Jurnal Penalaran dan Riset Matematika

ANALYSIS OF STUDENTS' UNDERSTANDING OF ALGEBRA CONCEPTS BASED ON APOS THEORY: A STUDY IN LINEAR ALGEBRA COURSES

Ferryansyah — 2026-04-30

Understanding algebraic concepts is an important prerequisite for advanced mathematics learning because it involves a transition from symbolic manipulation to structural thinking and proof. This study analyzes students’ understanding of algebraic concepts in a Linear Algebra course using the APOS (Action, Process, Object, Schema) theoretical framework. The method is descriptive qualitative, with systematic application of APOS indicators in the domain of Linear Algebra. Data were collected through conceptual tests and analysis of proof and problem-solving tasks. Data analysis involved reduction and categorization based on APOS development. The results showed three patterns of understanding: (1) students in the low-ability category failed to meet the criteria for the Action, Process, Object, and Schema stages; (2) the medium category showed partial comprehension—reaching the Process stage and parts of the Object stage on routine problems but failing at the Action stage for abstract constructive problems; and (3) the high category generally reached the Schema stage on constructive problems but showed failure at the Action stage on problems requiring proofs of basic axioms, or vice versa. The findings suggest emphasizing development of the Action stage and the process–object linkages to strengthen transfer to the Schema. Practical recommendations include gradual constructive tasks, mediated proof-of-concept learning, and APOS-indicator-based formative assessment.

THE EFFECT OF PROBLEM-BASED LEARNING IMPLEMENTATION ON STUDENTS’ PROBLEM-SOLVING ABILITY IN PROBABILITY TOPICS

Nely Salu Padang — 2026-04-30

This study aims to determine the effect of implementing the Problem-Based Learning (PBL) model on students’ problem-solving skills in probability. This study uses a quantitative approach with an experimental method. The study population consists of students at STIE Jambatan Bulan who are enrolled in the Statistics course. The sample comprises 32 students divided into two groups: 16 students in the experimental group, who received instruction using the Problem-Based Learning model, and 16 students in the control group, who received conventional instruction. The research instrument consists of a problem-solving ability test on probability material. Data analysis was conducted through normality tests, homogeneity tests, and hypothesis testing using the t-test at a 5% significance level. The results showed that the average problem-solving ability of students in the experimental class was 83.187, while the average problem-solving ability of students in the control class was 73.125. The results of the hypothesis testing showed that the calculated t-value (t-hitung) of 4.312 was greater than the critical t-value (t-table) of 1.697; therefore, H0 was rejected and H1 was accepted. Thus, the implementation of the Problem-Based Learning model has a positive effect on students’ problem-solving skills in probability. The Problem-Based Learning model has proven to be more effective than conventional teaching methods in improving students’ ability to understand, analyze, and solve problems related to probability concepts in statistics courses.

IMPLEMENTING THE PROJECT-BASED LEARNING MODEL TO IMPROVE STUDENT LEARNING OUTCOMES AT SMPN 01 SUKOWONO

Fila Fitliatul Rahmah — 2026-04-30

This study was conducted to examine student learning outcomes as indicators of learning achievement through preliminary interviews conducted at SMPN 01 Sukowono, Jember Regency. The findings revealed that teachers still predominantly applied teacher-centered instructional approaches, resulting in low student engagement, boredom, and limited understanding of the learning material, which consequently affected students’ mathematics achievement, particularly on the topic of three-dimensional geometric shapes with flat surfaces during the 2023/2024 academic year. This study aimed to determine the improvement in the learning outcomes of 25 students in Class VIII D through the implementation of the Project-Based Learning (PjBL) model. The research employed Classroom Action Research (CAR) using observation, tests, and documentation as data collection techniques. Data analysis focused on students’ achievement of the Minimum Mastery Criteria (KKM). The results demonstrated a significant improvement in student learning outcomes. In Cycle I, the classical mastery level reached 72%, with 18 students achieving mastery learning. In Cycle II, the mastery level increased to 100%, with all 25 students meeting the KKM standard. Therefore, the implementation of the PjBL model was proven effective in improving students’ mathematics learning outcomes by encouraging active participation, collaborative learning, and deeper conceptual understanding.

INTEGRATION OF ETHNOMATHEMATICS IN STRENGTHENING HIGH SCHOOL STUDENTS' NUMERACY LITERACY

Herwandi Sape — 2026-04-30

This study aims to analyze the integration of ethnomathematics in strengthening students’ numeracy literacy at SMA Negeri 3 Maros. The study was motivated by the low level of students’ numeracy literacy, which remains a major challenge in mathematics learning, particularly in understanding and solving contextual problems. Ethnomathematics is considered a relevant learning approach because it connects mathematical concepts with local cultural contexts, making learning more contextual and meaningful. This study employed a descriptive qualitative approach. The research subjects consisted of 32 students who completed a Likert-scale questionnaire, 3 students who participated in in-depth interviews, and 1 mathematics teacher who was also interviewed. Data collection techniques included questionnaires and in-depth interviews. Data analysis was conducted through the stages of data reduction, data display, and conclusion drawing. The findings revealed that the integration of ethnomathematics contributed positively to strengthening students’ numeracy literacy. A total of 84.3% of students stated that the use of local cultural contexts helped them understand the use of mathematical numbers and symbols in daily life, while 81.2% reported that they found it easier to analyze contextual mathematical problems when learning activities were linked to local culture. Interview results also indicated that ethnomathematics-based learning helped students understand mathematical concepts more concretely, improved their ability to solve numeracy problems, and enhanced their ability to interpret and communicate mathematical problem-solving processes. Furthermore, the mathematics teacher stated that integrating local culture into mathematics learning increased students’ participation and engagement during the learning process.