Students’ Self-Efficacy, Epistemological Beliefs and Mathematics Performance
- Jet Edward V. Ondaro
- Jose C. Dagoc, Jr
- 4577-4589
- Jul 16, 2025
- Education
Students’ Self-Efficacy, Epistemological Beliefs and Mathematics Performance
Jet Edward V. Ondaro., Jose C. Dagoc, Jr
College of Arts and Sciences, Notre Dame of Dadiangas University, General Santos City, South-cotabato, Philippines
DOI: https://dx.doi.org/10.47772/IJRISS.2025.903SEDU0329
Received: 20 May 2025; Accepted: 27 May 2025; Published: 16 July 2025
ABSTRACT
This study sought to determine the mathematics performance, the levels of self-efficacy and epistemological beliefs of the students of Notre Dame of Dadiangas University. Furthermore, it determined the association between students’ self-efficacy and epistemological beliefs and the influence they have on their mathematics performance. This is a predictive-correlational study. Results revealed that the students generally have sophisticated certainty of knowledge, stability of knowledge, structure of knowledge, speed of learning, and ability to learn beliefs, but have unsophisticated source of knowledge beliefs. Moreover, they too have high self-efficacy with generally low mathematics performance. It was also found that the students’ academic performance is significantly related to their self-efficacy, certainty of knowledge, stability of knowledge, structure of knowledge, speed of learning, and ability to learn beliefs. No significant relationship was established between the students’ source of knowledge beliefs and their mathematics performance. The students’ epistemological beliefs are significantly and positively related to their self-efficacy. Through regression, it was found that the students’ self-efficacy and epistemological beliefs have direct influence on their mathematics performance. With the aforementioned results, it was established that beliefs affect the students’ learning of mathematics.
Keywords: epistemological belief; self-efficacy; mathematics learning; improving academic performance; effects of beliefs on learning
INTRODUCTION
Effective teaching is not just mere content delivery; it necessitates understanding and engaging diverse learners. To foster active learning, teachers must recognize the unique characteristics and internal factors that motivate each student. This includes acknowledging the varied abilities and learning styles present in the classroom. While students may enter with different mathematical skills, teachers are responsible for ensuring all students achieve the learning objectives. Beyond abilities, factors like epistemological beliefs and self-efficacy play a crucial role in academic success. Teachers can leverage these internal factors through instruction, ultimately enhancing students’ mathematical performance. This study investigates the relationship between epistemological beliefs, self-efficacy, and mathematics achievement.
Po Hung Liu (2011) cites the studies of Fang (1996), Kang and Wallace (2004), Pajares (1992), and Schoenfeld (1985) which showed that belief systems affect the students’ learning and responses to behaviors in the classroom. Beghetto and Baxter (2012) claimed that in the development of mathematics competence, ability alone is not sufficient. They explained citing Bandura (1997) that students who otherwise have the ability to be successful in learning math but believe otherwise will give up likely in the face of challenge, underperform, and ultimately focus their attention and effort on other pursuits and endeavors. Moreover, they added that there is a need for future studies to develop a better understanding of the specific role that epistemological beliefs play in the improvement of mathematical understanding. Tejano (1999) like Beghetto and Baxter also sees a pressing need to give due importance and concern to the students’ epistemological beliefs since these beliefs in his view play an important part in every educational endeavour where learning and knowing are the principal emphases. As defined by Conley et al (2004), epistemological beliefs pertain to the beliefs about the nature of knowledge and knowing.
Schommer-Aikin and Duell (2013) narrate that the researchers on epistemological beliefs continue to grow as many different relationships have been found between epistemological beliefs and learning. They recommend like the recommendation of many other researchers to look into the effects of epistemological beliefs in combination with other variables. Harteis, Gruber, and Hertramph (2010) recounted the attention received by epistemological beliefs in the fields of educational and psychological researches (for example Hofer, 2004; and as seen in Harteis et al, 2010 are the researches of Harteis, Gruber and Lehner, 2006; Bauer, Festner, Gruber, Harteis, and Heid, 2004). Educational researches are interested in the role of epistemological beliefs in learning and academic achievement (De Backer, 2008). Hofer (2004) urges all that might be concerned to know about how students understand the epistemological aspects of their instructional environments, what practices are most salient, and how they are interpreted through the lens of existing beliefs and knowledge, which are also being altered in the process. Epistemological beliefs have become the focus of growing investigations as insights to students learning and motivation can be drawn from the understanding of these set of students’ beliefs (Buehl and Alexander, 2001). It is interesting to note as well that in the study of Guo, et al (2022), they discovered that epistemological beliefs are even more strongly related to academic achievement than the motivational constructs.
It is supposed that students’ beliefs about the learning of mathematics must be explored and addressed by changing these beliefs from their naïve (unsophisticated) state to their mature (sophisticated) state. Even how much effort educators exert and despite and in spite of the new and innovative strategies and instructional material they use if the student’s beliefs in learning mathematics are negative, nothing will ever happen-no learning, nor can understanding take place within the learner.
Schommer (1990) posits that epistemological beliefs are multidimensional comprised of five dimensions, namely, omniscient authority (beliefs about the validity and the source of knowledge), certain knowledge (beliefs about the reliability of knowledge), simple knowledge (beliefs about the structure of knowledge), quick learning (beliefs about the speed of learning), and innate ability (beliefs about capacity for learning). These dimensions have been demonstrated to influence academic classroom learning and performance (Esterly, 2003; Schommer, 1990; Schommer, 1993). The study of Kardash and Scholes (1996) on the other hand found out that the students epistemological beliefs affect how they integrate and acquire new knowledge.
The other construct that this study focuses on is the learners’ self-efficacy. It is a personal belief that one will be able to do or accomplish something successfully (Goetz, et al, 1992; Feldman, 2013). Bandura (1982) stated that one’s judgment of his or her self-efficacy determines the type of tasks that he or she chooses, the amount of effort that will be put on those tasks, and eventually the level of performance one will have on those tasks.
Self-efficacy affects acquisition of learning in many ways. Those who have high self-efficacy do not give up easily on tasks where they first fail on and as such they accomplish more (Olson and Hergenhahn, 2009). Students with high level of self-efficacy have better control of the learning process, attribute failure not to absence or lack of ability but on lack of effort on their part, thus they persevere more, and they develop and engage on strategies by which they would be able to succeed (Woolfolk, 2013). Students’ self-efficacy affects learning and motivation making it an important variable that is why researchers working on the educational setting are increasingly focusing on it (Dinther, Segers, and Mien, 2011).
The ultimate goal of this study is to improve the mathematics performance of the students. The Philippines has been participating since 2018 in the Programme for International Students Assessment (PISA) which is an international assessment that tests the mathematics, reading and science knowledge and skill of students. In the 2018 PISA participated by 79 countries, the Philippines received the second lowest rank in mathematics and science. In the 2022 PISA participated by 81 countries, the Philippines ranked sixth from the bottom in mathematics with 81 countries participating. These results clearly show that many of our students in terms of mathematics proficiency fall below the international standards. At Notre Dame of Dadiangas University, the students’ mathematics performance in the basic college mathematics (GE 3) in school year 2018-2019 was only 2.75. A grade of 2.75 is a grade that is just one grade bracket better than barely passing. In that school year, 7.58% of the students failed while 18.72% barely passed (grade of 3.00). In the school year that followed there was no improvement recorded as the average grade in the basic mathematics remained at 2.75. However, 13% of the students failed in that school year which is a 5.42% percentage-point increase compared to the previous year, while 18% barely passed. Generally, then, the students’ mathematics performance is poor.
While there are researches on self-efficacy and epistemological beliefs and their effects on academic performance available these researches are not focused on mathematics self-efficacy and mathematics epistemological beliefs in five dimensions and their influence on mathematics performance. In the locale where this study is conducted, these variables and their relationships have not been investigated.
Knowing the level of self-efficacy of the students and its relation with the other set of beliefs that they too hold are interesting areas of exploration if one also has the goal of improving the academic performance of the students. A goal that rightfully belongs to institutions of higher learning.
Objectives
This study sought to determine the mathematics performance and the levels of self-efficacy and epistemological beliefs of students as well as the association between these constructs and their influence on the mathematics performance of the students.
MATERIALS AND METHODS
This study used a predictive-correlational research design. In a predictive- correlational design the relationships of variables are being identified and outcomes are being anticipated using one or more predictor variables and an outcome (criterion) variable (Creswell, 2012). The criterion variable is sometimes called dependent variable, while the predictors are sometimes referred to as the independent variable.
In this study, the type and strength of the association between epistemological beliefs and self-efficacy was determined. This part was purely correlational. In the final phase of this study, it was investigated if the students’ self-efficacy and epistemological beliefs (independent variables) can influence (predict) their mathematics performance (dependent variable). The Creswell (2012) characterization of the predictive-correlational design fits this study.
Respondents
The respondents of these study were the students of Notre Dame of Dadiangas University who took their GE 3 (Mathematics in the Modern World) in the first semester of school year 2021-2022 and had completed that course.
Sampling Design
The total number of students enrolled in the first semester of SY 2021-2022 was 3,711. Using the Slovin’s formula with margin of error set at 5%, the computed sample size was 361. There were three hundred ninety-three (393) students who participated in this study randomly selected from the colleges of health sciences, arts and sciences, business, education, and engineering and architecture.
Research Instruments
Two instruments were used in this research, namely, the Epistemological Beliefs Inventory Questionnaire (EBIQ) and the Academic Self-Efficacy Questionnaire (ASEQ).
The instrument for the determination of the students’ epistemological beliefs was adapted from the questionnaire developed by Ondaro (2016) which was patterned after the instrument developed by Wheeler (2007). Modifications were made in order to suit the purposes of this study. The questionnaire consists of 45 items and measures the GE 3-related epistemological beliefs of the students on the five dimensions proposed by Schommer (1990) in her model. These dimensions are (a) structure of knowledge, (b) source of knowledge, (c) stability or certainty of knowledge, (d) speed of learning, and (e) ability or control of learning. The items in every dimension were rated by the respondents using a 4 -point Likert scale ranging from strongly disagree (a rating of 1) to strongly agree (a rating of 4). Table 1 below contains the specifications for this instrument.
To measure the self-efficacy of the students, a researcher-made questionnaire was utilized based on the review of related literature. The items in the questionnaire were assessed by the respondents using a 4-point Likert. The questionnaire is called the “Mathematics Self-efficacy Questionnaire” or MSEQ. Three experts validated the MSEQ. An indicator for the mathematics self-efficacy was retained only if at least two of the experts have adjudged it as valid. If and when a validator gives suggestion for the improvement of an indicator, such was incorporated only if the suggestion gained the approval of the other validators.
The MSEQ was tested for its internal reliability using the Cronbach’s alpha. Thirty students participated in the pilot testing. The Cronbach’s alpha returned a value of .83. The EBIQ’ reliability was established using the test-retest method. The responses of those who participated in the pilot testing were correlated using the Pearson r and were tested for significant relationship. Results of the correlation showed a very high positive significant relationship between the scores in the first and the second testing. The r value was .87. Thus, it can be concluded that the two instruments are both highly reliable.
The EBIQ consists of beliefs for particular dimensions which are classified either as sophisticated or unsophisticated. The recording of the respondent’s rating used the “sophisticated” perspective. That is, an agreement for the beliefs viewed as unsophisticated would mean that the respondent holds an unsophisticated stance on a particular epistemological beliefs dimension, while a disagreement on beliefs viewed as unsophisticated would mean that the respondent holds a sophisticated stance on a particular dimension. Similarly, agreement for the beliefs viewed as sophisticated would mean that the respondent holds a sophisticated stance on a particular epistemological beliefs dimension, while disagreement on beliefs viewed as sophisticated would mean that the respondent holds an unsophisticated stance on a particular dimension. Thus, in recording, whatever rate which will be marked by a respondent in the instrument for beliefs classified as sophisticated was recorded as the respondent’s rate for that item. For the items classified as unsophisticated, the respondent’s rating would be taken in reverse.
In interpreting the mean rates, the following continuum was utilized together with their descriptions:
Mean Rating | Sophisticated Beliefs | Unsophisticated Beliefs | Level |
1.00 – 1.75
1.76 – 2.50 2.51 – 3.25 3.26 – 4.00 |
Strongly Disagree
Disagree Agree Strongly Agree |
Strongly Agree
Agree Disagree Strongly Disagree |
Very Unsophisticated
Unsophisticated Sophisticated Very Sophisticated |
Since the EBIQ quantitatively reports on the math related epistemological beliefs of the respondents, an overall mean rating on a dimension ranging from 1.00 to 2.50 would mean that the respondent generally holds an unsophisticated set of epistemological beliefs in that particular dimension, while an overall mean rating of 2.51 to 4.00 would mean that the respondent holds a sophisticated set of epistemological beliefs in that particular dimension.
The MSEQ also used a 4-point scale and scored the same way as the EBIQ. Items that do not show or pertain to an individual who is efficacious was reversely scored. The mean obtained was interpreted verbally as follows.
Mean Rating | Level |
1.00 – 1.75
1.76 – 2.50 |
Very low self-efficacy
Low Self-efficacy |
2.51 – 3.25 | High Self-efficacy |
3.26 – 4.00 | Very High Self-efficacy |
Data Gathering Procedures
The researcher administered online through google forms the Epistemological Beliefs Inventory Questionnaire (EBIQ) to determine the students’ level of mathematics related epistemological beliefs and the Mathematics Self-Efficacy Questionnaire (MSEQ) to determine the students’ self-efficacy level. The respondents were asked to answer in the sincerest and most honest way possible and confidentiality of responses was assured. The assistance of the college professors was sought to facilitate the distribution of the questionnaires.
The semestral grades of the students in their GE 3 were the basis of determining the mathematics academic performance of the students. These data were obtained from the university registrar.
The respondents’ responses on the EBIQ and the MSEQ were then organized, classified, and statistically analyzed in order to determine their general level of self-efficacy, epistemological beliefs and mathematics performance; establish the relationships between epistemological beliefs, mathematics performance and self-efficacy; and to ascertain if indeed epistemological beliefs and self-efficacy could influence the mathematics performance of the students.
RESULTS AND DISCUSSION
Presented in this section are the data gathered in this study as well as the discussion of the key findings.
Students’ Self-Efficacy Level
Table 1 shows that the mathematics students of Notre Dame of Dadiangas University generally have high level of self-efficacy (M= 2.84, SD = 0.45). There were ten indicators surveyed of which five had been rated low while the other five have been rated high to very high.
Results show that the respondents take time trying to solve mathematics problems even if those problems were difficult. They believe that through perseverance and effort their mathematics capabilities are improvable. They participate in class activities and make their ideas known as they are confident that their ideas can contribute to the pair or their group’s performance or output. They are confident that by themselves they can satisfactorily answer the questions and solve the problems given in their math quiz, assignment, and/or seat works. They are convinced that they can pass their math examination. They believe in their capabilities to understand the lessons/topics in their math class and to learn the mathematical skills needed in those lessons/topics. Lastly, they believe that they could achieve the goals that they set in their math class.
Table 1. Respondents Ratings on their Self- Efficacy
Indicators | Average Rating | Level |
I am not embarrassed or shy to ask my math teacher questions or clarifications whenever there are things I do not understand or get in the discussion/lecture or on his/her instructions. | 2.48 | Low Self-Efficacy |
I participate in pair or group works whenever such activities are given and I make my ideas known to my classmates as I am confident those ideas can contribute to the pair or our group’s performance or output. | 3.35 | Very High Self-Efficacy |
I welcome the opportunity to recite and explain my answer to the whole class. | 2.50 | Low Self-Efficacy |
I am confident that I can on my own satisfactorily answer the questions and solve the problems given in my math quiz, assignment, and/or seat works. | 2.78 | High Self-Efficacy |
I am convinced that I can pass my math examination. | 2.93 | High Self-Efficacy |
Even if the problems in my math class are difficult, I still take the time in trying to solve them. | 3.58 | Very High Self-Efficacy |
I believe in my capabilities to understand the lessons/topics in my math class and to learn the mathematical skills needed in those lessons/topics. | 3.25 | High Self-Efficacy |
I believe that I could achieve the goals that I set in my math class. | 3.14 | High Self-Efficacy |
I believe that my mathematics capabilities can be improved with perseverance and effort on my part. | 3.54 | Very High Self-Efficacy |
I am easily discouraged whenever I experience failure or difficulty in my math class. | 2.32 | Low Self-Efficacy |
I feel anxious whenever I attend my mathematics class. | 2.04 | Low Self-Efficacy |
In times that I fail or do not achieve my expectation or goals in an activity or assessment in my math class, I feel that it is due to the math abilities that I have and not due to lack of effort or persistence on my part. | 2.22 | Low Self-Efficacy |
General | 2.84 | High Self-Efficacy |
Levels of Students’ Epistemological Beliefs
There are five dimensions of epistemological beliefs according to Schommer’s Model, namely, source of knowledge, stability of knowledge, structure of knowledge, speed of learning, and ability to learn beliefs. As to the levels, the students could either have sophisticated or unsophisticated level of these beliefs. The degree of sophistication or unsophistication of these beliefs had also been determined.
Presented in table 2 are the source of knowledge beliefs. Only two of these beliefs had been determined as sophisticated to very sophisticated while the other seven had been determined to be unsophisticated to very unsophisticated. Generally, the source of knowledge beliefs of the students are unsophisticated with the overall mean of 2.10 and a standard deviation of 0.31. This means that they believe that their mathematics knowledge comes mainly and mostly from their teachers, they will learn best watching their teacher work on examples rather than working on the practice problems themselves, for them to solve the mathematics problems they needed to be taught the correct or right procedures, they accept whatever their teachers say, and they also believe that the success of mathematics instruction is determined entirely by their teacher.
Table 2. Respondents Ratings on their Source of Knowledge Beliefs
Source of Knowledge Beliefs | Average Rating | Level |
Learning mathematics depends MOST on having a teacher who explains each and every detail in the book. | 1.60 | Very Unsophisticated |
I learn mathematics BEST when watching my teacher work on example problems rather than I working on the practice problems myself. | 1.58 | Very Unsophisticated |
If my mathematics teacher gave really clear lectures with plenty of good example problems, I would NOT have to practice so much on my own. | 2.29 | Unsophisticated |
The quality of a mathematics instruction is determined ENTIRELY by the teacher. | 1.90 | Unsophisticated |
What I get from my mathematics class depends mostly on the effort I invest. | 3.40 | Very Sophisticated |
I accept anything that my mathematics teacher says. | 1.84 | Unsophisticated |
Mathematics is something I could not learn on my own. | 1.95 | Unsophisticated |
To solve problems in mathematics I have to be taught the right or correct procedure. | 1.42 | Very Unsophisticated |
In my mathematics class, I can be creative and discover things on my own. | 2.89 | Sophisticated |
General | 2.10 | Unsophisticated |
Table 3. Respondents’ Ratings on their Stability of Knowledge Beliefs
Stability of Knowledge Beliefs | Average Rating | Level |
Most of what are proven as valid conclusions in mathematics are already known. | 2.02 | Unsophisticated |
Mathematics is really just knowing the right formula for the problem. | 2.02 | Unsophisticated |
I prefer a mathematics teacher who shows students different strategies in solving problems. | 3.56 | Very Sophisticated |
Mathematics is nothing but numbers, symbols, shapes & figures, and/or formulas. | 2.63 | Sophisticated |
The application of the concepts taught in mathematics to different disciplines changes as knowledge on those disciplines grows. | 3.29 | Very Sophisticated |
There is usually one best way to solve problems in mathematics. | 1.89 | Unsophisticated |
In mathematics, the answers are always either right or wrong. | 1.94 | Unsophisticated |
Creativity has no place in a mathematics class. | 3.03 | Sophisticated |
All mathematics professors would probably come up with the same answers to questions in their field. | 2.27 | Unsophisticated |
General | 2.52 | Sophisticated |
Table 3 above presents the stability of knowledge beliefs of the students. Five of these beliefs are unsophisticated while the other four have levels ranging from sophisticated to very sophisticated. The grand mean is 2.52 interpreted as sophisticated with a standard deviation of 0.31. The students have a sophisticated stability of knowledge (M= 2.52, SD = 0.31) beliefs. They believe that there are different ways by which mathematics can be solved as such creativity has a place in a mathematics class. They also believe that mathematics is more than numbers, symbols, shapes, figures; and that the way mathematics concepts are applied in other disciplines changes as knowledge in those disciplines grows.
Table 4. Respondents Ratings on their Structure of Knowledge Beliefs
Structure of Knowledge Beliefs | Average Rating | Level |
It is important to know why a theorem/assumption is valid rather than just memorize it. | 3.44 | Very Sophisticated |
When learning mathematics, I can understand the material better if I relate it to the real world. | 3.28 | Very Sophisticated |
When applying the properties or concepts taught in the mathematics, it is important to understand how these properties/concepts relate to one another to arrive at a solution. | 3.43 | Very Sophisticated |
Concepts taught in mathematics are NOT related to each other. | 2.98 | Sophisticated |
Mathematics is mostly facts that have to be memorized. | 2.40 | Unsophisticated |
I learn BEST if I am given the opportunity to make conjectures and validate them on my own. | 2.87 | Sophisticated |
I like to develop my skills in deductive reasoning. | 3.23 | Sophisticated |
Understanding how the topics or concepts in mathematics are being used in other disciplines helps me comprehend those topics/concepts. | 3.32 | Very Sophisticated |
General | 3.12 | Sophisticated |
The beliefs on the structure of knowledge are presented in table 4. Seven of these beliefs have levels ranging from sophisticated to very sophisticated. Only one of these beliefs has an unsophisticated level. Generally, the beliefs on the structure of knowledge of the students are sophisticated (M = 3.12, SD = 0.32). The students’ beliefs on the structure of knowledge are also sophisticated (M = 3.12, SD = 0.32). In fact, this is the set (or dimension) of epistemological beliefs which is the most sophisticated. The students believe that they should know how a mathematical theorem or assumption is valid instead of just memorizing it; they would be able to understand a material used in a mathematics class if they are able to relate it the real world; and they believe that mathematical concepts can be better comprehended if they are able to understand how these concepts are being used in other disciplines. For them to arrive to a solution, they must be able to understand first how the mathematical properties and concepts relate to one another. Mathematics for them is learned best if they are given the opportunity to make conjectures and validate them in their own which will eventually develop their skills in deductive reasoning.
For the speed of learning beliefs shown in table 5, four out nine fall in the category of sophisticated, three are very sophisticated, while only two are unsophisticated as depicted in table 5 above. The students’ beliefs in speed of learning are generally sophisticated (M= 2.81, SD = 0.32). The students’ beliefs on the speed of learning acquisition are generally sophisticated (M=2.81, SD = 0.32). The students believe that given enough time everyone can learn mathematics provided they really try. They believe that every time difficult mathematics problem is encountered, they have to stick to it until they have solved it, and it will help them if they will go back over on something presented in class that they did not understand. They believe that in order for them to perform better in their math class they have to spend more time looking for learning resources. For the students, it takes time to learn mathematics.
Table 5. Respondents Ratings on their Speed of Learning Beliefs
Speed of Learning Beliefs | Average Rating | Level |
It takes time to learn mathematics. | 3.59 | Very Sophisticated |
If I cannot solve a problem quickly, I get frustrated and tend to give up. | 2.42 | Unsophisticated |
When I encounter a difficult mathematics problem, I stick with it until I solve it. | 3.01 | Sophisticated |
Given enough time, almost everyone could learn mathematics if they really tried. | 3.45 | Very Sophisticated |
If I don’t understand something presented in class, going back over it later isn’t going to help. | 2.75 | Sophisticated |
If I can’t solve a problem in a few minutes, I am not going to solve it anymore. | 2.94 | Sophisticated |
If I know what I am doing, I should not spend more than a few minutes to complete a homework problem. | 2.23 | Unsophisticated |
It is frustrating to read a problem and not know immediately how to begin to solve it. | 1.70 | Very Unsophisticated |
In my mathematics class, I could have done better if I spend more time looking for learning resources. | 3.23 | Sophisticated |
General | 2.81 | Sophisticated |
Table 6. Respondents Ratings on their Ability to Learn Beliefs
Ability to Learn Beliefs | Average Rating | Level |
When I am having trouble in my mathematics class, understanding the source of my difficulty can make a big difference. | 3.31 | Very Sophisticated |
I am confident I could learn mathematics if I put in enough effort. | 3.48 | Very Sophisticated |
When I do not understand something, I keep asking questions. | 3.12 | Sophisticated |
Working on my difficulties in learning mathematics can improve my mathematical skills. | 3.46 | Very Sophisticated |
Mathematics is like a foreign language to me and even if I work hard, I will never really get it. | 2.57 | Sophisticated |
I knew at an early age that I will never learn mathematics. | 2.94 | Sophisticated |
If mathematics were easy for me, then I would not have to spend so much time on homework. | 2.09 | Unsophisticated |
It is frustrating when I have to work hard to understand a problem. | 2.03 | Unsophisticated |
I can learn new things, but I cannot really change the mathematics ability I was born with. | 2.29 | Unsophisticated |
With the right attitude and perseverance, I can learn mathematics. | 3.60 | Very Sophisticated |
General | 2.89 | Sophisticated |
Presented in table 6 are the ability to learn beliefs of the students. Seven of which have levels ranging from sophisticated to very sophisticated’ while three are unsophisticated. The ability to learn beliefs of the students are generally sophisticated (M = 2.89, SD = 0.40). Lastly, the ability to learn beliefs (M = 2.89, SD = 0.40) of the students are sophisticated. It is in their view that a big difference is made if they are able to determine the source of their difficulties in mathematics and by working on those difficulties their mathematical skills can be improved. For them with the right attitude and perseverance and if they put enough effort and work hard mathematics could be learned. They as well believe that they have to ask questions if they do not understand something.
In summary, the respondents have sophisticated stability of knowledge, structure of knowledge, speed of learning, and ability to learn beliefs. They generally have unsophisticated source of knowledge beliefs. These results are similar to the findings of Ondaro (2016) in a study that sought to improve the epistemological beliefs and the geometric understanding of the pre-service teachers of the major higher educational institutions in South Cotabato. In an earlier study of Doronila (2012) that developed a 3P Model on problem solving, the college students from Region XII have been found to have sophisticated beliefs in all the five dimensions, that is, including the source of knowledge beliefs.
Students’ Academic Performance
The average grade of the students (N = 393) enrolled in GE 3 in the 1st semester of school year 2021-2022 who were part of this study is 2.21 with the standard deviation of 0.51. One-hundred fifty-two of the respondents (38.68%) have grades 2.00 to 1.00 while two-hundred forty-one of them (61.32%) have grades 3.00 to 2.25.
Relationship between Self-efficacy, Epistemological Beliefs, and Academic Performance
One of the objectives of this study is to determine if the students’ academic performance relates to their self-efficacy and epistemological beliefs. The correlation (Pearson r) results together with their t and p-values are in table 8 below.
Table 8. Correlation between academic performance, self-efficacy and epistemological beliefs
Beliefs | Academic Performance |
Self-Efficacy | r = .21; t(391) = 4.19, p <.001 |
Source of Knowledge | r = .02; t(391) = 0.40, p =.688 |
Stability of Knowledge | r = .15; t(391) = 2.95, p = <.005 |
Structure of Knowledge | r = .12; t(391) = 2.38, p = .02 |
Speed of Learning | r = .13; t(391) = 2.65, p = .008 |
Ability to Learn | r = .16; t(391) = 3.26, p =.001 |
As shown in the table, the students’ mathematics performance has significant positive relationship with their self-efficacy (r = .21; t(391) = 4.19, p <.001), ability to learn beliefs r = .16; t(391) = 3.26, p =.001, stability of knowledge beliefs r = .15; t(391) = 2.95, p = <.005, speed of learning beliefs r = .13; t(391) = 2.65, p = .008, and structure of knowledge beliefs (r = .12; t(391) = 2.38, p = .02). It has to be noted that the source of knowledge beliefs and the academic performance have not been found to have a significant correlation r = .02; t(391) = 0.40, p =.688. Self-efficacy has been found to have the strongest correlation with academic performance while the weakest correlation is found to exist between academic performance and the structure of knowledge belief. These results suggest that students with high levels of self-efficacy and epistemological beliefs (except source of knowledge beliefs) have been observed to have higher mathematics performance.
Soldo (2023) in his study on the correlation of self-efficacy and mathematics academic achievement also found that these two constructs are positively correlated. A strong positive relationship between self-efficacy and academic performance was also determined in the study of Meng and Zhang (2023). According to Zakariya et al (2020) students with high self-efficacy use deep approaches to learning while students with low self-efficacy use only surface approaches. Students that use deep approaches to learning have better mathematics performance than those who utilize surface approaches. The results in this study are similar as well to that of Pamuk and Oztekin (2016) where they have discovered that the students with sophisticated epistemological beliefs are more successful in science. Moreover, the students’ epistemological beliefs have been found to be even more strongly correlated to their academic achievement than motivation (Guo, 2022).
Relationship between students’ self-efficacy and epistemological beliefs
The students’ epistemological beliefs have also been correlated with their self-efficacy. As shown in table 9, the different dimensions of students’ epistemological beliefs are significantly positively correlated with their self-efficacy. The ability to learn belief dimension has the strongest correlation with self-efficacy (r = .50; t(391) = 11.44, p <.001) while the stability of knowledge belief dimension has the weakest correlation with self-efficacy (r = .11; t(391) = 2.11, p =.035).
Table 9. Correlation between students’ self-efficacy and epistemological beliefs
Epistemological Beliefs | Self- Efficacy |
Source of Knowledge | r = .21; t(391) = 4.32; p <.001 |
Stability of Knowledge | r = .11; t(391) = 2.11, p = .035 |
Structure of Knowledge | r = .29; t(391) = 6.03, p <.001 |
Speed of Learning | r = .44; t(391) = 9.69; p <.001 |
Ability to Learn | r = .50; t(391) = 11.44, p <.001 |
These findings mean that students with higher levels of sophistication in their epistemological belief have higher levels of self-efficacy as well. These results find concurrence in the study of Panergayo (2023) where a direct relationship was also found between the students’ self-efficacy and epistemological beliefs.
Influence of Self-efficacy and Epistemological beliefs on Academic performance
In order to determine if the students’ mathematics performance can be influenced by their self-efficacy and epistemological beliefs multiple regression analysis was carried out.
Table 10. Multiple Regression Analysis Results on the Predictive Ability of Self-efficacy and Epistemological Beliefs on Academic Performance
Sources of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | R | R2 |
Regression | 6.428 | 6 | 1.071 | 4.372 | <.001 | .252 | .064 |
Residual | 94.586 | 386 | 0.245 | ||||
Total | 101.015 | 392 |
It has been found that when taken all together, the students’ self-efficacy and epistemological beliefs can influence the students’ academic performance (F(6,386) = 4.372, p<.001, R2 = .064). Further analysis revealed that only the students’ stability of knowledge beliefs and their self-efficacy have the ability to influence their mathematics academic performance. In particular, an increase in the level of self- efficacy and the more sophisticated the students’ stability of knowledge beliefs become, the better their academic performance will be. The coefficient of determination reveals that 6.40% of the variations in students’ mathematics academic performance are attributable to the variations in the students’ self-efficacy and stability of knowledge beliefs. This implies that self-efficacy and stability beliefs both have a significant direct influence on the students’ mathematics performance. In other words, an increase in the levels of these constructs produces an increase in the mathematics academic performance of the students.
Results in the study of Aurah (2013) showed self-efficacy to have a strong influence on academic performance. In the studies of Negara, et al (2021) and Ugwuanyi et al (2020), it has been established that mathematics self-efficacy is a significant predictor of mathematics performance. The study of Belecina and Ocampo (2016) discovered not only a significant correlation between epistemological beliefs and mathematics performance, but the ability of the former to influence the latter. The more recent study of Meng and Zhang (2023) supports this result as well as they found that self-efficacy has a direct influence on academic performance of university students and has an indirect influence on their academic performance with the intermediating effect of academic engagement.
CONCLUSION
The NDDU students have a good mathematics performance who believe in their ability to gain and achieve the standard and goals they set in their mathematics subject. They believe that it takes time to learn mathematics and they are capable of learning mathematics with perseverance, hard work, and the right attitude. For them, mathematics is growing and that mathematical concepts are interrelated and best understood if applied in real life. However, they believe more that mathematical knowledge comes from external sources rather than self-generated (internal).
The student’s self-efficacy and ability to learn beliefs have a significant influence in their mathematics academic performance. Moreover, students with more sophisticated ability to learn, structure and stability of knowledge beliefs and who have higher levels of self-efficacy have better performance in mathematics.
It is therefore imperative that mathematics teachers develop, design and use teaching strategies and class activities that enable and support students to develop sophisticated epistemological beliefs and enhance their self-efficacy as these beliefs promote learning. It has to be aspired in terms of teaching that students become generators or discoverer of mathematical knowledge so that learning becomes enduring and gratifying. Building on their successes students would be able to view mathematics as something that could be learned successfully and would increase their confidence in confronting more complex problems in mathematics.
Future researchers may consider other students’ beliefs that could have a stronger influence on their learning of mathematics. The different factors affecting the students’ beliefs like effectiveness of teaching strategies, students’ motivation and the impact of these factors may be explored to shed more light on the complex process of how students learn mathematics especially in the environment where technology is advancing and is being used. The scope of the study to include other institutions of higher learning may be integrated in the research design to improve the acceptability of the results and findings. Lastly, as beliefs take time to develop and mature, a longitudinal study may be done to explore the impact of these beliefs on the students’ learning.
ACKNOWLEDGMENT
The authors wish to commend the following persons who in one way or another have contributed to the completion of this research work: : Dr. Rogen Doronila who served as our adviser; the GE 3 students of NDDU for school year 2021-2022 together with their professors, who served as the respondents of this study; and Ms. Karen Paglinawan, Ms. Jasmine Ponciano, and Mr. Joemar Sumalinog who served as validators of the research instruments.
Thank you also to the members of the research council for their insightful comments and recommendations that improved this paper and the staff of the research and publication center for all the support and assistance.
And finally, to the Divine Providence whose presence in this work was constantly felt.
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