Redesigning number pattern instruction: A didactical design grounded in learning obstacle analysis for junior high school students
DOI:
https://doi.org/10.59965/pij.v3i2.41Abstract
The concept of number patterns is an essential prerequisite for arithmetic sequences and series, yet a preliminary study of 15 eighth-grade students at SMP Islam Riyadhussolihin NW Bukit Tengger revealed that most students still experienced learning obstacles when solving problems on even-odd, triangular, square, and rectangular number patterns. This study aimed to identify the types of learning obstacles experienced by students, to design a hypothetical didactical design grounded in these findings, and to examine its effectiveness through classroom implementation. A qualitative approach using Didactical Design Research (DDR)—comprising prospective, metapedadidactic, and retrospective analysis—was employed. Data were collected through a learning-obstacle diagnostic test, classroom observation, and semi-structured interviews with selected students, then analysed using source and method triangulation. The findings revealed that the dominant obstacle was ontogenic-psychological in nature, reflected in students’ carelessness and haste in completing tasks, alongside conceptual obstacles related to the prerequisite concept of even and odd numbers. Based on these findings, a Hypothetical Learning Trajectory (HLT) comprising four sequential didactical situations, anticipated student responses, didactical-pedagogical anticipations, and a Student Worksheet (LKS) was developed. Implementation of the HLT reduced learning obstacles, although new difficulties emerged and were subsequently accommodated through a revised didactical design. This study contributes to enriching Didactical Design Research literature on number patterns while producing a classroom-ready instructional package for secondary mathematics teachers.
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