Publication History
Submitted: November 18, 2023
Accepted: November 27, 2023
Published: December 11, 2023
Identification
D-0165
Citation
Emmanuel P. Abuzo (2023). Mathematics Anxiety, Learning Culture, Aptitude and Problem-Solving Ability of Senior High School Students: A Structural Model. Dinkum Journal of Social Innovations, 2(12):676-702.
Copyright
© 2023 DJSI. All rights reserved.
676-702
Mathematics Anxiety, Learning Culture, Aptitude and Problem-Solving Ability of Senior High School Students: A Structural ModelOriginal Article
Emmanuel P. Abuzo ^{1}* ^{ }
- Sawata National High School, Davao del Norte, Philippines; abuzoemmanuel@gmail.com
* Correspondence: abuzoemmanuel@gmail.com
Abstract: The study was conducted to develop the best fit model of problem-solving ability. Specifically, it established the relationship among mathematics anxiety, aptitude, and learning culture. Descriptive correlational and causal-comparative designs were utilized in this study. The data were gathered from Cluster I’s senior high school students, Division of Davao del Norte. Sets of adopted survey questionnaires were used as instruments for mathematics anxiety and learning culture. An aptitude was measured through the mathematics 10 final grades, and the NCAE results in mathematics. The problem-solving ability was measured using a researcher-made test. The findings revealed that the learners’ level of problem-solving skills was beginning. Among the four steps, which are understanding a problem, devising a plan, carrying out the plan, and looking back, only understanding a problem obtained developing level. All other factors were beginning. The mathematics anxiety extent of Senior High School learners was a fair amount of anxiousness. The three mathematics anxiety factors: test anxiety, numerical anxiety, and subject anxiety, are all in a fair amount of anxiousness. The students agreed that the sound learning culture of the school is much evident. Moreover, the students agreed that the positive atmosphere in the learning culture in terms of peers was apparent. The constructivist teaching approaches were evident. The positive learning environment was evident in the school, and the learning facilities were favorable. There was a significant relationship among mathematics anxiety, learning culture, aptitude, and problem-solving ability. The model suggested a high level of mathematics aptitude supported by peers, teaching approaches, learning environment, and learning facilities was the critical factor in better problem-solving ability in mathematics.
Keywords: problem-solving ability, mathematics anxiety, aptitude, structural equation model
- INTRODUCTION
By improving its curriculum, DepEd sought to improve education. The DepEd Mathematics Curriculum aimed to teach critical thinking and problem-solving. The curriculum stressed the importance of students’ problem-solving skills, which require reasoning to break down issues, assess answers, and make arrangements (Proctor, 2018). The foundation for skillful and productive adulthood is higher-order thinking and problem-solving (Susanti & Retnowati, 2018). DepEd and CHED’s Enhanced Basic Education Curriculum promoted problem-based learning and higher-order thinking for the scientific approach (RA 10533). Despite DepEd efforts, students still struggle to master problem-solving (Surya & Putri, 2017). The 2018 Programmed for International Student Assessment (PISA) results showed that Filipino secondary students performed poorly in Reading Comprehension, Science, Mathematics, and Problem-solving (de Borja, 2020). Despite these primary cores in mathematics education, teachers were frustrated because students were less aware of learning concepts in daily assignments and evaluations (Surya & Putri, 2017). Even after teachers spent time teaching fractions and integers, students couldn’t measure them in maths problems (Santos-Trigo, 2020). The Philippine Mathematics Curriculum Framework (2016) requires students to master quantitative problem-solving, which involves computation, and qualitative problem-solving, which involves data interpretation. Students need thinking skills to solve quantitative and qualitative problems. Filipino students’ least problem-solving skills are converting to a mathematical statement, mathematical methods, and mathematical concepts, according to Alcantara and Basca (2017) Alcantara and Basca (2017) noted mathematics anxiety as a constraint. Problem-solving performance was negatively impacted by mathematics anxiety (Hembree, 2016). Mathematics anxiety represents anxious learners’ feelings of unease, vulnerability, dread, and confusion when solving mathematical problems (Yuliani et al., 2019). Lack of confidence, trust in math ability, and students’ career choices are linked (Blotnicky et al., 2018). Mathematics anxiety is important because teachers should be concerned about students’ emotional issues that hinder maths problem solving. Student math anxiety and problem-solving ability are strongly correlated with school learning culture (Hembree, 2016). Learning culture is crucial to observing and improving students’ problem-solving skills. Additionally, comfortable homeroom conditions, adequate learning facilities, and a positive atmosphere help students focus and perform well (Leonard, 2018). Environmental forces influence a person’s growth. Social, cultural, physical, and mental cultures improve education (Chauhan, 2017). The school’s positive learning culture enhances learning. Students spend most of their energy in class (Rafanan & De Guzman, 2020). Additionally, the school’s learning environment greatly affects students’ critical thinking (Darling-Hammond et al., 2020). Aptitude helps students solve problems. A learner’s aptitude is their ability to solve practical, logical, conceptual, or other everyday problems. Any aptitude is a mix of intrinsic traits that show his ability in any field. Current Philippine education focuses on giving students information, teaching them how to learn, and writing their thinking to solve problems and building skills to handle them (Flores, 2019). In the current educational framework, students must obtain data, use information, make decisions about capacity, basic reasoning, explanatory skills, critical thinking, inventiveness and creative demeanour, fitness for examining, quantitative capacity, multidisciplinary information, PC aptitudes, relational skills, delicate skills, authority, working in a group, uplifting mentalities, and a broader worldview. Students develop these skills and abilities with metacognitive skills (Kamphaus, 2019). Maths scored 50.70 on the 2017-2018 National Achievement Test (NAT) for Senior High School of the Division of Davao del Norte. The MPS of critical thinking was 47.82, with 25.71% of takers achieving near mastery and 59.09% achieving low mastery. Poor performance strongly suggests poor higher-order thinking and problem-solving. Lack of interpretation, analysis, reasoning, factual knowledge, and theoretical learning led to low test scores. Many research methods link learners’ problem-solving abilities to abilities and skills belief, perceptions and efficacy, teaching strategies and pedagogies, and technology-based instruction. According to NAT 2018, understanding students’ problem-solving ability is still common, especially in Davao del Norte’s Division. The study’s proponent has not found any research on the causal relationship between mathematics anxiety, learning culture, aptitude, and problem-solving ability. The scenario led the researcher to search for ways to improve student problem-solving. In this case, the researcher wants to build a model of how mathematics anxiety, learning culture, and aptitude affect problem-solving. The need to conduct this study was established because its results could raise awareness of the proposed beneficiaries and suggest a plan to improve learners’ mathematics performance.
- LITERATURE REVIEW
The Mathematical Problem-solving Theory of Schoenfeld (1985) stressed that the development of problem-solving results from the learner’s feelings towards the problem, the learner’s cognitive capacity, and the learner’s learning setting culture. The interaction among the learner’s aptitude to process information, the learner’s mathematics anxiety in solving the problem, and task set-up that includes the environment’s learning culture are essential factors in solving a problem. In line with problem-solving abilities, the theory of Problem-Solving by Polya (1985) was utilized. Accordingly, cognitive processes take place during problem solving, which include mobilizing, coordinating, and collecting. When a problem is complex, they must put more focus on interpreting and understanding the contention that defines the problem. Polya emphasized that essential memory elements like solved problems, theorems, concepts, and research needs to be retrieved in the long-term memory. Connecting the elements of previously studied facts to the issue is a vital step in resolving the problem. Resolving the issue needs to be described, distinguished, used, and contextualized. Since there was an issue, the entire conception was strengthened, or some parts were approached from several viewpoints to arrive at a solution. The development of this ability is affected by intrinsic and extrinsic factors. The Debilitating Anxiety Theory of Carrey et al. (2014) was used to study mathematics anxiety. Mathematics fear leads to problem-solving skills’ accordingly, mathematical distress often manifests at the pre-processing, during the calculations, and data retrieval stages. Anxiety in mathematics was associated with decreased cognitive reflection while solving word problems in mathematics. Learners avoid processing mathematical problems due to anxiety, which leads to deteriorating mathematics performance. Moreover, the theory emphasized that different anxiety sources must be subjected to investigation to be crafted a holistic approach to address this problem. Bloom’s (1976) Theory of School Learning was also used as the foundation for learning culture in this research. Students can build and strengthen their problem-solving skills through associations and exchanges with other students, teachers, and physical environments, according to the theory. The school should create a learning environment that enables students to maximize their ability to exchange and socialize with others by cooperating, talking, and feedback to maximize problem-solving skills. Also, learning culture is the critical determinant in the improvement of knowledge and skills. Students learn from this lens by engaging and adhering to environmental guidelines, expectations, and more. Furthermore, the theory emphasized that a more comprehensive understanding of the development of the learners’ problem-solving skills will be achieved if the school’s learning culture is included in the investigation. Finally, the research into aptitude in this study was based on John Sweller’s Cognitive Load Theory (1988). According to the theory, the best conditions for learning a solution to a problem are those that are compatible with the human cognitive architecture. To develop problem-solving skills, students need comprehensive mathematical knowledge in their long-term memory. The long-term memory subjects are sophisticated structures that allow students to interpret, think, and solve problems instead of a group of rote facts. The theory suggests that students must obtain the necessary knowledge and information so that these data can be easily retrieved if mathematical problem-solving is needed. These structures allowed learners to treat multiple elements as one element. They are the cognitive structures that form the basis of knowledge. Also, someone who acknowledges his capacity and has a high objective can better improve his problem-solving skills or learn to be more effective. In this learning phase, cognitive skills and aptitudes enhance problem-solving skills. The hypothesized figure established the relationship among mathematics anxiety, learning culture, aptitude, and problem-solving ability. In the diagram, the relationship is defined among mathematical anxiety, learning culture, ability to solve problems. The study also measured indicators heavily loaded with problem-solving ability. Moreover, the relatedness among mathematics anxiety, learning culture, aptitude, and problem-solving identifies a set of the simultaneous regression equation. The results strengthened the model because of Schoenfeld’s (1985) theoretical model, which explained the linkages between learning variables and the learners’ problem-solving ability. In this study, learning variables refer to Mathematics Anxiety, Learning Culture, and Aptitude.
- MATERIALS AND METHODS
The study made use of descriptive, correlational, and causal-comparative designs. Descriptive was used to describe the status of the situation as it existed at the time of the study to explore the causes of a particular phenomenon. This study is also a correlation because it involved collecting data to determine whether the relationship exists between two or more quantifiable variables. This descriptive survey dealt with quantitative data about the said phenomenon. The quantitative aspect is an appropriate schedule for gathering the data designed for the target respondents to answer the questions. The process of gathering the data was based on the use of questionnaires. The focus of the study was to develop and employ mathematical models, theories, and hypotheses about the phenomena. This nature was also exhibited by the use of empirical data in the interval level of measurement from participants’ responses in the mathematics anxiety, learning culture, aptitude, and problem-solving ability. This study also focused on fitting the data to hypothesized models mathematics anxiety, learning culture, aptitude, and problem-solving ability. Hence, a causal design was employed to describe the relationships among the observed variables and latent variables of the study. The study was conducted at the secondary schools of Cluster 1 in the Division of Davao del Norte, offering Senior High School Program. The following secondary schools of the said cluster offer Senior High School Program: Sawata National High School, Linao National High School, Datu Balong National High School, Pinamuno National High School, Sagayen National High School, Sonlon National High School, Asuncion National High School, New Corella National High School, Mesaoy National High School, Limbaan National High School, Sta. Fe National High School, Davao del Norte Sports Academy. The respondents of this study were the grade 11 students enrolled in the School Year 2019 – 2020 at the secondary schools of Cluster 1 in the Division of Davao del Norte.
Table 01: Distribution of the respondents of the study
School | Population | Sample | Percentage |
A | 45 | 37 | 3.14% |
B | 31 | 27 | 2.29% |
C | 55 | 48 | 4.07% |
D | 123 | 108 | 9.17% |
E | 167 | 140 | 11.88% |
F | 218 | 174 | 14.77% |
G | 232 | 211 | 17.91% |
H | 119 | 92 | 7.81% |
I | 283 | 246 | 20.88% |
J | 44 | 35 | 2.97% |
K | 57 | 48 | 4.07% |
L | 19 | 12 | 1.02% |
Total | 1473 | 1178 | 100.00% |
Table 1 shows respondent distribution. Cluster 1 has 1178 grade 11 students for 2019–2020. There were 1178 respondents, with 679 students (57.64%) taking TVL tracks and 487 (41.34%) taking academic tracks. Out of 487 students, 191 took GAS, 107 ABM, and 84 STEM. Twelve sports-track students (1.02% of respondents) participated. The researcher used convenience sampling. Student-respondents were oriented by the researcher before receiving the questionnaire. He explained the research’s purpose and benefits. He also stressed that his respondents must volunteer for this research and not receive credit or pay. He also discussed their identities and responses’ confidentiality. RA 10173, the “Data Privacy Act of 2012,” requires that personal information be discarded to protect individuals from unauthorized processing, so he made sure no names were visible in the data. The Revised Mathematics Anxiety Rating Scale and Learning Culture Questionnaires from various authors were used. Their aptitude was determined by their Mathematics 10 final grades and NCAE results. The researcher-made questionnaire after first-quarter General Mathematics competencies measured problem-solving ability. An expert panel tested these instruments for face and content validity before administration. The instruments were tested by 37 Grade 11 senior high school students at Sto. Tomas National High School for reliability. Cronbach’s alpha values indicated acceptable reliability. The Bukidnon State University College of Education Dean approved this study’s data collection. After that, the Schools Division Superintendent of Davao del Norte authorized the study in Cluster 1. After receiving the Schools Division Superintendent’s approval, the researcher sent the letter to the study’s school heads to convince them to administer the questionnaire. The researcher personally handed the questionnaires to the student-respondents for clarification. The researcher took the questionnaire after respondents answered. Next, answers were meticulously counted. Statisticians analyzed the data using appropriate statistical methods. The analysis informed the conclusions and recommendations.
- RESULT AND DISSCUSSION
The basis of the presentation is on the statements of the problem in chapter 1. This report starts with the Problem-Solving ability followed by the extent of Mathematics anxiety. Then, the learning culture and then the aptitude described by the Mathematics 10 final grades and the Mathematics ability from the NCAE results. Finally, the variables that best predict the problem- solving ability and the best fit model.
4.1 The Level of Problem-Solving Ability
Table 2 shows the overall problem-solving ability level of the learners. It can be seen that the problem-solving ability is at the beginning level. Likewise, the result shows that in all the steps to solve a problem, students were at the beginning level except for understanding the problem, which is at the developing level. This indicates that the students are at a very low level in terms of problem-solving ability.
Table 02: Overall Level of Problem-Solving Ability
Variable | Transmuted Grade | Level of Problem-Solving Skills |
Understanding the Problem | 77 | Developing |
Devise a Plan | 74 | Beginning |
Carry-out the Plan | 71 | Beginning |
Look back | 70 | Beginning |
Problem-Solving Ability | 73 | Beginning |
Grade 11 students performed poorly in problem-solving. Students struggle to analyse and solve math word problems. Real-world math skills are not fully developed by respondents. This means that the necessary knowledge and skills to solve mathematical problems have not been acquired and developed. This suggests that students did not learn how to investigate and understand mathematics in practice. Students have trouble looking for clues to solve problems. Due to limited knowledge, students struggle to create or use the right formula. This knowledge and skill gap causes students to misrepresent and misinterpret the problem. Since their formula is wrong, they may create the wrong process. This poor problem-solving ability is shown by a lack of understanding. Making possible solutions shows how students understand procedures. Table results indicate students have not mastered this competency. Since the skill to process problem-solving information is still developing, the ability to structure and organise relevant information is underdeveloped. Students are reluctant or avoid solving problems due to this poor ability. They don’t look for more clues and relevant information to solve the problem. According to observation, they accept defeat and leave the issue unresolved. Another group of students is “bahala na” and accepts what happens. Students’ attitudes and traits compromise critical and logical thinking. Students’ inability to solve problems will under develop these core mathematics curriculum goals.
Table 03: Level of Problem-solving Ability in terms of Understanding a Problem
Transmuted Grade | Percent | Level of Problem-Solving Ability |
90 – 100 | 12.4% | Advanced |
85 – 89 | 20.5% | Proficient |
80 – 84 | 24.5% | Approaching Proficiency |
75 – 79 | 16.8% | Developing |
Below 75 | 25.8% | Beginning |
Mean: 64.83
Transmuted: 77 |
Developing |
According to table 3, learners’ problem-solving skills include understanding. Most students improved their problem-solving skills, as shown in the table. This indicates that learners had a low ability to understand the problem and identify clues to solve it. They may have trouble visualising and illustrating the problem into a diagram or math equation. They need close supervision for problem-situation or concept comprehension. The results indicate that the learners’ ability to solve a problem is not sufficient in relation to understanding the problem. It means that they have the skills at this stage to translate the problem into a mathematical statement or illustrating the problem, but inadequate. Because of this inadequacy, students are dependent on the teacher or other experts to lay out the problem. Assistance in understanding the problem is evident at this level. The result implies that the students struggle to comprehend the problem. Students may obtain portions of the information but may struggle to recall essential elements necessary to solve the problem. This lack of understanding of the problem caused them to make bad decisions. The students find it very hard to think about the outcome and repercussions of their decisions since they were just working on the parts but have not understood the whole picture of the problem. Due to poor comprehension, students struggle to identify the condition, the necessary data, and the missing variable. At this ability, students become confused on how to separate various parts of the condition to introduce suitable notation. They find it hard to write down the necessary information needed to solve the problem, especially when there are many distractors given. Oftentimes, they were surprised how easy the problem was after the teacher solved it on the board.
Table 04: Level of Problem-Solving Ability in terms of Devise a Plan
Transmuted Grade | Percent | Level of Problem-Solving Ability |
90 – 100 | 9 % | Advanced |
85 – 89 | 15.1% | Proficient |
80 – 84 | 18.3% | Approaching Proficiency |
75 – 79 | 17.7% | Developing |
Below 75 | 39.9% | Beginning |
Mean: 59.27
Transmuted: 74 |
Beginning |
Table 4 showed the mean percentage of learners’ plan-making problem-solving ability. The results show that students are very poor at making plans. It appears that students struggle to organise their findings into a plan. Learners lack a strategy for problem-solving. They struggle to identify a pattern in the given information to solve the problem. Students struggle in the following direction to meet problem requirements because they don’t understand the problem. Students’ problem-solving planning depends on how much information they gather. Math concepts and applications were not understood well enough to create a solution. Students struggle to link the data to the missing element. This inability to find connections makes it hard for students to find a pattern or model the problem. The results suggest that students with this skill struggle to set up an equation or map to solve the problem. Creating a plan often requires prior knowledge or experience. The results suggest that students struggle to find a similar solved problem. Students can’t relate the unknown to a familiar problem with the same or similar unknown, as shown by their poor problem-solving skills. Students struggle to imagine more accessible information to solve the problem because they can’t relate it to previous problems. Students struggled to simplify the problem. More often, students struggled to find useful information from the given or find other data to determine the unknown. Students cannot consider all key concepts due to the poor problem-solving plan.
Table 05: Level of Problem-solving Ability in terms of Carry-out the Plan
Transmuted Grade | Percent | Level of Problem-Solving Ability |
90 – 100 | 0.9% | Advanced |
85 – 89 | 3.7% | Proficient |
80 – 84 | 9% | Approaching Proficiency |
75 – 79 | 14.6% | Developing |
Below 75 | 71.9% | Beginning |
Mean: 45.24
Transmuted: 71 |
Beginning |
Table 5 shows learners’ plan-executing problem-solving ability. The results show that students failed to implement the solution plan. This description suggests students struggle with the problem. After deciding on a solution, they struggle to follow it. Insufficient previous steps lead to poor plan execution by students. The result showed that students have trouble executing the plan due to its poor foundation and formulation. Students can see their poor formula and concept use. Since this phase depends on the previous step, devising the plan, students’ weak ability to create a plan to solve the problem makes them weak at executing it. Their answers are inaccurate and inappropriate. Moreover, the ability to check the model or formula while solving it is lacking. The results also showed that students accepted their answers without further evaluation. Executing the plan requires formulating the process without violating math rules. The students’ underdeveloped skill hinders plan execution. According to the table, this led to poor use of the important mathematical concept, idea, or theory to solve the problem. Students must verify each step of the plan before executing it. Due to their poor plan execution, they struggle to determine if each step is appropriate. Students have basic knowledge from previous lessons, but they struggle to apply it accurately to the problem at hand because they can’t prove each step in their plan is correct. Due to their poor mathematical concept utilisation, students were determined to find a solution if their answer was wrong. Most students implemented their plan randomly. Students created a botched solution that failed. This indicates that students’ critical thinking is underdeveloped.
Table 06: Level of Problem-solving Ability in terms of Look Back
Transmuted Grade | Percent | Level of Problem-Solving Ability |
90 – 100 | 2.4% | Advanced |
85 – 89 | 5.1% | Proficient |
80 – 84 | 8.8% | Approaching Proficiency |
75 – 79 | 12.7% | Developing |
Below 75 | 70.9% | Beginning |
Mean: 41.21
Transmuted: 70 |
Beginning |
Table 6 showed the mean percentage of learners’ looking-back problem-solving ability. Poor answer verification is shown in this table. This result shows that students don’t know how to check their work after checking the answer by looking at the problem. They were careless in checking the plausible solution, especially using units of measurement or finding something wrong. Students have poor solution verification skills. Students often accept their answers without assessing whether they solve the problem or are reasonable. Students’ inability to countercheck their work shows they can’t discuss their problem-solving steps or strategy. This inability to thoroughly discuss their steps led the student to misinterpret the results and misunderstand the problem.
4.2 The Extent of Mathematics Anxiety
Three aspects determined the respondents’ mathematics anxiety, namely, test anxiety, numerical anxiety, and subject anxiety. Table 7 presents the summary table of Mathematics anxiety. It denotes that the students have experienced a tolerable amount of worries, uneasiness, or nervousness towards mathematics. This description suggests that the students have considerable enthusiasm but are somewhat uneasy about mathematics.
Table 07: Extent of Mathematics Anxiety
Variable | Transmuted Grade | Level of Problem-Solving Skills | Variable |
Test Anxiety | 2.82 | 0.39 | Fair amount of anxiousness |
Numerical Anxiety | 2.69 | 0.56 | Fair amount of anxiousness |
Subject Anxiety | 2.67 | 0.54 | Fair amount of anxiousness |
Overall | 2.73 | 0.40 | Fair amount of anxiousness |
The result indicates manageable math anxiety in students. Students can reduce their math anxiety by asking peers or teachers questions. Students relax and feel comfortable with the subject through peer and teacher interaction. They felt little anxiety during the exam. Every day, students applied math fundamentals with confidence. The result also shows that students are less afraid to study instructional mathematics.
Table 08: Extent of Mathematics Anxiety in terms of Test Anxiety
Indicators | Mean | Standard Deviation | Qualitative Description |
Taking a quiz in a math subject. | 2.92 | 0.67 | Fair amount of anxiousness |
Receiving your final math grade. | 2.90 | 0.83 | Fair amount of anxiousness |
Taking the mathematics section of a standardized exam (e.g., NAT and NCAE). | 2.89 | 0.60 | Fair amount of anxiousness |
Thinking about an upcoming math test 1 hour before. | 2.87 | 0.82 | Fair amount of anxiousness |
Studying for a math test | 2.83 | 0.55 | Fair amount of anxiousness |
Realizing you have to take a certain number of math classes to fulfill requirements in your major. | 2.83 | 0.73 | Fair amount of anxiousness |
Opening a math or stat book and seeing a page full of problems. | 2.82 | 0.74 | Fair amount of anxiousness |
Being given a “pop” quiz in a math class | 2.82 | 0.74 | Fair amount of anxiousness |
Table 8 shows Grade 11 maths test anxiety. They have moderate test anxiety. It means students have manageable math anxiety. This implies that they are not anxious about maths tests but not confident about them. Students today aren’t afraid of maths tests. In my experience, students have asked their maths teacher for quizzes. The results indicate that students can handle maths exams. Students trust their own methods for remembering teacher instructions. The table shows moderate anxiety in the students, so this confidence is not fully developed.
Table 09: Extent of Mathematics Anxiety in terms of Numerical Anxiety
Indicators | Mean | Standard Deviation | Qualitative Description |
Being given a set of numerical problems involving subtraction problems to solve on paper. |
2.75 |
0.73 |
Fair amount of anxiousness |
Being given a set of numerical problems involving division problems to solve on paper. |
2.75 |
0.74 |
Fair amount of anxiousness |
Reading a cash register receipt after your purchase. | 2.74 | 0.71 | Fair amount of anxiousness |
Being given a set of numerical problems involving multiplication problems to solve on paper. |
2.67 |
0.92 |
Fair amount of anxiousness |
Being given a set of numerical problems involving addition problems to solve on paper. |
2.60 |
0.92 |
A little amount of anxiousness |
Overall | 2.69 | 0.56 | Fair amount of anxiousness |
Number-based mathematics anxiety is shown in table 9. The results show that students have manageable numerical anxiety about maths. Subtraction has the highest mean of the four fundamental operations. Subtraction problems made students nervous more than other basic operations. As shown in the table, this anxiety is manageable. Problems in addition made students the least nervous compared to other fundamental operations. This means students are not nervous about solving simple computational mathematics problems, but they are not optimistic.
Table 10: Extent of Mathematics Anxiety in terms of Subject Anxiety
Indicators | Mean | Standard
Deviation |
Qualitative
Description |
Listening to another student explaining a
Math formula. |
2.79 | 0.74 | Fair amount of
anxiousness |
Enrolling in a math course. | 2.77 | 0.81 | Fair amount of
anxiousness |
Attending into a math course. | 2.74 | 0.79 | Fair amount of
anxiousness |
Watching a teacher work on an algebraic
Equation on the blackboard. |
2.61 | 0.96 | Fair amount of
anxiousness |
Buying a math textbook. | 2.41 | 0.95 | A little amount of
anxiousness |
Overall | 2.67 | 0.54 | Fair amount of
Anxiousness |
Table 10 shows subject anxiety in mathematics. The respondents’ moderate anxiety suggests that students had some concerns about math’s. It suggests they are moderately anxious about maths. Results show students felt slightly anxious during math discussions. This shows that students still fear math’s. Since the students’ anxiety was manageable, it wasn’t too bad. The results indicate that students are confident but slightly nervous about math. Engaging and relatable discussions reduce students’ anxiety. Subject anxiety is second to least when observing a teacher discuss algebraic equations on a blackboard, according to the table. This means that the teacher’s methods and demeanor during learning activities help students relax. The findings indicate that students participated in concept discussions, especially when the teacher did. This math discussion makes students nervous. Since DepEd gave public high school students maths books, they felt less anxious when buying them. Most students in this study are in remote areas, so few need new reference materials. Most students relied on teacher references. As a result, manageable anxiety persists.
4.4 The Level of Learning Culture
Table 11 presents the overall learning culture with peers, teaching approaches, learning environment, and learning facilities as variables. The overall learning culture entails that the students observed the positive relationship between peers, constructivist approaches to learning, a positive learning atmosphere, and the functionality of learning facilities to promote student learning.
Table 11: Level of Learning Culture
Variables | Mean | Standard Deviation | Qualitative Description |
Peers | 3.63 | 0.91 | Agree |
Teaching Approaches | 3.58 | 0.54 | Agree |
Learning Environment | 3.56 | 0.56 | Agree |
Learning Facilities | 3.50 | 0.68 | Agree |
Overall | 3.55 | 0.43 | Agree |
The result shows the school’s good learning culture. This indicates that students found the school’s learning culture satisfactory. Students saw a way to help each other. Teachers create engaging, relatable learning activities. School activities improve learning. Teachers also use school facilities to design learning activities. The results show that students believe teachers’ math activities can improve their performance. Math’s becomes less scary and more relatable at school. Most students today saw the math classroom as a place to work together. This interaction helps students support and challenge each other’s strategic thinking. Additionally, these learning activities encourage students to use mathematical thinking. The assignments let students explore, explain, extend, and evaluate their progress. Students saw teachers accept their differing opinions. Moreover, teachers were optimistic about mathematics and students’ math skills.
Table 12: Extent of Learning Culture in terms of Peers
Indicators | Mean | Standard Deviation | Qualitative Description |
My peers are supportive of me. | 3.66 | 0.95 | Agree |
I feel free to approach my peers for help more than I do my teachers. | 3.63 | 0.91 | Agree |
The feedback I receive from my peers is realistic and helpful. | 3.62 | 0.85 | Agree |
My ability to solve problems improves when I can ask a peer. | 3.62 | 0.97 | Agree |
I learn from my peers. | 3.62 | 0.92 | Agree |
I can communicate freely with my peers. | 3.56 | 0.90 | Agree |
My self-confidence is higher, and I am independent with my peers. | 3.50 | 0.90 | Agree |
I am less anxious when applying my knowledge in mathematics in the presence of other peers than my instructors. |
3.50 |
0.89 |
Agree |
Being taught by my peers increases my interaction and collaboration with other students. | 3.49 | 0.89 | Agree |
Overall | 3.63 | 0.91 | Agree |
Table 12 shows peer-based learning culture. Based on these findings, peers foster positive learning. This suggests that students noticed a positive school environment from peers. This means students fairly observed peer cooperation. The results indicate a positive peer learning culture. Peers’ approval of students is evident. This suggests that students see their classmates as guides as they learn math concepts. Since they can express their feelings more freely than their teacher while learning maths, they feel less anxious when explaining their understanding to peers.
Table 13: Extent of Learning Culture in terms of Teaching Approaches
Indicators | Mean | Standard Deviation | Qualitative Description |
It is allowed to conduct assignments in pairs or in groups. | 3.66 | 0.95 | Agree |
I am encouraged to study in pairs or in groups throughout the semester so that I can tell and explain the subject matter to each other. |
3.63 |
0.88 |
Agree |
The course/subject is organized in a way that students can help each other. | 3.63 | 0.91 | Agree |
I can share ideas with peers. | 3.62 | 0.97 | Agree |
During the course, the class is divided into groups to discuss, investigates, or solve a problem. | 3.62 | 0.92 | Agree |
Peers help me when processing the subject matter. | 3.60 | 0.85 | Agree |
I am encouraged to study for the examination in pairs or in groups. | 3.56 | 0.90 | Agree |
There are possibilities to share my own experiences with peers. | 3.50 | 0.90 | Agree |
Peers explain to me the subject matter. | 3.50 | 0.89 | Agree |
Group assignments are assigned, in which one final report has to be handled in by each group. | 3.49 | 0.89 | Agree |
Overall | 3.58 | 0.54 | Agree |
Table 13 shows how teaching methods reflect learning culture. Students generally agree that constructivist teaching methods are present in the learning culture. This indicator’s constructive measure is prevalent. This suggests that students noticed that teachers used methods that didn’t leave them behind. The results showed that teachers’ constructive strategies helped students understand math concepts. Teachers designed activities so students learned the concept alone or with peers. This method helps students confirm that they understand how their peers learned the concept. Cooperation and mathematics learning are promoted by this method. Collaborative learning allowed students to build knowledge. The DepEd Mathematics Curriculum emphasised constructivist education through cooperative learning. Junior high school mathematics incorporates Individualized-Cooperative Learning (ICL). This suggests that senior high school maths teachers used this constructive teaching strategy with collaborative learning to teach. The teacher didn’t ignore letting students work in pairs or groups boosts cooperative learning. Organised and meticulously planned group investigation tasks helped students learn by helping each other.
Table 14: Level of Learning Culture in terms of Learning Environment
Indicators | Mean | Standard
Deviation |
Qualitative
Description |
The assignments we carry out are related to our daily lives. In these assignments, we have to apply what we have learned. |
3.63 |
0.88 |
Agree |
When I have to study something, the teacher tells me first why it is important to know about the subject. |
3.62 |
0.85 |
Agree |
The teacher tells us what value the lesson topic has for future use. | 3.60 | 0.91 | Agree |
The teacher asks us what we have already known about the lesson topic. | 3.60 | 0.85 | Agree |
We are allowed to decide for ourselves which tasks we work on. | 3.59 | 0.87 | Agree |
We are allowed to develop assignments on our own, which we can carry out in our own way. | 3.57 | 0.86 | Agree |
The teacher asks me what I did to arrive at the solution of an assignment. | 3.57 | 0.89 | Agree |
We are allowed to develop our own assignments to work on. | 3.55 | 0.85 | Agree |
In our lessons, we not only use textbooks but also other things like newspapers, the computer, or a video. |
3.53 |
0.91 |
Agree |
We can determine how to carry out assignments the teacher gives. | 3.53 | 0.90 | Agree |
The teacher makes us think about the way we have to learn. | 3.53 | 0.91 | Agree |
The teacher asks us to collect information independently on the lesson topic. | 3.53 | 0.90 | Agree |
I get assignments in which I have to use knowledge from different school subjects. | 3.51 | 0.88 | Agree |
Table 14 shows the learning environment’s learning culture. Students agree that the school has a good learning environment. The environment encouraged students to participate in teaching and learning. This makes the school’s learning environment relatable and conducive. Students observed that teachers create a welcoming learning environment. Students are more motivated to learn the concept because the teacher stressed its importance. The results also showed that teachers consider students’ experiences in relation to concepts. The teacher’s learning activities were relevant to the students’ experiences.
Table 15: Level of Learning Culture in terms of Learning Facilities
Indicators | Mean | Standard Deviation | Qualitative Description |
In our school, the cooling and/or lighting systems are in good condition. | 3.58 | 0.87 | Agree |
We can determine how to carry out assignments the teacher gives. | 3.53 | 0.90 | Agree |
The teacher makes us think about the way we have to learn. | 3.53 | 0.91 | Agree |
The teacher asks us to collect information independently on the lesson topic. | 3.53 | 0.90 | Agree | |
In our school, adequate multi-media resources for instruction. | 3.52 | 0.90 | Agree | |
In our school, the buildings are in good condition. | 3.52 | 0.85 | Agree | |
I get assignments in which I have to use knowledge from different school subjects. | 3.51 | 0.88 | Agree | |
I get assignments that require me to do research. | 3.50 | 0.90 | Agree | |
In our school, adequate instructional materials in the library. | 3.49 | 0.88 | Agree | |
Overall | 3.49 | 0.68 | Agree |
Table 15 shows learning culture in terms of facilities. Students agree that the learning culture and facilities are good. The mean shows that learning culture’s constructive measure in learning facilities is clear. It means students observed learning facilities and classrooms’ physical functionality. The result indicates that the school prioritised classroom comfort. Students noticed that senior high school classrooms are comfortable. The classroom is well-ventilated and lit. Students saw the school’s learning facilities used for teaching and learning. Students noticed that computers, calculators, and mobile apps were used in learning, which made the discussion more engaging. The result suggests the DepEd prioritised school facilities. To make the senior high school classroom comfortable, the school provided good lighting and ventilation. Most senior high school classrooms were newly built and designed for learning. Modern classrooms are electrified, lit, and ventilated. The results also show that DepEd improves education by providing schools with facilities. The results show teachers used these facilities to teach and learn. Teachers created activities that used these tools. The results indicate frequent use of learning equipment, so letting it damage is addressed. This shows that government spending on these devices and facilities was worthwhile.
4.5 The Level of Aptitude
Table 16 shows the aptitude of Senior High School students in terms of Mathematics 10 final grade. The overall Mathematics aptitude of Senior High School students indicates that the student has developed the fundamental knowledge, skills, and core understandings and can transfer them independently through performance tasks.
Table 16: Level of Aptitude in terms of Mathematics 10 Final Grade
Grade | Percent | Qualitative Description | |
90 – 100 | 1.36% | Outstanding | |
85 – 89 | 86.08% | Very Satisfactory | |
80 – 84 | 9.93% | Satisfactory | |
75 – 79 | 2.63% | Fairly Satisfactory | |
Mean | 85.43 | Very Satisfactory |
Students can identify situations requiring mathematics concepts and interference based on the result. Students can extract data and use representational mode. They can solve math problems using basic algorithms, formulas, procedures, and conventions. This shows students can interpret results literally. The majority of student maths grades are based on performance tasks. Students can demonstrate learning with products or performances. Few respondents said some of their performance tasks were checking their notebooks for writing. Others had a portfolio of quizzes without reflections on their lessons. Some teachers didn’t give them notebook or portfolio rubrics. However, many students recounted their maths experiences. Some built a skeletal structure of a building to illustrate polynomial functions, while others made an art illustrating arithmetic and geometric sequences. Grades should be used to help future maths teachers design activities that meet students’ needs. Previous maths grades can indicate how to handle students’ learning abilities.
Table 17: Level of Aptitude in terms of Mathematics Ability in NCAE Results
Grade | Percent | Qualitative Description |
90 – 100 | 0.59% | Outstanding |
85 – 89 | 85.23% | Very Satisfactory |
80 – 84 | 13.33% | Satisfactory |
75-79 | 0.76% | Fairly satisfactory |
Below 75 | 0.08% | Did not meet expectations |
Mean | 85.41 | Very satisfactory |
Table 17 shows student NCAE math aptitude. NCAE maths aptitude results are very good, indicating that students at this level have developed the fundamental knowledge, skills, and core understandings and can transfer them independently through performance tasks. Additionally, this result shows that students can apply their maths skills to their chosen field. Some Cluster I schools schedule weekly reviews. Preparing for standardised tests like NAT and NCAE helps students prepare. Some schools spend on review materials and practice test sheets to familiarise students with the exams. This school practice improves student scores.
4.6 The Relationship between Mathematics Anxiety and Problem-Solving Skills
The result shows that math anxiety hinders problem-solving. Students’ problem-solving ability decreases with math anxiety. There is also statistical evidence to reject the null hypothesis. Statistics show that maths anxiety affects Senior High School students’ problem-solving ability. The results show that these anxieties negatively affect student problem-solving. Students’ problem-solving ability decreases as their anxieties rise. When students are anxious about maths, they have trouble solving problems. When math anxiety is high, students avoid solving problems. Math anxiety impairs performance and causes students to avoid maths.
4.7 The Relationship between Learning Culture and Problem-Solving Ability
This suggests that learning culture affects student problem-solving. The results do not support the null hypothesis that learning culture does not affect students’ problem-solving skills. Students’ problem-solving skills improve with learning culture. Students’ problem-solving ability is slightly improved by peers and teaching methods. Positive peer relationships and effective teaching methods help students solve problems. However, learning environment and facilities appear to have little impact on student problem-solving.
4.8 The Relationship between Aptitude and Problem-Solving Ability
This suggests that student problem-solving ability increases math achievement. Additionally, Mathematics 10 final grade improves students’ problem-solving skills. Math NCAE results positively correlate with problem-solving ability. The results show that aptitude affects student problem-solving. The results suggest that students must understand their previous discussions and master the previous mathematics competencies to solve problems better. They must remember these skills so they can use them when solving maths problems. Good competency mastery indicates long-term memory. Students with better aptitude and problem-solving skills can retrieve this information efficiently.
4.9 Influence of Mathematics Anxiety, Learning Culture, and Aptitude on Problem-Solving Skills
The Mathematics 10 final grades and NCAE results for aptitude, test anxiety, and subject anxiety for mathematics anxiety, teaching approaches, peers, and learning environment for learning culture as significant predictors of problem-solving ability. Furthermore, test anxiety and subject anxiety for mathematics anxiety displayed a negative standardized beta among all significant problem-solving ability predictors. The regression model in the table has an r2 equivalent to 0.450. This result implies that 45% of the variation in problem- solving ability is accounted for the variation in these factors. This implies that aside from the independent variables identified, other factors not mentioned in this study can affect the students’ problem-solving ability. The regression equation of the problem-solving ability of the students is:
PA=11.263(TAP)– 8.387(TA) + 6.827(P) – 3.277(SA) + 2.585(NR)+ 1.783 (LE) + 1.643(MF) – 285.701
where:
PA: Problem-Solving Ability | TA: | Test Anxiety |
TAP: Teaching Approaches | SA: | Subject Anxiety |
LE: Learning Environment | P: | Peers |
MF: Mathematics 10 Final Grade | NR: | NCAE results |
The equation above shows that teaching approaches have the greatest numerical coefficient on problem-solving ability, followed by test anxiety, peers, subject anxiety, NCAE results, learning environment, and mathematics 10 final grades. Assuming all variables are constant, the regression model suggests that every 11.263 unit increase in teaching approaches increases problem-solving ability by one unit. The model shows that teachers’ lesson delivery and activity planning affect the interaction between mathematics anxiety, learning culture, and student problem-solving ability.
4.11 Structural Models Testing
This study analyses the relationships between the study’s exogenous and endogenous variables and the best fit problem-solving model. Exogenous variables consist of three factors: test anxiety, numerical anxiety, and subject anxiety; four factors: peer, teaching approaches, learning environment, and learning facilities; two factors: grade in Mathematics 10, and NCAE mathematics ability results; and the endogenous variable: understanding the problem. The hypothesized models in chapter 1 were evaluated using statistical tools to determine coefficient statistical significance and model fit indices.
Test of Hypothesized structural Model 1
Figure 1 presents the structural model 1, which describes the causal relationships of the exogenous variables, which are mathematics anxiety (MANX), mathematics aptitude (MAPT), and learning culture (LECUL), and the endogenous variable, which is the problem-solving ability (PROBSA). Furthermore, figure 6 presents the three-factor structure of mathematics anxiety, namely test anxiety (TEST_ANX), numerical anxiety (NUM_ANX), and subject anxiety (SUB_ANX); the four-factor structure of Learning Culture, namely peer (PEER_LC), teaching approaches (TEAP_LC), learning environment (LEEN_LC) and learning facilities (LEFA_LC); the two-factor structure of Mathematics Aptitude, namely grade in Mathematics 10 (MGRAD_AP), and mathematics ability results in NCAE (NCAE_AP); and four-factor Problem-Solving Ability, namely understanding the problem (UTP_PS), devise a plan (DAP_PS), carry-out the plan (COP_PS), and look back (LOOB_PS).
Figure 01: Structural Model 1 on Problem-Solving Ability of Students
Figure 1 shows the variables’ standardised solution relationship. Exogenous variables explain 84% of model variance. Other exogenous variables affect problem-solving ability, which this analysis does not cover. The length of time students master concepts may also affect their problem-solving ability. The senior high school maths curriculum is pretty extensive. congested. Some teachers jumped to the next competency without validating student mastery to meet the time frame. The division-wide periodic test contributes to this bad plan. The test covered all quarter competencies. If the teacher didn’t talk to students, they couldn’t pass the 20% exam. In addition to teaching, most teachers have other duties. Teachers often have to leave class for urgent tasks. Table 18 shows the direct, indirect, and total effects of exogenous variables on endogenous variables. Mathematics anxiety, aptitude, and learning culture affect students’ problem-solving skills. Math aptitude affects problem-solving ability the most, while learning culture has the least direct effect. Math aptitude affects problem-solving more than mathematics anxiety and learning culture when these exogenous variables interact. Math aptitude increases problem-solving ability, while mathematics anxiety decreases and learning culture increases it slightly.
Table 18: Standardized Direct, Indirect and Total Effect Estimates of Structural Model 1
Latent Variables | Direct Effect | Indirect Effect | TotalEffect |
Mathematics Anxiety | -0.282 | 0 | -0.282 |
Mathematics Aptitude | 0.760 | 0 | 0.760 |
Learning Culture | 0.056 | 0 | 0.056 |
Moreover, this result was in conformance with the study of Priya (2017) stated that mathematics aptitude has a highly significant relationship to problem-solving ability, while mathematics anxiety has a moderate negative relationship. The positive impact of mathematics aptitude, which attributes to the cognitive faculty, supersedes the effect of the other factors (Nugroho, 2018). The result of Table 18 implies that the greater the final grade of Mathematics 10 and the NCAE mathematics ability, the higher the students’ ability to solve problems. Likewise, the better teaching approaches, peer interaction, learning environment, and learning facilities, the better learning culture of the school, which resulted in better problem-solving ability. However, the higher the subject anxiety, numerical anxiety, and test anxiety, the higher the anxiousness of the students towards mathematics which resulted in a poor problem-solving ability. Furthermore, as learning culture increases by one unit, the problem-solving ability of the students will increase by 16.358, given that other variables are held constant.
Table 18: Goodness of Fit Measures of Structural Model 1
INDEX | CRITERION | MODEL 1 FIT VALUE |
CMIN/DF | < 2.00 | 5.149 |
P – value | > 0.05 | 0.000 |
NFI | > 0.95 | 0.952 |
TLI | > 0.95 | 0.947 |
CFI | > 0.95 | 0.961 |
GFI | > 0.95 | 0.963 |
RMSEA | < 0.05 | 0.059 |
Legend: | CMIN/DF – Chi-Square/ Degrees of Freedom | NFI – Normed Fit Index |
GFI – Goodness of Fit Index | TLI – Tucker-Lewis Index | |
RMSEA – Root Mean Square Error of Approximation | CFI – Comparative Fit Index |
Table 18 presents the criterion of each index, indicating the qualification of a good model to determine if the hypothesized model is good or not. As shown in the table, hypothesized model 1 does not satisfy the criterion. The Chi-Square/Degrees of Freedom (CMIN/DF) was 5.149, which is greater than 2.00, the P-value was 0.000, which is less than 0.05, Tucker-Lewis Index (TLI) was 0.947, which is less than 0.95, and Root Mean Square Error of Approximation (RMSEA) was 0.059 which is greater than 0.05. The Normed Fit Index (NFI), Comparative Fit Index (CFI), and Goodness of Fit Index (GFI) had indices that satisfied the criteria to have a model fit. The result in this table implies that structural model 1 is not a good model to describe the problem-solving ability of the learners.
Test of Hypothesized Structural Model 2
Figure 2 presents the structural model 2, which describes the causal relationships of the exogenous variables, which are the mathematics anxiety (MANX) and learning culture (LECUL), and the endogenous variable, which is the problem-solving ability (PROBSA). Furthermore, figure 2 presents the three-factor structure of mathematics anxiety, namely test anxiety (TEST_ANX), numerical anxiety (NUM_ANX), and subject anxiety (SUB_ANX); the four-factor structure of Learning Culture, namely peer (PEER_LC), teaching approaches (TEAP_LC), learning environment (LEEN_LC) and learning facilities (LEFA_LC); and four- factor Problem-Solving Ability namely understanding the problem (UTP_PS), devise a plan (DAP_PS), carry-out the plan (COP_PS), and look back (LOOB_PS).
Figure 02: Structural Model 2 on Problem-Solving Ability of Students
As presented in figure 2, there is a direct relationship between the variables in terms of a standardized solution. The amount of variance explained by the combined influence of the exogenous variables in the model is 34%. The result indicates that 66% of the data are explained by the other variables not included in this analysis. Table 19 presents the direct, indirect, and total effects of the exogenous variables to an endogenous variable concerning model 2. Mathematics anxiety and learning culture have direct effects on the problem-solving ability of the learners. Mathematics anxiety manifested a direct negative effect while learning culture has the least influence on the level of problem-solving ability. In addition, model 2 suggests that mathematics anxiety has a large negative effect on the problem-solving ability of the learners. Meanwhile, the learning culture has a small direct influence on problem-solving ability. This indicates that when analyzing separately, students with greater anxiousness towards mathematics have the poor problem-solving ability in mathematics. On the other hand, students situated in the positive learning culture have a good mathematics problem-solving ability.
Table 19: Standardized Direct, Indirect and Total Effect Estimates of Structural Model 2
Latent Variables | Direct Effect | Indirect Effect | Total Effect |
Mathematics Anxiety | -0.579 | 0 | -0.579 |
Learning Culture | 0.074 | 0 | 0.074 |
As shown in Table 20 are the resulted regression weights on the effect measured variables to latent variables. The result showed that all the latent variables significantly predicted problem- solving ability since all the computed p-values are less than the level of significance at 0.05.
Table 20: Standard Regression Weights of Structural Model 2
Variables | Estimate | S.E. | C.R. | Beta | P | ||
PROBSA | <— | MANX | -20.585 | 1.800 | -11.434 | -.579 | *** |
PROBSA | <— | LECUL | 21.655 | 5.796 | 3.736 | .074 | *** |
UTP_PS | <— | PROBSA | 1.000 | .634 | |||
DAP_PS | <— | PROBSA | .985 | .074 | 13.225 | .601 | *** |
COP_PS | <— | PROBSA | .808 | .063 | 12.781 | .556 | *** |
LOB_PS | <— | PROBSA | .424 | .066 | 6.370 | .233 | *** |
SUB_ANX | <— | MANX | 1.000 | .651 | |||
NUM_ANX | <— | MANX | .981 | .061 | 16.092 | .617 | *** |
TEST_ANX | <— | MANX | .879 | .052 | 16.928 | .788 | *** |
LEFA_LC | <— | LECUL | 1.000 | .062 | |||
LEEN_LC | <— | LECUL | 3.999 | .770 | 5.192 | .303 | *** |
TEAP_LC | <— | LECUL | 17.157 | 4.043 | 4.244 | 1.339 | *** |
PEER_LC | <— | LECUL | 10.297 | 2.211 | 4.657 | .710 | *** |
The result in table 21 indicates that the higher the approaches used by the teacher in the classroom, the interaction among peers, learning environment, and learning facilities contribute to a better learning environment which leads to a good problem-solving ability. Moreover, students who are very anxious about the subject, numerical applications, and taking examinations facilitate higher mathematics anxiety which eventually contributes to poor problem-solving ability. Table 21 presents the criterion of each index, indicating the qualification of a good model. As seen in the table, Chi-Square/Degrees of Freedom (CMI/DF) does not satisfy the criteria since it is more than 2.00. The P-value is less than 0.05, and the Root Mean Square Error of Approximation (RMSEA) is greater than 0.05. The indices mentioned above do not also satisfy the criterion. However, the Normed Fit Index (NFI), Tucker-Lewis Index (TLI), Comparative Fit Index (CFI), and Goodness of Fit Index (GFI) were the indices that satisfy the criterion since the value of their indices were more than 0.95. The result implies that model 2 is not a good model to describe the problem-solving ability of the learners.
Table 21: Goodness of Fit Measures of Structural Model 2
INDEX | CRITERION | MODEL 2 FIT VALUE |
CMIN/DF | < 2.00 | 5.529 |
P – value | > 0.05 | 0.000 |
NFI | > 0.95 | 0.959 |
TLI | > 0.95 | 0.954 |
CFI | > 0.95 | 0.966 |
GFI | > 0.95 | 0.968 |
RMSEA | < 0.05 | 0.062 |
Legend: | CMIN/DF – Chi-Square/ Degrees of Freedom | NFI – Normed Fit Index |
GFI – Goodness of Fit Index | TLI – Tucker-Lewis Index | |
RMSEA – Root Mean Square Error of Approximation | CFI – Comparative Fit Index |
Test of Hypothesized Structural Model 3
Figure 3 presents the structural model 3, which describes the causal relationships of the exogenous variables, which are mathematics anxiety (MANX), and mathematics aptitude (MAPT), and the endogenous variable, which is the problem-solving ability (PROBSA). Furthermore, figure 3 presents the three-factor structure of mathematics anxiety, namely test anxiety (TEST_ANX), numerical anxiety (NUM_ANX), and subject anxiety (SUB_ANX); the two-factor structure of Mathematics Aptitude, namely grade in Mathematics 10 (MGRAD_AP), and mathematics ability results in NCAE (NCAE_AP); and four-factor Problem- Solving Ability namely understanding the problem (UTP_PS), devise a plan (DAP_PS), carry-out the plan (COP_PS), and look back (LOOB_PS). It can be observed in figure 8 the direct relationship between the variables in terms of a standardized solution. The amount of variance explained by the combined influence of exogenous variables in the model is 84%.
Depicted in Table 22 are the direct, indirect, and total effects of the exogenous variables on an endogenous variable. Both mathematics anxiety and mathematics aptitude have a direct effect on problem-solving ability. Mathematics anxiety has a negative direct effect on problem- solving ability. Meanwhile, mathematics aptitude has a more significant direct effect on problem- solving ability compared to mathematics anxiety. The direct effect of mathematics aptitude suggests that more significant influence on mathematics problem-solving ability, while mathematics anxiety has a small negative impact. This implies that students with higher mathematics aptitude possess a higher ability to solve mathematical problems. Meanwhile, students who have mathematics anxiety have the poor problem-solving ability.
Figure 03: Structural Model 3 on Problem-Solving Ability of Students
Table 22: Standardized Direct, Indirect and Total Effect Estimates of Structural Model 3
Latent Variables | Direct Effect | Indirect Effect | Total Effect |
Mathematics Anxiety | -0.281 | 0 | -0.281 |
Mathematics Aptitude | 0.760 | 0 | 0.760 |
Moreover, mathematics anxiety and mathematics aptitude have a significant relationship to problem-solving ability (Yonson, 2017). However, mathematics aptitude has a more significant effect compared to mathematics anxiety. Acquiring the essential concepts and having practical skills of applying these concepts are greater contributory factors of the development of problem- solving skills (Rohmah & Sutiarco, 2018). Soto-Andrade (2020) stated that the problem-solving skills of the learners could be seen more through their mathematics aptitude over mathematics anxiety.
Table 23: Standard Regression Weights of Structural Model 3
Variables | Estimate | S.E. | C.R. | Beta | P | ||
PROBSA | <— | MANX | -9.861 | 1.611 | -6.120 | -.281 | *** |
PROBSA | <— | MAPT | 10.570 | .881 | 11.998 | .760 | *** |
UTP_PS | <— | PROBSA | 1.000 | .627 | |||
DAP_PS | <— | PROBSA | .944 | .064 | 14.770 | .570 | *** |
Variables | Estimate | S.E. | C.R. | Beta | P | ||
COP_PS | <— | PROBSA | .793 | .056 | 14.202 | .540 | *** |
LOB_PS | <— | PROBSA | .562 | .064 | 8.766 | .306 | *** |
SUB_ANX | <— | MANX | 1.000 | .652 | |||
NUM_ANX | <— | MANX | .989 | .061 | 16.209 | .623 | *** |
TEST_ANX | <— | MANX | .871 | .051 | 17.088 | .782 | *** |
NCAE_AP | <— | MAPT | 1.000 | .652 | |||
MGRAD_AP | <— | MAPT | 1.674 | .107 | 15.668 | .708 | *** |
Test of Hypothesized Structural Model 4
Figure 4 presents the structural model 4, which describes the causal relationships of the exogenous variables, which are mathematics anxiety (MANX), mathematics aptitude (MAPT), and learning culture (LECUL), and the endogenous variable, which is the problem-solving ability (PROBSA).
Figure 04: Structural Model 4 on Problem-Solving Ability of Students
It can be observed in figure 4 the direct relationship between the variables in terms of a standardized solution. The amount of variance explained by the combined influence of exogenous variables in the model is 64%. Furthermore, 36% of the data is influenced by the other variable not identified by this model. Furthermore, figure 9 presents the four-factor structure of Learning Culture, namely peer (PEER_LC), teaching approaches (TEAP_LC), learning environment (LEEN_LC), and learning facilities (LEFA_LC); the two-factor structure of Mathematics Aptitude, namely grade in Mathematics 10 (MGRAD_AP), and mathematics ability results in NCAE (NCAE_AP); and four- factor Problem-Solving Ability namely understanding the problem (UTP_PS), devise a plan (DAP_PS), carry-out the plan (COP_PS), and look back (LOOB_PS). Depicted in Table 24 are the direct, indirect, and total effects of the exogenous variables on an endogenous variable. Both mathematics aptitude and learning culture have a direct effect on the level of problem-solving ability. Mathematics aptitude has a more direct effect on the level of problem-solving ability of the learners compared to the direct effect of learning culture.
Table 24: Standardized Direct, Indirect and Total Effect Estimates of Structural Model 3
Latent Variables | Direct Effect | Indirect Effect | Total Effect |
Mathematics Aptitude | 0.779 | 0 | 0.779 |
Learning Culture | 0.105 | 0 | 0.105 |
Shown in Table 25 are the resulted regression weights on the effect measured variables to latent variables. The result showed that all the latent variables significantly predicted problem- solving ability since all the computed p-values are less than the level of significance at 0.05.
Table 25: Standard Regression Weights of Structural Model 4
Variables | Estimate | S.E. | C.R. | Beta | P | ||
PROBSA | <— | MAPT | 10.269 | .779 | |||
PROBSA | <— | LECUL | 7.140 | .105 | |||
UTP_PS | <— | PROBSA | 1.000 | .650 | |||
DAP_PS | <— | PROBSA | .939 | .068 | 13.719 | .588 | *** |
COP_PS | <— | PROBSA | 1.000 | .714 | |||
LOB_PS | <— | PROBSA | 1.613 | .100 | 16.062 | .746 | *** |
NCAE_AP | <— | MAPT | 1.000 | .276 | |||
MGRAD_AP | <— | MAPT | 3.372 | 1.171 | |||
TEAP_LC | <— | LECUL | 3.216 | .986 | |||
LEEN_LC | <— | LECUL | .994 | .335 | |||
LEFA_LC | <— | LECUL | .753 | .062 | 12.205 | .532 | *** |
PEER_LC | <— | LECUL | .718 | .082 | 8.802 | .405 | *** |
To answer the research question related to that best represents the variables that predicted problem-solving ability, the original proposed structural model 1 needed some modification to fit the data. There were four generated structural models presented in the study. Table 26 shows the summary of the Standard Fit Indices of the four structural models.
Table 26: Summary of Standard Fit Indices of the Four Structural Models
Model | CMIN/DF | P-value | NFI | TLI | CFI | GFI | RMSEA |
1 | 5.149 | 0.00 | 0.952 | 0.947 | 0.961 | 0.963 | 0.059 |
2 | 5.529 | 0.00 | 0.959 | 0.954 | 0.966 | 0.968 | 0.062 |
3 | 8.699 | 0.00 | 0.909 | 0.878 | 0.918 | 0.961 | 0.081 |
4 | 1.301 | 0.156 | 0.994 | 0.997 | 0.999 | 0.995 | 0.016 |
Standard Value | < 2.00 | > 0.05 | > 0.95 | > 0.95 | > 0.95 | > 0.95 | < 0.05 |
Only one of the four structure models meets the criteria in each index to model Senior High School students’ problem-solving ability. The null hypothesis that no structural model best fits problem-solving ability is rejected because the fourth model meets goodness of fit criteria. The best predictor of math aptitude and learning culture is students’ problem-solving ability. For a model to fit, all criteria indices must be within acceptable limits. Chi-square/degree of freedom should be less than 2, p-value greater than 0.05, and Root Mean Square of Error Approximation Value less than 0.05. The Normed Fit Index, Tucker-Lewis Index, Comparative Fit Index, and Goodness of Fit must exceed 0.95. The first structural model showed causal relationships between mathematics anxiety, aptitude, learning culture, and problem-solving ability, but it was unsuitable. The fourth structural model showed the causal relationships between math aptitude, learning culture, and problem-solving. Structural model 4’s indices fit best. Model 4 fits best among the four structural models. This structural model implies that there is enough statistical evidence to reject the null hypothesis that no structural model best fits Senior High School students’ problem-solving skills. To illustrate the purported theory mentioned above, the researcher developed the Students Capacity in Answering Life-Like Problem in Mathematics (SCALE PIM) Model, which is illustrated in figure 5. The development of this conceptual model is anchored with different theories.
Figure 05: Problem-Solving Capability of Learners (P-SCaLe) Model
This model shows how student aptitude, school learning culture, and math anxiety affect problem-solving ability. The DepEd maths curriculum stressed problem-solving. With this mandate, every school must understand how major factors affect student problem-solving. This study aims to model problem-solving maturity. These theories underpin this model: Debilitating Anxiety Theory for math anxiety, Theory of School Learning for learning culture, Cognitive Load Theory for math aptitude, and Theory of Problem Solving for problem-solving ability. Like a scale, problem-solving ability leans towards more weight. The scale points left if the left platform has more weight. The indicator points right if it has more right weights. Negative and positive problem-solving ability exist. If negative contributors are prominent, the indicator will be red-alarming. The weight of the positive will also tilt students’ problem-solving ability towards the green side. Contributors outnumber negatives. Schoenfeld’s 1985 Mathematical Problem-solving Theory supports this interaction. Students’ math problem-solving ability is greatly influenced by negative and positive contributors. Negative contributors include mathematics anxiety, while positive contributors include aptitude and learning culture. For students to solve problems better, the school must foster these positive traits. Model 4 states that students’ mathematical aptitude is the main factor in their problem-solving ability. Problem-solving ability starts with aptitude. The scale stands firm on this foundation. This means students must master math prerequisites. Regular practice will help retain this knowledge. Cognitive Load Theory underpins this model, which requires students to retain enough maths knowledge in their long-term memory (Sweller, 1988). Rational thinking and reasoning produce problem-solving. In other words, the student must have vital knowledge he can use to solve problems. Mastering previous mathematics helps develop problem-solving skills and new math concepts. According to P-SCaLe Model, the school must focus on improving students’ aptitude and learning culture to develop their problem-solving skills. Model 4 suggests that aptitude directly affects problem-solving ability, so teachers must ensure students understand previous mathematics lessons. Though learning culture has a lower beta weight than aptitude, the school must not ignore its positive direct effect on problem-solving. Figure 10 shows that aptitude supported by learning culture must outweigh mathematics anxiety to improve problem-solving ability. Thus, the school must foster a positive learning environment and students should master mathematics to improve problem-solving.
- CONCLUSION AND RECOMMENDATIONS
Based on the findings of the study, the following conclusions were drawn: 1) the learners demonstrate the beginning level in problem-solving ability; 2) the learners have tolerable experiences of worries, uneasiness, or nervousness towards mathematics; 3) The learners perceived that the sound learning culture of the school was much evident; 4) The learners had developed the fundamental knowledge and skills and core understanding and can transfer them independently through performance tasks; 5) mathematics anxiety in terms of test anxiety, numerical anxiety, subject anxiety, learning culture in terms of peer, teaching approaches, learning environment, learning facilities, and aptitude in terms of Mathematics 10 final grade and NCAE results in mathematics were correlated to problem-solving ability; 6) Test anxiety (TA) and subject anxiety (SA) for mathematics anxiety, teaching approaches (TAP), peers (P), and learning environment (LE) for learning culture, Mathematics 10 final grade (MF) and NCAE results in mathematics (NR) for mathematics aptitude were predictors of problem-solving ability (PA) with the equation: PA=11.263(TAP)– 8.387(TA) + 6.827(P) – 3.277(SA) + 2.585(NR) + 1.783 (LE) + 1.643(MF) – 285.701; 7)Mathematics aptitude and learning culture are the strong determinants of problem-solving ability. The problem-solving ability of Senior High School learners is best anchored to the mathematics aptitude and supported by learning culture. With the findings and conclusions stated previously, the following are the recommendations: 1) the school administrators may consider designing a program that will lessen, if not maintain, the anxiety level of the students towards mathematics, like strengthening and empowering the capacity of the Guidance Office to conduct different psychosocial activities so that students can open up; 2) teachers may see to it that the students master the competencies in mathematics 10. Mastery of the key concepts in Junior High School mathematics must be closely monitored to give the learners appropriate intervention; 3) teachers and administrators may design a scheme that will enhance the learners’ mathematics ability in taking NCAE, like an integration of the NCAE Review Schedule to the Class Schedule of the students; 4) teachers may employ varied appropriate teaching approaches that will cater to the students’ learning needs so that understanding the fundamental concepts will not be compromised. They should design learning activities where the students have opportunities to share their understanding with their peers; 5) the administrators may encourage the teachers to involve in different activities where professional growth is nurtured. Attending seminars and workshops and enrolling to graduate studies are highly suggested so that teachers will be more equipped with appropriate teaching strategies to address the students’ different learning needs; 6) teachers may secure that the learning activities are relevant to the students’ experiences as well as the availability of the learning opportunities present in the learners’ environment; 7) Administrators may ensure the conduciveness of the classroom. Functional facilities must be present in the school to ensure the optimal learning of the subject. Teachers must also incorporate appropriate technologies and equipment in their teaching-learning process.
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Publication History
Submitted: November 18, 2023
Accepted: November 27, 2023
Published: December 11, 2023
Identification
D-0165
Citation
Emmanuel P. Abuzo (2023). Mathematics Anxiety, Learning Culture, Aptitude and Problem-Solving Ability of Senior High School Students: A Structural Model. Dinkum Journal of Social Innovations, 2(12):676-702.
Copyright
© 2023 DJSI. All rights reserved.