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Hypothetical Learning Trajectory for Negative Integer in Differentiated Instruction: A Prospective Analysis in Didactical Design Research Andriatna, Riki; Sujadi, Imam; Kurniawati, Ira; Wulandari, Arum Nur; Nursanti, Yuli Bangun; Kanya Barndt
Hipotenusa: Journal of Mathematical Society Vol. 8 No. 1 (2026): Hipotenusa : Journal of Mathematical Society
Publisher : Program Studi Tadris Matematika Universitas Islam Negeri (UIN) Salatiga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18326/hipotenusa.v8i1.2195

Abstract

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.
EKSPERIMENTASI PEMBELAJARAN MATEMATIKA MENGGUNAKAN MODEL PEMBELAJARAN MURDER DENGAN BRAIN GYM TERHADAP KEMAMPUAN PEMECAHAN MASALAH SISWA DITINJAU DARI RESILIENSI MATEMATIS SISWA Millentika Rachmadani; Dyah Ratri Aryuna; Riki Andriatna
Jurnal Karya Pendidikan Matematika Vol 12, No 2 (2025): Jurnal Karya Pendidikan Matematika Volume 12 Nomor 2 Tahun 2025
Publisher : Universitas Muhammadiyah Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26714/jkpm.12.2.2025.91-101

Abstract

This study aims to determine the effect of learning models on students' mathematical problem-solving abilities in terms of their mathematical resilience. The type of this research is quasi-experimental. The population of this study is the 11th-grade students of SMA Negeri 2 Sukoharjo for the 2023/2024 academic year, consisting of 4 11th-grade classes with a focus on Science and Mathematics. The sample used consists of two classes, with 36 students from class XI 2B as the experimental class and 35 students from class XI 1 as the control class, selected through cluster random sampling. Data collection was carried out using tests and questionnaires. The data analysis technique used is a two-way ANOVA with unequal cells, followed by a multiple comparison test using the Scheffé method. The research results show that the mathematical problem-solving ability of students who received the MURDER learning model with Brain Gym is better than that of students who received the MURDER learning model, both in general and at each level of mathematical resilience. Additionally, at each level of mathematical resilience, students show differences in mathematical problem-solving ability, both in general and in each learning model. In the MURDER learning model with Brain Gym, students with moderate mathematical resilience have better mathematical problem-solving ability than those with high and low resilience. Meanwhile, in the MURDER learning model, students with high mathematical resilience have better mathematical problem-solving ability than those with moderate and low resilience.