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

Riki Andriatna; Imam Sujadi; Ira Kurniawati; Arum Nur Wulandari; Yuli Bangun Nursanti; Kanya Barndt

doi:10.18326/hipotenusa.v8i1.2195

Authors

Riki Andriatna Universitas Sebelas Maret
Imam Sujadi Universitas Sebelas Maret
Ira Kurniawati Universitas Sebelas Maret
Arum Nur Wulandari Universitas Sebelas Maret
Yuli Bangun Nursanti Universitas Sebelas Maret
Kanya Barndt Thepsatri Rajabhat University, Thailand

DOI:

https://doi.org/10.18326/hipotenusa.v8i1.2195

Keywords:

didactical design research, hypothetical learning trajectory, negative integer, prospective analysis

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.

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