Interval: Indonesian Journal of Mathematical Education

Design and Evaluation of a Guided Discovery-Based Calculus Module on Derivatives with Islamic Values Integration

2026-05-14T08:39:34+07:00

Purpose of the study: This study aims to develop and evaluate a guided discovery-based calculus module on derivatives integrated with Islamic values to support students’ conceptual understanding, independent learning, and spiritual awareness in higher education mathematics learning.

Methodology: This study employed a Research and Development (R&D) method using the 4D model (define, design, develop, disseminate). Data were collected through questionnaires, validation sheets, and documentation. Instruments included expert validation sheets and student response questionnaires. Data were analyzed using descriptive quantitative and qualitative techniques with a Likert scale (1–4).

Main Findings: Results show that the module achieved valid criteria across material, media, and Islamic values aspects after revision. Material validation increased to 3.75, media design to 3.8, and Islamic values to 4.0. Limited trial results indicated an average score of 3.56, categorized as very attractive. These findings confirm that the module is feasible and well-received by students.

Novelty/Originality of this study: This study presents an integrative calculus module combining guided discovery learning with Islamic values on derivative topics. It simultaneously addresses cognitive and spiritual aspects within a single instructional design. This approach provides a holistic learning resource and contributes to advancing mathematics education by integrating pedagogical strategy and value-based learning.

An Exploratory Study of Students’ Mathematical Problem-Solving Ability Based on Wankat and Oreovocz Theory

2026-05-14T09:20:23+07:00

Purpose of the study: This study aims to explore students’ mathematical problem-solving ability based on the Wankat and Oreovocz theory by identifying how students perform across each stage of the problem-solving process in order to provide a comprehensive description of their abilities.

Methodology: This study employed a qualitative descriptive approach using purposive sampling, involving six students from class VII E at SMP Negeri 19 Bandar Lampung. Data were systematically collected through observation, written essay tests, and semi-structured interviews, and analyzed using data reduction, data display, and conclusion drawing with triangulation techniques for validation purposes.

Main Findings: The results show that most students achieved high problem-solving ability, with 59.26% in the excellent category and 25.93% in the good category. Students performed best at the motivation stage (“I Can”) but showed lower performance in planning, evaluation, and generalization stages. High-performing students completed all stages systematically, while lower-performing students experienced difficulties beyond initial stages, especially in selecting appropriate strategies and verifying solutions.

Novelty/Originality of this study: This study offers a detailed stage-based analysis of students’ mathematical problem-solving ability using the Wankat and Oreovocz framework, focusing on students’ actual performance rather than instructional strategies. It provides new insights into specific difficulties at each stage, particularly in planning, and contributes to advancing knowledge on how structured problem-solving frameworks can be applied to analyze students’ cognitive processes.

Comparative Effectiveness of AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education Approaches on Students’ Mathematical Reasoning Ability

2026-05-14T08:35:31+07:00

Purpose of the study: This study aims to compare the effectiveness of the AIR (Auditory, Intellectually, Repetition) and Realistic Mathematics Education (RME) approaches in improving students’ mathematical reasoning ability at the senior high school level.

Methodology: This study employed a quantitative quasi-experimental method with a posttest-only design, using essay-based test instruments, interviews, observations, and documentation; data were analyzed using descriptive statistics, Liliefors normality test, F-test homogeneity, and independent sample t-test with statistical calculation procedures.

Main Findings: The results showed a significant difference between the two approaches, where the AIR approach produced higher mean scores than the RME approach in students’ mathematical reasoning ability. Statistical testing indicated tvalue > ttable, confirming that AIR is more effective in enhancing students’ reasoning skills compared to RME.

Novelty/Originality of this study: This study provides a direct comparative analysis between AIR and RME approaches within a single quasi-experimental framework, focusing specifically on mathematical reasoning ability and offering empirical evidence to support instructional decision-making in mathematics education.

Examining the Effectiveness of Multiple Representation (SiMaYang) Learning Model on Students’ Mathematical Conceptual Understanding: The Role of Self-Efficacy

2026-05-14T08:35:28+07:00

Purpose of the study: This study aims to examine the effectiveness of the Multiple Representation (SiMaYang) learning model on students’ mathematical conceptual understanding and to determine the role of students’ self-efficacy in influencing differences in conceptual understanding outcomes.

Methodology: This study employed a quantitative approach with a quasi-experimental method using a 2×3 factorial design. Data were collected using essay tests and Likert-scale questionnaires. Statistical analysis included Liliefors normality test, Bartlett homogeneity test, independent t-test, and two-way ANOVA with unequal cells, followed by Scheffé test using statistical software.

Main Findings: Results showed that the SiMaYang learning model produced higher mathematical conceptual understanding than conventional learning. Self-efficacy significantly affected students’ conceptual understanding, where high self-efficacy students performed better than others. No interaction effect was found between learning model and self-efficacy. SiMaYang model consistently improved understanding across all self-efficacy levels, indicating independent contributions of instructional model and affective factors.

Novelty/Originality of this study: This study integrates cognitive and affective aspects by simultaneously examining the effect of the SiMaYang learning model and self-efficacy within a single analytical framework. It provides a more comprehensive understanding of learning effectiveness by using factorial design analysis, offering new insights into how instructional strategies and internal beliefs independently influence mathematical conceptual understanding.

Development of a Didactical Design Based on Research and Development for Teaching Cones and Cylinders to Improve Junior High School Students’ Conceptual Understanding

2026-05-14T09:22:09+07:00

Purpose of the study: This study aims to develop a didactical design based on Research and Development to improve junior high school students’ conceptual understanding of cones and cylinders by addressing their learning obstacles through structured instructional materials.

Methodology: This study employed a Research and Development approach adapted from Borg and Gall and Sugiyono models. The research involved eighth-grade students, using interviews, observation sheets, validation instruments, and questionnaires. Data were analyzed using descriptive qualitative and quantitative methods with Likert scale scoring. Expert validation involved mathematics education lecturers and teachers. Small-scale and large-scale trials were conducted to evaluate the developed module’s feasibility and effectiveness in mathematics learning on cones and cylinders.

Main Findings: The developed didactical design module showed significant improvement after expert validation and revision. The results indicated very good criteria in content quality, language clarity, and media design. Student responses in small-scale and large-scale trials reached 90–94%, categorized as very good. The module effectively reduced learning obstacles and improved students’ conceptual understanding of cones and cylinders. The findings confirm that the instructional material is valid, practical, and effective for classroom implementation.

Novelty/Originality of this study: This study develops a didactical design module integrating learning obstacle analysis specifically for cones and cylinders using an R&D approach. The innovation lies in its structured adaptation of students’ cognitive difficulties into instructional design. It contributes a context-specific mathematics learning module that enhances conceptual understanding and provides a practical model for developing geometry-based teaching materials.

Exploring Sociomathematical Norms Based on Students’ Interest in Mathematics Learning: A Qualitative Study at the Junior High School Level

2026-05-14T08:35:35+07:00

Purpose of the study: This study aims to explore sociomathematical norms based on students’ interest in mathematics learning at the junior high school level, and to identify how different levels of learning interest influence students’ interaction, participation, and communication during mathematics learning activities.

Methodology: This study used a descriptive qualitative approach with purposive sampling involving six students. Instruments included Likert-scale questionnaires, observation sheets, and semi-structured interview guidelines. Data were collected through observation, interviews, and questionnaires, and analyzed using the Miles and Huberman model with triangulation techniques.

Main Findings: Students mostly show good sociomathematical norms, with the majority categorized at a moderate level of learning interest. Students with high interest demonstrate very good participation and communication, while those with moderate interest show consistent but less optimal interaction. Students with low interest tend to be passive and have difficulty expressing mathematical ideas clearly.

Novelty/Originality of this study: This study integrates sociomathematical norms and learning interest in a single qualitative analysis, focusing on students’ real classroom behavior. It provides a deeper understanding of how different levels of interest shape interaction and communication, offering a more comprehensive perspective compared to previous studies that examined these aspects separately.