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ISSN No. 2454-6186 | DOI: 10.47772/IJRISS | Volume IX Issue X October 2025
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Mathematics Self-Efficacy Sources and Mathematics Engagement
among Secondary School Students in Nyimbwa Sub-County,
Luweero District
1
Makhulo Anthony,
2
Dr. Henry Ampeire Kariisa,
3
Dr. Roberts O. Wandera,
4
Dr Batiibwe Marjorie
Kabuye
1
Ndejje University, Uganda
2,3
Makerere University, Uganda
*Corresponding Author
DOI: https://dx.doi.org/10.47772/IJRISS.2025.910000459
Received: 12 October 2025; Accepted: 22 October 2025; Published: 15 November 2025
ABSTRACT
Mathematics engagement occurs when the student engages in the activity that is directed towards doing
mathematics, learning mathematics, completing mathematics tasks and participating in school mathematics.
This study aimed at establishing the relationship between Mathematics Self-Efficacy Sources and engagement
among secondary school students in Nyimbwa Sub-county in Luweero District, Uganda. It specifically
intended to examine the relationship between mastery experience and mathematical engagement of students,
determine the relationship between vicarious experience and mathematical engagement of students, establish
the relationship between verbal persuasion and mathematical engagement of students and examine the
relationship between physiological state and mathematical engagement of students. The study adopted a cross-
sectional correlational research design. A sample of 240 respondents participated in the study. Data were
collected from primary sources. Questionnaires and interview guides were used to collect data. Data were
analyzed using descriptive statistics and Pearson correlation to determine the relationship between different
variables. Findings revealed that mastery experience relates to mathematics engagement among secondary
school students, vicarious experience relates negatively to mathematical engagement among secondary school
students, verbal persuasion relates positively with mathematics engagement among secondary school students
and that physiological state relate with mathematical engagement among secondary school students in
Nyimbwa Sub-county in Luweero District. The study recommends that Government needs to educate and
sensitize the mathematics teachers to cater for their students’ wellbeing, carry out effective teaching to enable
them have mastery experience in order to get engaged in mathematics and excel in their academics.
INTRODUCTION
Mathematics is the science and study of quality, structure, space and change of numbers and it is a compulsory
subject to all students from primary one to senior four in Uganda. This is so because it provides foundational
knowledge and skills for other subjects such as; sciences, art, social studies and even music (Kyungmee,
2008). Since being a compulsory subject, students are expected to engage with the subject and be confident
when engaging with the subject.
Globally, the study of the concept of student engagement dates far back to the 17
th
century (UNICEF, 2020)
and has since been concerned with emotional and behavioral withdrawal or disengagement from school, with
behavioral engagement focusing on participation and emotional engagement focusing on identification
(Fredricks et al., 2004). Both are fundamental in the Participation–Identification Model which entails visible
indicators of students’ participation in school activities (Finn’s, 1989). Specifically, low behavioral
Engagement leads to students not finishing school. Each dimension of student engagement has been measured
using different variables (Eccles, 2016). Lawson (2013) conceptualized student engagement as a dynamic
between their psychological dimensions and features of their learning environments.
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Different studies on factors that have contributed to the students engagement in mathematics have been
conducted for-example affective engagement which is defined as positive and negative emotional reactions to
one’s academic environment (e.g., teachers, classmates, school); and, cognitive engagement (Fredricks et al.,
2004). Gender and age are doubtless relevant to any consideration of mathematics engagement (Rosander &
Bäckström, 2012). With this in mind, the first set of engagement factors derives from a recent
multidimensional motivation and engagement framework (Bobis et al., 2011; Liem & Martin, 2012; Martin,
2007, 2009) that suggests a number of cognitive and behavioral factors in the form of adaptive engagement for
which cognitive involves; clearly thinking, paying attention and behavioural including; asking questions and
class communication.
However, little is known about the influence of self-efficacy experiences on students’ engagement in
Mathematics. Self-efficacy is the pivot to success. Believing one’s own strengths supports one even under
undesirable situations and conditions (Ishfaq, 2011).Whether personally or at professional level, self-reliance
matters a lot in achieving the aims set by an individual. Being successful requires consistent performance and
this heavily depends upon how an individual deals with the situations or changes coming forth in his life. Self-
efficacy means self-confidence, self-reliance, and trust in oneself. Self-efficacy is regarded as one’s optimistic
self-reliance. Bandura (1977) clarified self-efficacy as a sportsperson’s trust that he has the required talent to
generate a desired output.
Within the African region, student engagement was given emphasis in the 1990s and has an extensive research
base (Fredricks, Blumenfeld, & Paris, 2004) and is shown to be a highly complex and multi-faceted construct.
It is possibly as a result of this complexity that little has been done to formally define engagement (Finn &
Voelkl, 1993) or to study engagement in terms of interventions in the school setting (Fredricks, Blumenfeld, &
Paris, 2004; Finn & Voelkl, 1993). Researchers, psychologists and educators also differ in opinions of what
constitutes engagement, how the construct can be measured and what factors combine to result in engagement.
However, in this region, most research into engagement acknowledges three commonly identified dimensions:
affective (sometimes labeled ‘emotional’) engagement, behavioral engagement and cognitive engagement
which put emphasis on student’s self-efficacy experiences.
In the Ugandan schooling context, affective engagement can be considered the beliefs, attitudes and emotions
as experienced by students. Aspects of affective engagement have been variously considered as anxiety,
interest, and boredom (Connell & Wellborn, cited in Kong, Wong, & Lam, 2003); interest, achievement
orientation, anxiety and frustration (Kong et al., 2003); identification with teaching staff or peers, and sense of
belonging (Horn-Hasley, 2007). Behavioral engagement is identified by Fredricks, (2004) as one of the three
ways of engagement together with emotional and cognitive engagements. According to (Bandura, 1986), self-
efficacy plays an important role in determining behavior and feelings of confidence about a specific problem
and is also crucial for an individual’s capacity to solve that problem. Research has generally confirmed a
relationship between mathematics self-efficacy and student performance, though different sizes of correlation
were reported, often depending on the types of self-efficacy measures that were used (Multon, Brown, and
Lent, 1991).
Despite all the efforts by the government of Uganda through the Ministry of Education in enhancing student
engagement in mathematics in Nyimbwa Sub-county, learning mathematics has remained a complex process
(Moenikia & Zahed-Babelan, 2010). Both cognitive and emotional factors are influential in achievement in
mathematics and in retention (Singh et al., 2002). Therefore, how students learn mathematics is an issue as
well learning the course content (Cano & Berbén, 2009; Goktepe-Yildiz & Ozdemir, 2018; Segers et al.,
2008). Mathematics curricula were given prominence with this feature when emotional factors such as interest,
attitudes and perception which influenced learning in particular were noticed (NCTM, 2014). In addition to
those components, several socioeconomic factors, and factors such as the influence of families, peers, and
schools which affect learning mathematics are also available. Research on engagement, attitudes and learning
approaches- which are influential in achievement in mathematics have received interest in recent years due to
the fact that it is difficult to change variables related to home and family (Cagirgan & Soyturk, 2021; Singh et
al., 2002). Besides, the above-mentioned influences are greatly important for students in learning mathematical
concepts (Liston & O'Donoghue, 2010). However, all the above create the contextual gap thus paving away for
this study.
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Problem Statement
Students’ engagement in mathematics is of great importance in the teaching and learning of mathematics
because: it raises the effectiveness of mathematics learning and teaching (Nayir, 2015), plays a mediatory role
between attitudes towards mathematics and academic achievement as students with higher engagement can
develop positive attitudes towards the subject which in turn will raise academic achievement in mathematics
(Lijie et al., 2020, Nayir (2015). Also students with higher engagement in mathematics have higher chances of
continuing offering the subject at the higher levels of education and engage in careers that require mathematics
as an essential subject (Gopal et al. (2018). Because of the importance attached to engagement in mathematics
by students and teachers as well, the government of Uganda through Ministry of Education and Sports and
other educational stakeholders has put in place a number of strategies aimed at increasing student engagement
in mathematics; among these is the revision of curriculum to reduce on the load, provision of adequate revision
materials for mathematics, employment of qualified mathematics teachers across board, increase of salaries for
science teachers and establishment of loan education schemes to students with mathematics and other science
subjects.
Despite the aforementioned initiatives by the government of Uganda to increase secondary school students'
engagement in mathematics, their engagement still remains low. If this issue of secondary school pupils' low
engagement in mathematics is not resolved, it will have an impact on the government's strategy of vision 2040,
which calls for transforming Uganda into a middle-income country through technological growth given that
one of the main subjects credited with advancing technology is mathematics. Students in lower courses may
have inaccurate opinions of mathematics due to inadequate participation, creating a negative precedent. In
Luweero District, engagement of students in mathematics has been found to still be ‘wanting’ (SESEMAT,
2008) where it was reflected on the teachers’ methodologies of teaching. Mathematical Engagement was found
to be influenced by various factors yet in this specific study concentration will be put on how students’self
beliefs can realize engagement (Birgen, 2004).
This study therefore sought to establish the relation between Mathematics Self-Efficacy Sources and
mathematics engagement among secondary school students in Nyimbwa sub-county, Luweero District.
LITERATURE REVIEW
A thorough review of both theoretical and empirical literature was done in the process of conducting this
study. Identifying the gaps that this study aimed to fill was the main focus of the literature review. The study
was guided by Social Cognitive Theory by Bandura (1994). The theory was used basing on various attributes
embedded therein to guide this study. Social Cognitive theory deals with “can I” questions; it is a drive
preceding the above-mentioned explanations. Self-efficacy beliefs influence learners’ cognitive, behavioral
and affective beliefs towards mathematics.
The theory states that people make judgments of their capabilities to organize and execute actions required to
attain designated types of performances. Self-efficacy is not concerned with skills one has but with the
judgments of what one can do with whatever skills one possesses. Self-efficacy, then, is an individual’s belief
that he or she can perform a particular task or behavior. It is a person’s beliefs about own abilities to control
her/his level of performance and events that influence his/her life. Students with strong self-efficacy are harder
workers, engage more frequently, have greater persistence in tasks and persevere in face of difficulties more
often than students with low self-efficacy (Bandura, 1977).
Bandura (1992) states that self-efficacy beliefs produce feelings, thoughts, motivations and behaviors through
four processes: the cognitive process, the motivational process, the affective process, and the selection process.
These were used to underpin data from students’ practices and beliefs. Cognitively, did students think they
could accomplish tasks? Research has shown that cognitive performance is enhanced by possessing self-
efficacy beliefs (Bouffard & Bouchard, 1990). Cognitive performance is influenced by three factors: how
people understand ability, one’s ability versus ability of others, and performance feedback. Students view
ability either as acquirable skills or as inherent amount. It has been found that students who believe they can
acquire skills and build their abilities have a high sense of personal efficacy and those that believe they are
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born with only certain amount of ability have very low efficacy (Wood & Bandura, 1989). Through this
assertion, this study seeks to explore how students perceive the relationship between their self-efficacy beliefs
or abilities and engagement in the mathematics classroom.
Students also perceive their own ability based on the performance of others (Bandura & Jourden, 1991).
Students’ efficacy beliefs were weakened when they saw others scoring higher and performing better;
however, their personal efficacy was strengthened when they realized they were progressively gaining.
Performance feedback can also affect feelings of efficacy. Efficacy is enhanced when feedback is positive and
is centered around what is achieved versus negative attention (Jourden, 1992).
The second process is motivation which is enhanced and sustained by clear and challenging goals (Bandura &
Cervone, 1986). Students remain engaged if the work that they are completing is within or just beyond their
abilities. Motivation is enhanced by self-efficacy beliefs (Bandura, 1994). Self-efficacy beliefs determine the
goals students set for themselves, the persistence of students to complete tasks, and the student’s ability to
overcome a sense of failure and continue to persevere, even though disappointment.
The third process is affective process, which is emotional center of self-efficacy. Did the student feel that she
could handle the emotional consequences of first contemplating and then attempting a task? Perceived coping
self-efficacy and thought control efficacy can work together to help students reduce their levels of stress and
withdrawal behaviors (Ozer & Bandura, 1990). Last, is selection or choice related processes that are shaped by
beliefs of personal efficacy. The types of activities students choose to participate in, the environments students
place themselves in, even the career options they choose to investigate are influenced by self-efficacy
(Bandura, 1994).
The theory shows that there are four sources of self-efficacy (Bandura, 1994). It develops from mastery
experiences; this is an experience that has been met with either success or failure. While experiences of
success foster healthy personal efficacy, experiences of failure only weaken a student’s sense of personal
efficacy. The second source of efficacy beliefs is through vicarious experiences (Bandura, 1994). It has been
found that if students see others, especially students who deem to be their equals, succeeding, then they will
feel they are able to accomplish similar tasks. However, if students see another student put forth a large
amount of effort and fail, they will not feel they are capable to same task.
Not only does being successful and seeing others succeed build efficacy! Verbal persuasion is the third source
of self-efficacy. This is aided by building efficacy beliefs (Bandura, 1994). Students can be persuaded that they
have the abilities to accomplish a task. Achievement is improved through verbal encouragement (Schunk,
1985). It is not an easy endeavor, especially if persuasion is followed quickly by an experience of failure.
The fourth source of efficacy beliefs is the physiological states of the students. Is the student expectant in his /
her moods? Students’ moods, physical conditions, and stresses are indicators for efficacy beliefs (Bandura,
1994). Basing on this source, one can easily ask if the teachers provide a classroom environment that was
stress-free. Did students feel that teachers affect their engagement in the mathematics classroom by setting the
“mood?”
Mastery Experiences as Source Mathematics Self-efficacy and Mathematical Engagement
Mastery experiences are experiences of previous success and failure in specific tasks that shape an individual’s
beliefs that he/she can perform similar task (Bandura, 1977). In the context of mathematics, mastery
experiences involve firsthand encounter with successful or failure in mathematical problem-solving and task
completion. When students successfully overcome mathematical challenges and achieve desired outcome, they
develop a belief in their capabilities to perform similar tasks in future. Allowing students to develop a sense of
accomplishment and mastery over mathematical concepts and skills is essential in fostering positive self-
perception and building a solid foundation for mathematical engagement among secondary school sstudents.
The importance of mastery experiences in mathematical engagement is further supported by the National
Council of Teachers of Mathematics (NCTM, 2000) which emphasizes the need to provide students with
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opportunities to engage in problem-solving and reasoning tasks that allow them to experience success and
build confidence in their mathematical abilities. By providing students with appropriately challenging tasks,
support and feedback, mathematics teachers can foster mastery experiences that promote mathematical
engagement and long-term success.
Silver et al. (2020) show that mastery experience derives from the phrase “seeing is believing” to underscore
the importance of providing people tangible evidence of success. When people actually see for themselves and
cope effectively with difficult situations, their sense of mastery is likely to be heightened. Such experiences
serve most successful when goals and strategies are specific with clear identification. In a study by Rosli et al.
(2019), it is indicated that concrete, specific and proximal (short-range) goals provide greater incentive,
motivation and evidence of efficacy to science subjects than goals that are abstract, vague and set in the distant
future. Specific goals allow students to identify specific behaviors needs for successful achievement and to
know when they have to succeed. For example, the most effective interventions for phobias and fears involve
“guided mastery”—in vivo experience with the feared object or situation during therapy sessions, or between
sessions as “homework” assignments. Recent technological advances allow the use of “virtual reality”
experiences in treating phobias and fears. In cognitive treatments of depression, learners are given structured
guidance in arranging success experiences that will counteract low-self-efficacy expectancies (De Talancé,
2016).
Chen and Usher (2013) investigated the four hypothesized sources of self-efficacy from a different perspective.
They hypothesized that students tend to differ in how they rely on self-efficacy source information. Some
students regard mastery experiences as more important than the other three sources, while others may rely on
those sources of efficacy information m more equitably. By utilizing Latent Profile Analysis, they examined
latent patterns, or profiles, of the relations among efficacy-relevant experiences and beliefs reported by 1,225
middle and high school students. The results revealed that there are four types of profiles. Although the four
efficacy sources Bandura hypothesized revealed to have different weights in the four types of profiles, results
support past findings indicating that mastery experiences are a powerful source of self-efficacy.
Vicarious Experiences as Source of Mathematics Self-Efficacy and Mathematics Engagement
Learning can be experienced when learners view the performances of others, ie; what types of actions effective
or non-effective for their own enactment of a task (Mc Cown et al., 1996). According to social cognitive theory
(Schunk, 2000), vicarious experiences can accelerate learning over what would be possible if students perform
every behavior in order to learn. This is especially true when trying to learn complex skills such as riding a
bike, swinging a golf club, or using computers in the classroom. By observing experts, teachers, and other
models, learners may get a head start toward their own mastery of difficult tasks. Self-efficacy beliefs are
influenced by observations of behavior of others such as through a learner interacting with a fellow learner or
with the teachers, watching videos and the consequences of those behaviors. Educationists use this
information to form expectancies about behavior and consequences, depending on extent to which learners
believe that they have similar experiences with the persons under observation (Fung et al., 2018). To Bandura
(1997), vicarious experiences generally have weaker effects on self-efficacy expectancy than to performance
experiences.
According to Conger and Keane (1981), vicarious learning and imagination can be used to teach new skills and
enhance self-efficacy for skills. For example, modeling films and videotapes have been used successfully to
encourage socially withdrawn children to interact with other children. The child viewing the film sees the
model child, someone much like himself or herself, experience success and comes to believe that he or she too
can do the same thing. In vivo, modeling has been used successfully in the treatment of phobic individuals.
This research has shown that changes in self-efficacy beliefs for approach behaviors mediate adaptive
behavioral changes (Williams 1995).
Vicarious experiences in other words involve observing other people successfully completing a task (Lei et al.,
2018). Whereby when one has positive role models in life (especially those who display a healthy level of self-
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efficacy) - one is more likely to absorb at least a few of those positive beliefs about the self. Social role models
including older sibling, older friends, camp-counselors, parents, aunts and uncles, grandparents, teachers,
coaches, and employers have an important influence towards self-efficacy among the observer persons or the
learners. In addition, in interpreting the results of their actions, it is realized that students build their efficacy
beliefs through the vicarious experience of observing others (Schnitzler et al., 2020).
Vicarious experiences have been used to increase students’ self-efficacy, or confidence, for performing tasks
similar to those performed by observed models (Bandura, 1986; Ertmer et al. 2003). It comprises of personal
beliefs about one’s capability to perform at specified levels and, as such, is considered to be the “key factor of
human agency.’’ While not as strong of a source of efficacy information as personal mastery experiences,
vicarious experiences often offer a more feasible method for enhancing pre-service teachers’ self-efficacy for
technology integration, especially given the lack of resources and logistical difficulties involved in providing
students with relevant mastery learning opportunities (Ertmer et al., 2003).
Ertmer et al. (2003) had remarked that vicarious experiences increase students’ self-efficacy or confidence to
perform tasks similar to what had been performed by an observed model. In a study conducted by Albion and
Gibson (2000), it was found that vicarious learning could not be strong as mastery experience in relating to
self-efficacy among students. But, vicarious experiences offer a more feasible method for enhancing pre-
service teachers’ self-efficacy for technology integration, especially given the lack of resources and logistical
difficulties involved in providing students with relevant mastery learning opportunities. The study also
established that technology also offers effective means for delivering vicarious experiences. In a study that
explored the effectiveness of electronic models for increasing pre-service teachers’ self-efficacy for technology
integration, Ertmer et al. (2003) showed a significant increase in students’ judgments of confidence after
viewing successful models in a hypermedia environment. Similarly, Albion and Gibson (2000) got same
results after observing realistic examples of technology integration in an interactive multimedia environment in
which pre-service teachers showed significant increase in self-efficacy for technology integration. Driscoll et
al. (2003) demonstrated benefits of observing dialogue-like discourse (as opposed to monologue-like
discourse) that were modeled by a virtual tutor in a computer-supported environment. That is, overhearing
dialogues containing deep questions helped learners recall information and thus, increased their learning
outcomes.
Vicarious learning has also been portrayed through meaningful group discussions. According to Koschmann et
al. (1996), meaningful group discussions lead to cognitive benefits by engaging students in deep reflections on
their ideas. By exchanging ideas and considering others’ perspectives, learners are prompted to reflect on their
existing ideas as well as to integrate new ideas from friends into their existing knowledge. The cognitive
processes involve asking questions, providing explanations or response to questions, and elaborating on one’s
ideas to provide these explanations, which had been said (Cohen, 1994). Slavin (1996) had pointed that as long
that experience had taken place, then vicarious learning is within the learners. Cochran-Smith and Lytle (1999)
described how teachers’ engagement in collaborative dialogue can enable learners to acquire knowledge and
co-create new understandings that are adaptive. Albion and Gibson (2000) emphasized the importance of
teaching using collaboration in multimedia-based, problem-solving environments, stating that the efficacy of
problem-based learning stems from discussions among group members who desire to use examples from
others so that they could learn.
Verbal Persuasion experiences as source of Mathematics Self-efficacy and Mathematics Engagement
The third factor for self-efficacy is called social persuasion. When people are persuaded verbally that they can
achieve or master skills for certain tasks, they are more likely to do those tasks. Having others’ verbal support
attainment or mastery of a task goes a long way in supporting a person’s belief in himself or herself. This
implies that Self-efficacy beliefs are influenced by our observations of the behavior of others and the
consequences of those behaviors. Educationists use this information to form expectancies about our own
behavior and its consequences, depending on the extent to which they believe that they are similar to the
person under observation.
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Efficacy beliefs are influenced by what others say to us about what they believe we can or cannot do. The
potency of verbal persuasion as a source of self-efficacy expectancies is influenced by such factors as the
expertness, trustworthiness and attractiveness of the source, as suggested by decades of research on verbal
persuasion and attitude change (Eagly & Chaiken, 1993). Verbal persuasion is a less potent source of enduring
change in self-efficacy expectancy than performance experiences and vicarious experiences.
In a qualitative study, Van Zee and Minstrell (1997) indicated that students’ thinking was enhanced during
peer interactions in terms of talking to each other and their teachers, problem representation, explanation,
justification, monitoring and evaluation. Van Zee and Minstrell (1997) suggested that when teachers engage in
reflective answering of their background, they encourage their students to clarify their meanings in life.
Students also got examples to emulate despite various challenges during teaching – learning.
Physiological state as Source Mathematics Self-efficacy and Mathematical Engagement
Physiological state is the condition or state of the body or bodily functions that involves the physical condition
and the physiological state. Physiological state is so vital for successful adaptation to environment as well as
learning. The emotional, physical and psychological well-being of a person can influence how they feel about
their personal abilities in a particular situation. Bandura (1982) stated that if a learner or an individual struggles
with depression or anxiety, he or she might find it harder to have a healthy level of well-being. This statement
raised a question from different scholars whether it is impossible to build self-efficacy while suffering from
some struggles? Of course not, but boosting self-efficacy is a much easier task when one feels healthy and
well.
Physiological and emotional states influence self-efficacy and engagement while learning as it is associated to
poor performance or perceived failure with aversive physiological arousal and success with pleasant feeling
states. According to Bandura (1997), when a person becomes aware of unpleasant physiological arousal, he /
she is more likely to doubt competence than another one with physiological state. Likewise, comfortable
physiological sensations are likely to lead to feelings of confident in ability and situation at hand.
Physiological is an indicator of self-efficacy expectancy, and extend beyond autonomic arousal. In activities
involving strength and stamina, such as exercise and athletic performances, perceive efficacy is influenced by
experiences as fatigue and pain.
Physiological state furthermore is said to be a construct of: anxiety, stress, fatigue and mood. Thus, students
learn to interpret their physiological arousal as an indicator of personal competence by evaluating their own
performances under differing conditions. Strong emotional reactions to school-related tasks can provide cues
to expected success or failure and yet high anxiety can undermine self-efficacy and any form of engagement.
Therefore, students who experience a feeling of dread when going to a particular class or towards
mathematical engagement each day are more likely to interpret their apprehension as evidence of lack of skill
in that area. In general, increasing students’ physical and emotional well-being and reducing negative
emotional states strengthen self-efficacy and mathematics engagement (Delfino, 2019).Perhaps the greatest
limitation of research that has been conducted on the sources of self-efficacy and engagement has been the
manner in which sources have been operationalized and assessed.
Skilling et al. (2016) stated that teacher physiological practices must be intentional towards student
engagement. The intentions of teachers must be integrated into instructional strategies that are flamed to play a
large role in student engagement whilst learning. Such strategies must be pro-active and active, involve
students working in groups and discussions, employ problem-based learning as the teacher facilitates, and ask
students to explain their thinking. In a survey of Kindergarten to Grade 12, Smith and Star (2007) found that
instruction that involved manipulative, hands-on activities, real-world problems, and student groups had
positive impacts on engagement across all grade levels studied.
There are a number of studies that have correlated attitudes as a physiological fact variable and mathematics
engagement; as well as achievements. However, few correlations have been supported as right while
researchers oppose the importance or efficacy to such correlations. According to Vandecadelaere et al. (2012),
attitude towards mathematics is significant and a crucial aspect that need to be studied. The questions remain
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how to measure attitude physiologically towards mathematics engagement. Attitude as a physiological state
needs other variables to be measured, apart from the common known of positive, negative and indifferent
attitude. This is because schools are constructed on policy which compels students / learners into a certain
defined situation (Edigar, 2012).
METHODOLOGY
This study employed mixed methods approach where by both quantitative and qualitative data were collected.
Cross-sectional design and correlational research design were adopted to determine the relationship between
sources of mathematics self-efficacy and mathematics engagement among students in secondary schools in
Nyimbwa sub-county. The study targeted a population of 408 S.2 students and 10 teachers in the six (6)
secondary schools in Nyimbwa Sub-county. The sample size of the study was 240.
This study employed both stratified random sampling and purposive sampling techniques say the classes of
senior two students and teachers since it was a well representative of the population in the selection of the
sample. Concerning qualitative data, interviews were conducted to determine the consistency of results
collected by quantitative means with senior two mathematics teachers of each secondary school to participate
in the study together with focus group discussion with some selected learners of the class. For teachers,
purposive sampling was used. An interview guide was also used to determine the consistence of the
quantitative data collected. This involved personal interviews with the S.2 mathematics teachers and focus
group discussion with the selected S.2 learners.
Quantitative data obtained from questionnaires were analyzed by descriptive and inferential statistics utilizing
the Statistics Package for Social Sciences (SPSS V.21) while Qualitative Data Analysis including in depth
interviews was done by identifying themes, categories and patterns emerging from the information collected.
The data was analyzed to ascertain the accuracy, credibility, consistency, and usefulness of the information as
recommended by Cohen, Manion, & Morrison (2017). The study observed the following ethical measures:
Ethical clearance,
Informed Consent and Voluntary Participation and Confidentiality, Privacy and anonymity including adhering
to APA Manual 7
th
edition to avoid plagiarism.
RESULTS AND DISCUSSION
This study sought to investigate the relationship between sources of mathematics self-efficacy and
mathematics engagement of students in secondary schools in Nyimbwa sub-county, Luweero District. To
gather information on this theme data was collected quantitatively and qualitatively from various respondents.
Quantitatively, 240 questionnaires were administered to senior two students in the six secondary schools in
Nyimbwa sub-county, Luweero District and interviews from ten s.2 mathematics teachers for the selected
schools were held. 129 questionnaires were returned fully completed; this represents a response rate of 53.8%.
According to Amin (2004) in a survey, a response rate of over more than half should yield valid findings hence
the response rate in this study was deemed appropriate to yield valid findings.
Background Characteristics
This section presents the background characteristics of the S.2 learners who participated in this study. These
included gender, age, type of school, PLE score, level of education of father, level of education of mother and
career prospect. The response is presented in Table 4.1;
Table 4.1: Descriptive Statistics on the Background Characteristics (N=129)
Variables
Values
Frequency
Percent (%)
Gender
Male
77
56.0
Female
52
44.0
Age
10-15
42
35.0
16-20
87
65.0
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Type of school
Mixed
92
63.9
Single
37
36.1
PLE score
4-12
72
45.0
13-23
43
31.0
24-29
13
15.0
30-34
01
9.0
Source: Primary data, 2022
Findings in the study showed that students rated themselves highly in the following aspects of mathematics
engagement:.
Relationship between Mastery Experience as Source of Mathematics self-efficacy and Mathematics
Engagement
Table 4.3: Descriptive Statistics of Students’ Rating on Items Related to Mastery Experience as a Source of
Mathematics Self-Efficacy
Response (N = 129)
Never
Rarely
Sometimes
Often
Always
Mean
SD
Overall rating
0 (0%)
0 (0%)
79 (61.2%)
21
(16.3%)
29
(22.5%)
3.61
0,832
Often
0 (0%)
25 (19.4%)
0 (0%)
104
(80.6%)
0 (0%)
3.61
0.794
Often
104
(80.6%)
25 (19.4%)
0 (0%)
0 (0%)
0 (0%)
1.19
0.397
Never
0 (0%)
0 (0%)
55 (42.6%)
29
(22.5%)
45
(34.9%)
3.92
0.88
Often
0 (0%)
0 (0%)0
(0%)
46 (35.7%)
0 (0%)
83
(64.3%)
4.29
0.962
Often
0 (0%)
54 (41.9%)
0 (0%)
75
(58.1%)
0 (0%)
3.58
0.495
Often
Source: Primary data, 2022
Overall, the results indicate that students in this study have a positive view of their mastery experiences in
mathematics. However, there is some variations in the students’ responses with some students reporting higher
levels of mastery experiences than others. This can be observed from the higher values of standard deviations.
Qualitative results are in agreement with quantitative results whereby one of the Teachers mentioned that;
“In my mathematics class, students with mastery skills in the subject are more engaged than those without
mastery experience” (Field Data, 2022). The researcher thought that students that lack mastery experience
generally don’t like to be engaged in mathematics.
Furthermore, another teacher asserted that
“I was told by some of my students that they don’t like the subject (Mathematics) because they can’t seem to
master any concepts and our friends who are good at it thinks that we are not serious and this discourages their
engagement in the Mathematic ”(Field data, 2022).
In yet another response with the teachers, one of them indicated that
“I believe that having a mastery experience is good as it helps students feel motivated to undertake any topical
challenge in mathematics and thus increase on their engagement in the subject” (Field Data, 2022).
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Relatedly, another teacher interviewee mentioned that “students who don’t engage in mathematics always
perform poorly in the subject because they don’t appreciate it and share with their colleagues who have some
mastery experience” (Field Data, 2022).
Relationship between Vicarious Experience as Sources of Mathematics Self-Efficacy and Mathematics
Engagement
Table 4.5: Descriptive Statistics of Students’ Rating on the Extent to which they experienced the Following
Six Items Related to Vicarious Experience as Source of Mathematics Self-Efficacy
Responses (N = 129)
Never
Rarely
Sometimes
Often
Always
Mean
SD
Overall rating
0
(0%)
0
(0%)
0
(0%)
0 (0%)
129
(100%)
5.00
0.000
Always
0
(0%)
0
(0%)
24
(18.6%)
0
(0%)
105
(81.4%)
4.63
0.781
Always
24
(18.6%)
0
(0%)
0
(0%)
0
(0%)
105
(81.4%)
4.26
1.563
Always
0
(0%)
0
(0%)
0
(0%)
29
(22.5%)
100
(77.5%)
4.78
0.419
Always
0
(0%)
0
(0%)
30
(23.3%)
29
(22.5%)
70
(54.3%)
4.31
0.827
Always
0
(0%)
0
(0%)
0
(0%)
29
(22.5%)
100
(77.5%)
4.78
0.419
Always
Source: Primary data, 2022
The study furthermore indicated that students in this study have a positive view of their vicarious experiences
in mathematics. However, there is some variations in the students’ responses with some students reporting
higher levels of vicarious experiences than others. This can be observed from the higher values of standard
deviations.
Qualitative results are in agreement with quantitative results whereby one of the teachers mentioned that
“When students have vicarious experiences, they have less chances of engaging in mathematics” (Field Data,
2022). Furthermore, another teacher asserted that “I believe students who have more vicarious stand lesser
chance of getting engaged in mathematics than their fellows as I have been able to witness in my teaching
mathematics ”(Field data, 2022).
In yet another response with the teachers, one of them indicated that
“I believe that vicarious experience is good for encouraging students to be engaged in mathematics subject
among secondary schools students as I have been able to understand it over the years while teaching
mathematics subject” (Field Data, 2019).
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Relationship between Verbal Persuasion as Sources of Mathematics Self-Efficacy and Mathematics
Engagement
Table 4.7: Descriptive Statistics on Verbal Persuasion
Percentage Response (%)
Mean
SD Dev
Overall rating
Never
Rarely
Sometimes
Often
Always
0
(0%)
0
(0%)
100 (50.2%)
30
(15.0%)
69
(34.8%)
3.84
.311
Never
0
(0%)
0
(0%)
20
(10.0%)
30
(15.0%)
149
(75%)
4.65
1.420
Sometimes
0
(0%)
0
(0%)
19
(9.0%)
150
(75.0%)
30
(16.0%)
1.59
.917
Never
0
(0%)
19
(9.0)
0
(0%)
10
(5.0%)
170
(86.0%)
1.51
1.143
Never
0
(0%)
0
(0%)
0
(0%)
30
(15.0%)
169
(85.0%)
1.23
.312
Never
0
(0%)
0
(0%)
0
(0%)
29
(15%)
170
(85.0%)
1.14
.498
Never
Source: Primary data, 2022
The study revealed that students who are persuaded are highly engaged in mathematics than those who are not
easily persuaded.
Qualitative results are in agreement with quantitative results whereby one of the participants expressed that
“I have been able to verbally persuade some of students in getting seriously engaged in mathematics and the
results have so been realized” (Field Data, 2022).
Another teacher participant mentioned
“My students just hate mathematics because of hearsay from the wrong perceptions in the school community
but with good verbal persuasion; students can get engaged in mathematics” (Field Data, 2022).
Relatedly, another teacher participant asserted that
“I believe that most of the students can well get engaged if teachers are motivated to persuade the students to
get engaged in mathematics and they do with other subjects. Students lack good career guidance about the
benefits of the subject and hence don’t give it much importance” (Field Data, 2022).
Another participant said
“I think that given serious attention by all the stakeholders, most of the students would improve on their
engagement in mathematics than they are doing now. Therefore, just a little push and motivation would
encourage more students get engaged” (Field Data, 2022).
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Relationship between Physiological (and emotional) State Experiences and Mathematics Engagement of
Students in Secondary schools in Nyimbwa Sub-County
Table 4.9: Descriptive Statistics of Students’ Responses to Items Related to Physiological State Experiences
during Mathematics Learning
Statements
Responses(N = 129)
Never
Rarely
Sometimes
Often
Always
Mean
SD
Overall rating
Just being in mathematics class
makes me feel stressed and
nervous
100
(77.5%)
29
(22.5%)
0
(0%)
0
(0%)
0
(0%)
1.22
0.419
Never
Doing mathematics work takes
all my energy
79
(61.2%)
50
(38.8%)
0
(0%)
0
(0%)
0
(0%)
1.39
0.489
Never
I start to feel stressed-out as soon
as I begin my mathematics work
99
(76.7%)
30
(23.3%)
0
(0%)
0
(0%)
0
(0%)
1.93
1.696
Rarely
My mind goes blank and I am
unable to think clearly when
doing mathematics work
80
(62%)
24
(18.6%)
25
(19.4%)
0
(0%)
0
(0%)
1.57
0.798
Never
I get depressed when I think
about learning mathematics
108
(83.7%)
21
(16.3%)
0
(0%)
0
(0%)
0
(0%)
1.65
0.312
Never
My whole class becomes tense
when I have to do mathematics
84
(65.1%)
45
(34.9%)
0
(0%)
0
(0%)
0
(0%)
1.7
0.957
Never
Source: Primary data, 2022
The results from the study furthermore asserted that students with good physiological state lead to better
mathematics engagement.
Qualitative results were in agreement with quantitative results whereby one of the participants expressed that
“Physiological state of students plays a pivotal role on student mathematical engagement” (Field Data, 2022).
Another participant mentioned
“My students in good physiological state are more engaged in mathematics than those with low physiological
state” (Field Data, 2022).
Relatedly, another participant asserted that
“I believe that most of the students that are with good physiological state are more mathematically engaged
than others that have low physiological state” (Field Data, 2022). Another participant said “I think that having
a high physiological mood is good for students’ engagement in mathematics among mu students” (Field Data,
2022).
CONCLUSIONS
Based on the findings of this study it can be concluded that; it’s statistically proved that mastery experience
positively relates to mathematics engagement, findings also pointed out that vicarious experience relates
negatively to mathematical engagement, furthermore results pointed out that verbal persuasion positively relate
with mathematics engagement, findings also pointed out that physiological state relate positively with
mathematical engagement all the above among secondary school students in Nyimbwa Sub-county in Luweero
District
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RECOMMENDATIONS
The study recommends; that teachers of mathematics should ensure they give regular feedback to the learners
in regards to their performances since they motivate them to engage more. Students have also got to know that
the failure in Mathematics of their peers does not necessarily mean they will fail as well. Furthermore about
the need by school authorities such as the head teacher, director of studies and teachers to continuously
consider rewarding and persuading their learners to engage more. Lastly that the government needs to educate
and sensitize the school administrators to cater for their students’ wellbeing, carry out effective teaching to
enable them have mastery experience in order to get engaged in mathematics and excel in their academics.
Areas for Further Research
The researcher suggests that further research should be done on the relationship between mastery experience,
vicarious experience, physiological state and mathematical engagement in different sub-counties. This will
help in creating awareness among head teachers on how to help the students become more engaged in
mathematics and hence improve their performance.
The researcher suggests that further research should be done to establish not only teachers’ understanding of
such evidence-based strategies, but also the degree to which these strategies are actually being implemented in
the classroom. This will help to understand the extent at which strategies of engagement are implemented. In
this respect, further research should look at how practicing teachers understand and foster behavioural
engagement, as well as establish whether these strategies are being implemented effectively.
The researcher also suggests that further research should seek to establish teachers’ understanding of the
importance of developing positive relationships as a strategy to increase students’ sense of belonging, and
subsequently, students’ emotional engagement in their learning. There is also a corresponding need to establish
if effective strategies to support students’ emotional engagement are in fact being implemented in the
classroom.
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