. The cross-case 
analysis conducted after composing the four individual cases surfaced evidence for each of the 
four sources of self-efficacy that yielded a set of findings that may provide a way of theorizing 
about a larger collection of cases, or particularly other students similarly situated (Stake, 2008). 

 
Mastery 
 Lack of, or inconsistent mastery experiences contributed to varying levels of self-efficacy 
for math among these students. Usher and Pajares (2006) concurred with Bandura (1986) that 
students’ perceived mastery experience serves as a contributing predictor of self-efficacy. As 
mastery learning is such a critical source of self-efficacy, when students fail to experience 
mastery learning the recurrence of failure compounds their agency for self-efficacy. Since the 
nature of learning mathematics relies so heavily upon prior knowledge, the developmental design 
of math instruction exposes the gaps in students’ previous learning experiences. In each of the 
four students, previous assessment results (low or inconsistent levels of achievement) indicated 
that many math concepts had not been mastered in preparation for 7th grade.  

Bandura (1986) asserted that mastery experience was the most influential source of 
efficacy as individuals can relate to their authentic experiences, rather than contrived or 
externally imposed (and possibly inauthentic) information. Accordingly, successful experiences 
raise efficacy while failures lower efficacy. Analysis of the four students revealed an exception 
in Maria from the other three students. For Maria, she drew upon her successes and reflected 
upon her failures to promote new mastery experiences. This additive notion of mastery 
experiences enhanced her overall self-efficacy. For Manuel, the inconsistency of his experiences 
did not seem to deter his approach to learning math, yet the mix of success with failure inhibited 
his growth in self-efficacy, perhaps repressing to some extent his potential for learning. Missy’s 
inaccuracy of abilities influenced her perception of mastery experiences perhaps obscuring her 
own awareness and masking her view of self. Meanwhile Bobby’s trend of decreasing 
achievement since 5th grade revealed that fewer mastery experiences may have contributed to his 
low self-efficacy and perhaps to his resistance to efforts to enhance his self-efficacy for math.    

 
Discussion 

 
The challenges of math achievement facing schools are not new nor are decrees for 

reform to math instruction. Research and policy proposals have outlined the need for increased 
emphasis on math and have provided startling data analyses while prescribing the steps to 
improve outcomes for students. Yet the deficiencies in math achievement persist. As set forth at 
the outset of this paper, the critical juncture of the middle grades exposes a host of issues 
affiliated with learning math. For consideration in this study, the self-efficacy for math of 
historically low-achieving students in an urban middle school provides a context for exploring 
the influences that impede deep engagement in math.  



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Balfanz and Byrnes (2006) showed the widening of achievement gaps for minority 
students enrolled in high-poverty middle schools. It is our assertion that the self-efficacy for 
math of students contributes to their willingness and readiness to engage in the abstract, logical 
mathematics, which comprises much of the standards-based curriculum of middle schools. 
Discerning the causes of low self-efficacy for students can inform decision-making related to 
instruction, course offering, and strategies to re-engage students during this critical stage in the 
educational experience.  

 
Approaches to Instruction 

Teachers can influence the self-efficacy of students by addressing the four multiple 
sources of these beliefs. Beyond a repertoire of instructional strategies based upon pedagogically 
sound teaching techniques, teachers that serve students with low self-efficacy for math will also 
need to utilize strategic motivation, to form a nurturing classroom environment, and to employ 
feedback mechanisms that reflect an awareness of students’ low self-efficacy.  

Effort is an important component in the process of learning math. As teachers observe 
students with low self-efficacy, they may likely conclude that these students merely refuse to put 
forth effort. Zimmerman (2000) asserts that self-efficacy beliefs predict student effort by 
illustrating the rate of performance and the expenditure of energy. Such beliefs also influence 
persistence, a related manifestation of self-efficacy. Therefore, understanding the causes of low 
self-efficacy can inform teachers’ perspective on student effort. Additionally, understanding the 
indicators of low self-efficacy could aid instructors in the classroom.  As with the students in this 
study, effort was usually reflective of their beliefs in their ability to succeed. Teachers who can 
discern these beliefs can reconsider their conclusions about similar students and address the 
sources of self-efficacy through their instructional practices.   

 
Re-engagement 
 Students with low self-efficacy for math require intense and recurring re-engagement 
strategies to counter their own beliefs about math. One such strategy involves the use of 
feedback. The binary nature (“correct” or “incorrect”) of a traditional approach to solving math 
problems leans toward poignant responses to student-generated answers. Students with low self-
efficacy have experienced recurrence of failure due to a lack of, or inconsistent frequency of, 
mastery experiences. The form and approach to feedback in these mastery experiences plays an 
important role in re-engaging students. For students living in poverty, failure and the obstacles to 
success present frequent reminders that teachers must help them overcome.  

When a teacher possesses an awareness of students’ low self-efficacy, they can construct 
feedback mechanisms that encourage students toward accurate mathematical thinking. William 
(2011) distinguishes between ego involving feedback and task involving feedback with clear 
implications for students with low self-efficacy. Ego involving feedback, such as grades or 
praise, is rarely effective and can actually lower student achievement. Rather, task involving 
feedback identifies for students what they need to do to improve and provides clear explanation 
of how to go about the process of improvement. For students with low self-efficacy for math, the 
recurrence of low grades or the absence of praise from their teacher further erodes their 
willingness to engage in the learning process, thus the need for feedback that promotes learning 
by helping students move forward in their learning (Heritage, 2010).  
 Usher (2009) asserts that students’ personal beliefs in their skills and abilities can impact 
their level of engagement in learning math, therefore the type of feedback a teacher provides can 



 Motivations for Learning    29 
 

either considerably enhance or further entrench those beliefs. With an awareness of the levels of 
self-efficacy among their students, a purposeful approach to feedback will provide an 
opportunity to support students toward overcoming the obstacles to learning math.   
 
  

Conclusion 
 

If we can recognize the causes of low self-efficacy for math, then changes can occur to 
combat the debilitating results of these beliefs among students. The four sources of self-efficacy 
identified by Bandura (1986) provide a framework for discerning the behaviors, responses, and 
feelings of students as they encounter math. The four students portrayed in this multi-case study 
provide a glimpse at the causes of low self-efficacy. According to Bandura and others, levels of 
self-efficacy can be influenced through personal context and derived outcomes, thus an 
awareness of these causes can inform educators regarding approaches to utilize to serve students.  
 For students at the turbulent stage of middle school, this intersection of past and future 
illuminates a critical juncture as their past years of schooling and experiences have shaped their 
beliefs about their own abilities and can impact their judgments about the future. This study 
considered the causes of low self-efficacy for students in a high-poverty school. The tenuous 
conditions of poverty may intensify the influence of the sources of self-efficacy. Therefore 
strategic responses from educators to engender resilience in students provide an approach to 
addressing low self-efficacy for math. Altering the trajectory of students such as those in this 
study will require purposeful attention to the sources and how they influence students in the 
precarious middle school years.  
 

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