Hipotenusa: Journal of Mathematical Society

The Integration of Technology in Ratio and Proportion Learning: A Systematic Literature Review

Lucy Asri Purwasi, Nyimas Aisyah, Yusuf Hartono, Budi Mulyono — Fri, 24 Apr 2026 00:00:00 +0000

Ratio and proportion are fundamental topics in mathematics taught from elementary school to college, with significant relevance in education and everyday life. This study aims to systematically review technology-based innovations in ratio and proportion learning over the past 13 years. A Systematic Literature Review method was used to identify, synthesize, and analyze 23 journals published between 2012 and 2025, utilizing the Scopus and Google Scholar databases. This literature review consists of three main stages: planning, implementation, and reporting the review. The analysis results show that the most dominant type of technology used is Game-Based Learning, followed by Web-Based Platforms. These technologies have significantly contributed to improving mathematical skills such as proportional reasoning, problem-solving, critical thinking, creativity, and communication, especially among elementary and secondary school students. Proportional reasoning was noted as the key skill most developed through the application of these technologies. Based on these findings, further research is recommended to design interventions that integrate technology and local culture, employ contextual and realistic approaches, and also consider affective domains, such as self-confidence, motivation, and values, which are still under-researched but play a crucial role in technology use. This is expected to significantly contribute to creating more meaningful and accessible learning experiences.

Hypothetical Learning Trajectory for Negative Integer in Differentiated Instruction: A Prospective Analysis in Didactical Design Research

Fri, 24 Apr 2026 00:00:00 +0000

Integers are one of the essential materials in mathematics, but provides its own difficulties for students, especially with regard to negative integers. This study aims to develop a hypothetical learning trajectory based on the results of the learning obstcale study. Specifically, the alleged learning trajectory is a conjecture on phase D students, namely Junior High School students based on the differentiation of the readiness aspects of high, medium, and low students. This study used development research with a didactical design research approach at the prospective analysis stage, namely analyzing the didactic situation before learning. The development results obtained a hypothetical learning trajectory based on the analysis of learning obstacle and literature review. Based on this, the hypothetical learning trajectory that is compiled consists of four stages starting from the concept of negative numbers, the concept of integers, counting operations on integers, and the properties of calculating operations on integers and their application. In addition to these four stages, the alleged learning trajectory also emphasizes the meaning of the minus sign as a prerequisite concept in integers. The integration of didactical situations in the hypothetical learning trajectory emphasizes the diversity of didactical situations towards students’ abilities as a form of differentiated instruction, especially in differentiating content.

Pedagogical Exploration of Ethnomathematics: Efforts to Contextualize Numeracy Strategies for Elementary School Children

Fri, 24 Apr 2026 00:00:00 +0000

This study aims to integrate ethnomathematics into numeracy instruction in non-formal education settings and to test the effectiveness of its application in improving the numeracy skills of elementary school-aged children through non-formal education, with the goal of creating contextual and meaningful learning experiences. The study was conducted in Sukodono Village, Pacitan, which possesses a wealth of contextual cultural practices that serve as a resource for numeracy learning. The methods used were a mixed-methods study with an ethnographic approach to explore cultural practices, as well as a one-group pretest–posttest pre-experimental design to test improvements in numeracy skills. The research subjects consisted of cultural experts, teachers, elementary school-aged children, and parents, with a sample size of 16 students selected using purposive sampling. Quantitative data were analyzed using a paired samples t-test and N-Gain, while qualitative data were analyzed using the Miles and Huberman model. The research findings indicate that various local cultural practices contain mathematical concepts relevant to numeracy learning, such as geometry, measurement, patterns, and comparisons, which were identified in the contexts of agate stones, the Ceprotan traditional ceremony, and Rontek art. The findings suggest a trend toward improved student numeracy skills, as evidenced by moderate N-Gain scores and significant differences in paired t-test results. These findings confirm that the integration of ethnomathematics into numeracy learning not only strengthens contextual conceptual understanding but also serves as a relevant and meaningful alternative learning strategy, particularly within non-formal education pathways rooted in local culture.

Effectiveness of Multisensory-Based Statistical E-Comic with Collaborative Learning to Enhance Deaf Students’ Mathematical Connection

Thu, 18 Jun 2026 00:00:00 +0000

Deaf students face challenges in understanding abstract mathematical concepts, especially the material of data concentration measures, due to limited verbal communication and lack of learning media that suits their characteristics. This study aims to examine the effectiveness of statistical e-comic based on multisensory approach integrated with collaborative learning model in improving mathematical connection ability of deaf students. The research approach used is mixed-methods with Single Subject Research (SSR) design type A-B-A. The subjects consisted of three deaf students of class VIII-B in SLB Negeri Ungaran who were purposively selected. Data collection techniques included mathematical connection tests, learning observations, semi-structured interviews, and visual documentation. Quantitative data was analysed using visual inspection charts within and between conditions, while qualitative data was analysed through reduction, presentation, interpretation, and conclusion drawing. The results showed that statistical e-comic media was effective in significantly improving deaf students' mathematical connections, both from cognitive (concept understanding), affective (motivation and attitude), and psychomotor aspects (digital skills and participation). The conclusion shows that statistical e-comic with multisensory approach and collaborative learning is able to bridge the gap of mathematical understanding contextually and applicatively.

Teaching of Mathematical Proof in Middle School Geometry: A Systematic Review of Technology-Enhanced Approaches

As Elly, Yusuf Hartono, Nyimas Aisyah, Hapizah — Fri, 19 Jun 2026 00:00:00 +0000

This study investigates approaches to teaching mathematical proof at the middle school level through a systematic literature review, focusing on a key challenge in mathematics education: the difficulty students face in transitioning from empirical to deductive reasoning. Mathematical proof is a foundational element of mathematical reasoning, yet many students struggle with this shift. This study synthesizes empirical research on instructional approaches, particularly those that integrate technology, such as dynamic geometry software, augmented reality (AR), and digital learning tools, to improve students' proof skills. Following the PRISMA 2020 protocol, a systematic review was conducted with searches in Scopus, Web of Science, ERIC, and Google Scholar for studies published between 2014 and 2025. Forty-two empirical studies met the inclusion criteria. The findings highlight that technology-enhanced approaches, especially the use of dynamic geometry software, significantly improve students' abilities in proof construction, validation, and reasoning compared to conventional methods. Furthermore, the study identifies common challenges faced by teachers, including limited pedagogical content knowledge and difficulties in guiding students through the transition to formal proof. The review underscores the need to integrate inquiry-based learning and technology tools to foster deeper understanding of proofs at the middle school level. The study’s contribution lies in synthesizing diverse instructional strategies and providing evidence-based insights for future educational practices. Implications for practice and future research are also discussed.

Philosophical Values of the Sedulur Sikep (Samin Tribe) of Bojonegoro: Contextual Resources for Mathematics Learning

Dwi Erna Novianti, Puput Suriyah, Ari Indriani, Nurul Nadiya Abu Hassan — Tue, 30 Jun 2026 00:00:00 +0000

This study aims to identify the philosophical values embedded in the Sedulur Sikep (Samin) community in Bojonegoro and reconstruct them into a contextual mathematics learning design. The study employed a qualitative ethnographic approach involving six participants, consisting of community leaders and members selected purposively based on their knowledge of Sedulur Sikep teachings and practices. Data were collected through participant observation, in-depth interviews, and document analysis. Data analysis was conducted using open coding, thematic categorization, and interpretive analysis to examine the relationship between cultural values and mathematics learning contexts. The findings indicate that the values of ora jumput (not taking others’ rights), ora bedok (honesty), and ora srei (not being greedy) function as ethical principles consistently reflected in social practices related to resource management, economic interactions, and everyday decision-making. These values were reconstructed into authentic contexts for mathematics learning through tasks involving fair distribution, procedural consistency, and decision-making under constraints. The integration of cultural values was framed through Contextual Teaching and Learning (CTL) and Realistic Mathematics Education (RME), positioning cultural practices as starting points for mathematical activity. The contribution of this study lies in proposing a learning design framework that connects Sedulur Sikep philosophical values with operational mathematical contexts. The findings extend ethnomathematics research beyond cultural identification toward the reconstruction of cultural values as resources for contextual mathematics learning design.

Are We Measuring Ability or Guessing?: CTT and IRT Evidence from a Multiple-Choice Assessment in Econometric Test

Ajeng Wahyuni, Yunaita Rahmawati, Maulida Nurhidayati, Muhtadin Amri — Tue, 30 Jun 2026 00:00:00 +0000

Multiple-choice tests are widely used in mathematics-related higher education courses because they are practical for assessing broad learning outcomes. Correct responses may not always indicate full conceptual mastery, as students may answer correctly through partial knowledge, distractor elimination, unintended item cues, or pseudo-guessing. This study evaluates the quality of a 20-item four-option multiple-choice econometrics assessment using Classical Test Theory (CTT) and Item Response Theory (IRT). The test was administered to 108 undergraduate students and was designed to measure econometrics competence as an applied mathematics construct, including quantitative and statistical reasoning, regression and model interpretation, hypothesis testing and inference, model assumptions and diagnostics, and data-based decision-making. CTT was used to examine item difficulty, item discrimination, while IRT was used to compare the 1PL, 2PL, and 3PL models and to diagnose pseudo-guessing. The results showed a mean score of 13.85 out of 20, KR-20 of 0.681, and Cronbach’s alpha of 0.677, indicating moderate but not strong internal consistency. CTT identified no difficult items, nine easy items, and three items with poor discrimination. The 1PL model had the lowest BIC and was therefore the most fit model, while the 3PL model was retained diagnostically because it estimates pseudo-guessing. Eight items, namely I01, I05, I06, I12, I15, I16, I18, and I20, had pseudo-guessing parameters above 0.25. These findings suggest that some correct responses may have been influenced by non-mastery factors. This study contributes to mathematics education by demonstrating how integrated CTT and IRT diagnostics can improve the validity of econometrics assessment as a measure of quantitative and statistical reasoning.

A Bibliometric Analysis of Critical and Creative Thinking in Elementary School Mathematics Learning

Aswin, Al Jupri, Dadang Juandi, Suhendra, Eyus Sudihartinih, Andi Sri Hardiana — Tue, 30 Jun 2026 00:00:00 +0000

Through a bibliometric approach, this study aims to analyze trends, main focuses, and potential future research themes related to critical and creative thinking skills in mathematics learning at the elementary school level. The data were obtained from the Scopus database covering the years 1997–2025 with the search keywords "critical thinking" OR "creative thinking" AND math* AND "elementary school", resulting in 125 documents analyzed using Biblioshiny R and VOSviewer software. The analysis results show that publications on this topic have increased significantly since 2016, with Indonesia having the highest number of publications. However, the United States and Taiwan dominate in terms of citation impact. Four main clusters were identified: innovative learning approaches (including STEM and problem-based learning), elementary education contexts, curriculum development and engineering education, and strengthening critical thinking skills through geometry and problem solving. Bibliometric visualization also shows that topics such as "creative thinking", "teaching and learning", and "educational computing" are growing and promising areas for further research. This study recommends integrating interdisciplinary and technological approaches in curriculum development and the need for increased international collaboration to strengthen research impact. These findings provide an important contribution to mapping the scientific landscape and the direction of developing mathematics learning that fosters higher-order thinking skills from an elementary school.

Statistical Literacy of University Students: An Analysis of Decision-Making, Evaluating, Communicating, and Interpreting Skills

Zulqoidi Habibie, Kartono, Wardono, Iqbal Kharisudin — Tue, 30 Jun 2026 00:00:00 +0000

This study aimed to analyze university students’ statistical literacy based on four indicators: decision-making, evaluating, communicating, and interpreting, as well as to examine differences in statistical literacy according to gender. A descriptive survey design was employed. The participants comprised 144 students from six universities across five provinces in Indonesia: Banten, Jakarta, East Java, Jambi, and Bengkulu, who were selected using non-probability sampling with a convenience sampling technique. Data were collected using an open-ended statistical literacy test developed based on response-skill indicators from the perspective of data consumers. The collected data were analyzed using descriptive statistics and the Mann–Whitney U test to determine whether significant differences existed between male and female students. The results revealed no statistically significant differences in statistical literacy between male and female students. Among the four indicators (decision-making (average 22.9), evaluation (75), communication (55.6), and interpretation (22.2)) students demonstrated relatively stronger performance in evaluating and communicating statistical information than in decision-making and interpreting. Analysis of students’ responses indicated that the main difficulties were related to understanding the context of statistical information, accurately interpreting data, integrating multiple statistical measures when making decisions, and effectively communicating information derived from graphs and datasets. These findings highlight the importance of integrating statistical knowledge with contextual understanding to support the development of statistical literacy among university students. The limitations of this study are evident in the data collected, namely the imbalance in the number of male and female students, which means the results cannot yet be generalized; further research is needed.

Mathematical Problem-Solving Abilities in Algebraic Operations through Realistic Mathematics Education (RME)

Izzati Mauren Sefira, Ali Shodikin — Tue, 30 Jun 2026 00:00:00 +0000

This study aims to describe the mathematical problem-solving abilities of seventh-grade students in algebraic operations through the RME approach, focusing on two aspects, how the characteristics of RME support or constrain students’ problem-solving processes, and students’ problem-solving performance based on three of Polyas’ stages. Problem-solving abilities were analyzed using three of Polya’s stages, understanding the problem, devising a plan, and implementing the plan. The looking-back stage was excluded as this study focuses on processes explicitly documented in students’ written responses. This study employed a descriptive qualitative approach with 11 seventh-grade students as research subjects. Data were collected through written tests and interviews. The results of the study show that the indicator implementing a plan was the most frequently mentioned in students’ responses. The indicator understanding the problem and formulating a plan remained relatively low, most students did not fully list the given and asked information, nor did they explicitly state their problem-solving strategies. The use of real-world contexts in RME helps students understand problem situations, but it has not yet fully encouraged structured planning. These findings indicate the need to strengthen the early stages of problem-solving in RME instruction so that students can solve problems more systematically.

Improving Numeracy Performance Through the GASING Method

Tue, 30 Jun 2026 00:00:00 +0000

Numeracy is foundational to academic success, yet many Indonesian primary school students struggle with mathematics under instruction that emphasises rote memorisation over conceptual understanding. This study examined the improvement in numeracy performance associated with the GASING (Gampang, Asyik, Menyenangkan / Easy, Enjoyable, Fun) method among primary school students and teachers in Bojonegoro District, Indonesia. A one-group pre-test–post-test design was employed with 97 students and 50 teachers who completed a 15-day intensive training programme covering five numeracy domains: number recognition, addition, multiplication, subtraction, and division. Performance was assessed using curriculum-aligned numeracy tests administered at pre-test and post-test. Paired-samples t-tests showed statistically significant gains across all domains. Students improved from a composite pre-test mean of 30.51 (SD = 17.55) to 83.08 (SD = 9.53), t(96) = 35.25, p < .001, Cohen's dz = 3.58, equivalent to a 2.72-fold gain; the largest domain gain was in division (6.28-fold). Teachers improved from 73.56 (SD = 13.11) to 97.70 (SD = 2.98), t(49) = 15.16, p < .001, dz = 2.14. Because the design included no control group, these results indicate improvement associated with the intervention rather than its isolated causal effect. The findings nonetheless suggest that the GASING method, delivered through an integrated teacher–student training model, is associated with substantial numeracy gains and with positive affective changes reported by participants.