Hipotenusa: Journal of Mathematical Society

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.

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

Wed, 10 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.

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.

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.