Modeling Students’ Self-efficacy in Mathematics during the COVID-19 Pandemic

Self-efficacy in learning mathematics helps the student to overcome difficulties and challenges in problem-solving during unprecedented times. This article aims to measure the level of students' self-efficacy and its determinants during the COVID-19 pandemic in learning mathematics online. The study considered primary data from 233 students selected in a non-random approach at Visayas State University, Baybay City, Leyte, Philippines through the aid of an online survey. The data were analyzed using some descriptive statistics calculation and regression analysis was used to model the students' self-efficacy and its factors. Results showed that, on average, the students' self-efficacy level is considered "moderate" amidst the pandemic. This means that most of these students are still having mathematical anxiety and experiencing hindrances in achieving good academic performance in mathematics online. The statistical model revealed that the demographic and learning profile of students is not significantly influencing the level of self-efficacy. In addition to that, the mathematics teachers' intervention has shown also an insignificant influence on the students' self-efficacy. In conclusion, students during the pandemic are having difficulty adopting a new type of learning (distant/online) due to their moderate level of self-efficacy. Hence, the study recommends that teachers must make the learning environment exciting and interesting to boost the students' motivation and self-efficacy in doing their mathematics tasks. Furthermore, teachers must give mathematics activities that are suitable and doable for online learning that enhances students' creative thinking.


Introduction
Teaching and learning mathematics online amid the COVID-19 pandemic is not an easy task for either teachers or students. Compared to face-to-face setup, online learning has revealed shortcomings in terms of delivering the lessons (El Firdoussi et al., 2020). In fact, several challenges and obstacles have been encountered by students in listening to online lectures and doing their mathematics tasks (Kanneganti et al., 2020;Ní Fhloinn and Fitzmaurice, 2021). According to Irfan et al. (2020), limited interaction between teachers and students was happening during online classes due to some barriers amid the pandemic. Likewise, students have no confidence in asking questions and expressing their ideas due to anxiety levels (Irawan et al., 2020). Teachers also have encountered difficulties in monitoring students' progress in their academic performance in mathematics (Casinillo, 2022). In that case, students' self-efficacy is important when facing obstacles in solving mathematics problems during a time of health crisis. According to the study of Rozgonjuk et al. (2020), self-efficacy has a large role in lessening mathematics anxiety. In the paper by Nurhikmah et al. (2021), self-efficacy is defined as a self-belief in students' potential to overcome difficult situations and find ways to get solutions to every mathematics problem. Apparently, mathematics requires analytical cognitive processes which most students are struggling to overcome in times of unprecedented situations . On the face of it, students must level up their self-efficacy to learn mathematics effectively despite of challenges they are facing in online education.
Most students in rural areas are encountering difficulty in accessing good internet connections for online classes (Irfan et al., 2020;Casinillo et al., 2022). In that case, most of them are not genuinely learning at their best. Nevertheless, their selfdetermination to learn and finish their academic program is the main reason why they continue their online education. In addition, self-efficacy in mathematics is vital in their difficult times in solving mathematics problems as part of their learning assessments (Jenßen et al., 2021;Kasturi et al., 2021). On the face of it, students' self-belief or selfdetermination must be activated so that they can overcome the challenges they are facing and can influence their motivation and confidence in learning (Aure & Jugar, 2017;Casinillo & Casinillo, 2020). Especially in the time of the COVID-19 pandemic, where their learning environment is not favourable and comfortable for students. According to Casinillo et al. (2022) and Simorangkir et al. (2021), mathematics learning during the pandemic has a lot of problems encountered by teachers and students as well as anxiety. In particular, there are barriers to systematically delivering the lessons due to internet connectivity. Students' progress and learnings are difficult to monitor and assess because of a lack of interaction and communication (Irfan et al., 2020;Onyema et al., 2020;Ní Fhloinn & Fitzmaurice, 2021). Hence, the study's framework aims to investigate the level of self-efficacy and the factors affecting it. The study considered the demographic profile of students and their learning experiences concerning their teachers as predictors of self-efficacy in mathematics. Results may provide policy and information to mathematics teachers that will improve their students' well-being and level up their self-efficacy.
Although several studies investigated self-efficacy learning during the COVID-19 pandemic, modeling self-efficacy and some of its factors have never been scrutinized. Perhaps, determining the causal factors of students' self-efficacy in learning mathema-tics can create a teaching strategy that will progress the students' cognitive thinking in problem-solving. In fact, this type of research has never been through in rural areas in the country Philippines, hence, this study is instantly realized. In general, this study intends to provide an explanation of the level of students' self-efficacy in mathematics during online education amid the pandemic. Specifically, the study aims to provide an answer to the following questions: (1) what is the demographic profile of college students; (2) what is the level of students' self-efficacy in mathematics; and (3) what are the significant causal factors of students' self-efficacy in mathematics amid the pandemic? The purpose of this article is to provide information and argument that may amend the present policy in mathematics education in the country Philippines. Additionally, results may provide concepts on how to improve the student's ability to cope with difficult times while learning mathematics. Results also may help students how to level up their confidence and motivation in solving mathematics problems. Moreover, results may give knowledge to mathematics teachers on how to deal with their students in a progressive way despite the challenges in online learning. Furthermore, findings may serve as a guide for teachers on how to improve their existing teaching strategy in mathematics and may also suffice as a benchmark for mathematics education researchers.

The Framework of the Study
In the study of Zimmerman (2000) and Bandura (1986), students' self-efficacy is defined as the ability to cope with various trials and it is a good source of motivation to initiate positive behavioral change. In that case, Rozgonjuk et al. (2020) stated that through self-efficacy, students can be self-determined in surviving mathematics problems during the time of the pandemic. Likewise, Özcan and Kültür (2021) have depicted that self-efficacy is a positive determinant in mathematics learning achievement since it creates full potential in becoming persevering students despite the challenges they are facing. Having a higher level of self-efficacy can sustain difficult situations and other obstacles because it provides a resilient behavior that improves their creative thinking ability (Lau et al., 2018;Masitoh & Fitriyani, 2018;Schöber et al., 2018;Nurhikmah et al., 2021).
Apparently, a social scientist has discovered that self-efficacy will develop the following aspects: mastery and vicarious experiences, emotional state, social persuasions, creativity, and self-determinations (Tschannen-Moran & McMaster, 2009;Bandura, 2018;Özcan & Kültür, 2021). On the face of it, students can develop a belief that executes planning and management to overcome difficult scenarios that they are facing in classroom activities. According to McAuley and Blissmer (2000), selfefficacy is a cognitive approach in which demographic profile, physiological factors, and environmental influences all operate as influencing factors. Hilton and colleagues (2020), reported that the demographic profile of students has something to do with their self-efficacy in learning. Yıldırım and Güler, (2022), stated that during the pandemic, self-efficacy is a belief that an individual is capable to exert an effort to motivate in doing solutions to problems during difficult situations. In fact, self-efficacy will positively influence the students on how they feel and think as well as act in doing their learning activities. In that case, students' self-efficacy can level up amidst the pandemic depending on how the teachers manage their students (Anderson et al., 2021). New and innovative teaching strategies during the pandemic can boost and lighten up students' self-efficacy which can help them learn effectively amidst the challenges and stressful learning environment (Garris & Fleck, 2022). Hence, the framework of this study is to correlate the level of students' self-efficacy and its determinants such as demographic profiles and teachers' engagement in online learning during the pandemic.

Methodology
The study dealt with a quantitative research design to depict students' selfefficacy level and its influencing causal factors amid the unusual situation. This design utilized a large sample size of students selected at non-random. The target respondents of this study were students of Visayas State University (VSU), Baybay City, Leyte who were enrolled in Mathematics in the Modern World (MMW) during the second semester (A.Y. 2021-2022). A non-probabilistic method was used in determining the sample respondents since the study considered an online survey that whoever students responded to the Google form survey automatically included in the list of participants.
The survey was open for about one month in the middle of the semester and 233 students filled up the survey. Prior to the survey, the ethics for research has been considered as follows: (1) a formal letter of consent was accomplished first to the teachers of the students; and (2) students were informed that their participation is voluntary, and the data collected are treated confidential and solely used for research only.
As for the research instrument for the dependent variable in this study, a surveystructured questionnaire for the general self-efficacy scale (GSS) was developed from the article of Schwarzer and Jerusalem (1995). The questionnaire was adapted in view of mathematics learning amid the COVID-19 pandemic. The questionnaire involves 10 questions with the response of a 4-point scale as follows: 1 -Not at all true, 2 -Hardly true, 3 -Moderately true, and 4 -Exactly true. In that case, to get the perception score of students, the sum was considered from the 10 questions. Hence, 10 is the lowest score (very low perception of self-efficacy) and 40 is the highest score (very high perception of self-efficacy). According to Schwarzer and Jerusalem (1995), the questionnaire is validated and found that GSS is associated with an individual's emotions, optimism, and work well-being. Additionally, the negative coefficients were set up for individual depression, stress, burnout, and anxiety level. Moreover, the questionnaire was also undergone an internal reliability test and found that Cronbach's alpha is between 0.76 and 0.90 which indicates that GSS is reliable. Table 1 presents the interval of values that the mean score might fall and its corresponding overall response as verbal description. For the independent variables, another structured and open-ended questionnaire was developed that contains the following students' profile and learning experiences: gender (0=female, 1=male), age (in years), hometown (0=Rural, 1=Urban), number of hours studying mathematics (per week), money spent for the internet connection (PHP per week), on-time submission of mathematics outputs (0=No, 1=Yes), interactions with teacher support online (0=No, 1=Yes), the teacher makes you feel comfortable and ready to learn (0=No, 1=Yes), and the teacher usually successful in helping you with your problems or questions (0=No, 1=Yes).
In summarizing the data gathered, descriptive measures such as mean (M), standard deviation (SD), minimum value (min), and maximum value (max) were employed for independent variables. Next, frequency, percentages, mean (M), standard deviation (SD), and coefficient of variation (CV) were used to describe and interpret the level of students' self-efficacy in mathematics amid the pandemic. Note that if the CV is less than 20%, then it is considered to be a consistent response (Reed et al. 2002).
In predicting the possible causal factors of students' self-efficacy, a regression model was constructed. On the face of it, the response perception score of the 10-item questions on self-efficacy in mathematics was summed up to be the independent variable of the regression model. Hence, the lowest score is 10 and the highest is 40. A low perception score means low self-efficacy and a high perception score means high self-efficacy in mathematics. Thus, the regression model takes the following form: where represents the level of students' self-efficacy learning mathematics, = 1, … , and is the number of respondents (MMW students), (∀t ∈ {0, 1, . . . , }) refers to the parameters of the model (1) to be estimated, (∀t ∈ {1, . . . , }) are the different independent variables in the model, and is the remaining random error. As for the validity of the model, diagnostic tests were performed and all calculation was done using STATA version 14 and all statistical inferences were tested at a 5% level of significance.

Descriptive Analysis
This section presents the demographic profile of students and teachers' roles during online learning as shown in Table 2. The average age of the students is close to 19.68 (SD=1.90) for which the minimum is 18 and the maximum is 34 years old. Dominant (69%) of these students are female and only 31% of them are male. This result is parallel to the study of Valenzona et al. (2022) that most of the MMW students at VSU are female. Additionally, most (76%) of these students are living in rural areas in Leyte where internet access is sometimes difficult and only 24% of these students are living in urban places. This result is consistent with the findings of Casinillo et al. (2022) who found that most of the university students in Leyte are living in remote areas in the province.
During online learning, the students' study hour is about 4.78 hours per week, however, some students do not study their lesson. On average, a student will have to spend 201.86 PHP (SD=372.86) for internet consumption and other expense for their online learning. Approximately, there are 56% of these students can submit their mathematics outputs on time, and about 44% of them submitted their outputs late or cannot submit at all. About 58% of the students said that their mathematics teachers have been interactive during online learning (Table 2). This means that teachers are engaging with their students concerning their lessons and giving them interesting activities that will boost their cognitive thinking. On the contrary, about 42% of the students said that their teachers are just giving them work activities without proper interaction with their students. This means that students are just given a deadline for submission to their learning task without engaging in a proper discussion online.
Almost all (96%) of these students said that their mathematics teachers provide a comfortable learning environment (Table 2). Apparently, academic ease is very important to students to somehow avoid depression and anxiety that makes them stressed and unproductive. Valenzona et al. (2022), stated that students should be given interesting and timely learning tasks and activities that favor the students' well-being during these unprecedented times. Moreover, about 94% of these students said that their mathematics teachers are successfully helping them in their academics and learning assessment (Table 2). According to Garris and Fleck (2022), learning during the pandemic has become less interesting, and enjoyable, and decreased in learning value. Hence, teachers must make effort to aid their students to maintain progress and continue learning despite difficult times.

Students' Self-efficacy in Mathematics
Unfortunately, there are 17.17% of these students do not have presence of selfefficacy (Table 3). This type of student does not have the ability to cope with stress and does not have the motivation to produce a solution in which they can learn effectively during the pandemic. In fact, Omar et al. (2021) stated that the pandemic situation has adversely created uncertainties in learning for students as well as the instructional process. Hence, it is important that students must have a coping mechanism in the form of self-efficacy to survive in their education during remote learning amid the pandemic. Simorangkir et al. (2021) found that self-efficacy and coping strategies will cause anxiety among students during the pandemic.
Additionally, there are also 18.88% of the students who have slight self-efficacy (Table 3). This type of student has little belief and confidence to face the obstacles and challenges in their class but not enough to efficiently learn and acquire sound knowledge during the pandemic. Especially since these types of students are learning mathematics, students must have a creative mind and analytical thinking that will be useful in problem-solving that is driven by self-efficacy. Schöber et al. (2018) depicted that a higher level of students' self-efficacy can help them in achieving good academic performance in mathematics.
Dominantly, 32.62% of these students have moderate self-efficacy in learning mathematics during the pandemic (Table 3). This type of student has an average belief that they can overcome the difficulties in their online education. However, still, these types of students are experiencing stress and depression due to the adverse impact of the pandemic on their learning process. According to the study of Aldhahi et al. (2022), students' experience the online learning during the pandemic is not easy in which they are moderately satisfied associated with moderate self-efficacy due to barriers and fewer interactions of remote learning.
Lastly, about 31.33% of the MMW students possess a high level of self-efficacy (Table 3). These students are confident and have self-determination that they can survive challenges and obstacles in any kind of problem-solving they might encounter in learning mathematics amid the pandemic. Zimmerman (2000) stated that through a high level of self-efficacy, students' only motive and focus is to learn even if the situation is hard. Moreover, Valenzona and colleagues (2022) expressed that students' innovativeness is very important in creating new ideas and solutions for mathematics problems which are associated with a high level of self-efficacy.

Statistical Model for Self-Efficacy and its Predictors
Table 5 depicts the statistical model that predicts the causal factors of students' level of self-efficacy in online learning during the time of the pandemic. With the assistance of the Breusch-Pagan test, it is shown that the model is not heteroscedastic (χ 2 =0.77, p-value=0.38) in which the variances are more or less homogeneous. This implies that the model revealed an equal variance in various categories being compared (Mátyás and Sevestre, 2013). In addition, with the aid of the Ramsey RESET test, it is revealed that the statistical model has no omitted-variable bias ( =2.26, p-value=0.08). This implies that the model does not leave out a relevant variable/s that predicts the students' self-efficacy level (Mátyás and Sevestre, 2013). Moreover, using the Variance Inflation Factor (VIF), the statistical model revealed that it has no multicollinearity problem between predictor variables in which by the rule of thumb the VIF is less than 10 (Allison, 2012). Furthermore, it is depicted by the Shapiro-Wilk W test that the statistical model's residuals are normally distributed (W=0.99, p-value=0.81) for which it shows that residuals are more frequent near its mean residuals (Mátyás and Sevestre, 2013). On the face of it, the model is considered to provide valid reasoning from its statistical outcomes. Note: a -dummy variable; b -Philippine Peso (₱); ns-not significant; ** -highly significant at 1% level.
The F-test (F=0.73, p-value=0.679) of the model is surprising in that it reveals no significant factor for students' self-efficacy in mathematics during the pandemic (Table 4). Even the t-test in predicting the individual independent variable has revealed no significant factor. This can be explained by debased level and low variation of the dependent variable (students' self-efficacy) (CV=18.98%) which indicates a consistent response as seen in Table 3. This implies that the moderate self-efficacy that they have is not influenced by their demographic profile (age, sex, hometown), learning experiences (study hours, money spent for internet access, submission of outputs), and teachers' causation (interaction of a teacher, teachers' comfort, teachers' helping hand) in the online learning process. Additionally, the model revealed a very low coefficient of determination or model fit (R 2 =0.029). This indicates that the predictors being incorporated in the model have explained a very low influence on students' self-efficacy and it is not significant at the 5% level. Hence, this implies that students' self-efficacy is being dominated by mathematical anxiety due to the adverse effect of the pandemic. Apparently, students are experiencing difficulty in learning their mathematics lessons due to the barriers and lack of interaction in online learning (Irfan et al., 2020). It is worth noting that if a student has a low level of self-efficacy, the student has a lower chance of learning effectively due to a lack of motivation in doing their tasks as a student (Schöber et al., 2018;Kasturi et al., 2021). Siegle and McCoach (2007) suggested that through teacher training concerning efficacy, students' mathematics selfefficacy can be increased. Hence, teachers must initiate training for themselves and integrate it into their classrooms. Moreover, teachers must create a lively classroom environment that boosts students' innovativeness to increase students' cognitive thinking and self-efficacy despite the challenges amid the pandemic .

Conclusion and Recommendation
The study depicted evidence that students during the pandemic are having a moderate level of self-efficacy in learning mathematics online. It means that students' belief and ability in solving mathematical problems during online education is relatively moderate due to the mathematical anxiety brought about by the pandemic. Students are not well motivated to learn and they are resistant to adopting the new context of learning. The statistical model revealed that no causal factors are affecting the students' self-efficacy during online learning.
This indicates that the self-efficacy of these students is negatively affected by the challenges and barriers in distance education and not influenced by their profile, experiences, and teacher influence. Conclusively, teachers must modify their strategies that are suitable for distance learning where their students can actively participate and develop self-efficacy. Teachers must create a favorable atmosphere and show a positive attitude during class discussions. Show kindness however authoritative that develops students' innovativeness and enjoyment in learning which can boost the students' motivation and mathematics self-efficacy.
Additionally, teachers must give realistic mathematics activities that are suitable and accomplishable for online learning. Plus, teachers must draw students' attention to their progress and compliment them on their daily achievements. Furthermore, the study recommends for future research to incorporate other influencing variables for mathematics self-efficacy such as coping mechanisms, resiliency, well-being and health, and economic factor, among others.