Analysis of elementary school students' errors in multilevel division operations (porogapit) based on skemp's theory

Mohammad Nurwahid; Bagus Hidayatulloh; Rosmaiyadi Rosmaiyadi

doi:10.32332/linear.v7i1.82-96

Authors

Mohammad Nurwahid Institut Alif Muhammad Imam Syafi'i
Bagus Hidayatulloh Institut Alif Muhammad Imam Syafi’i
Rosmaiyadi Rosmaiyadi Institut Sains dan Bisnis Internasional

DOI:

https://doi.org/10.32332/linear.v7i1.82-96

Keywords:

Student Errors, Multilevel Division, Porogapit, Skemp's Theory, Elementary School

Abstract

This study aims to analyze elementary school students' errors in solving multilevel division (porogapit) based on Skemp’s Theory of Understanding. The study employed a qualitative descriptive approach involving 20 fifth-grade students who had learned multilevel division. Data were collected through written tests and semi-structured interviews. From the test results, two students who demonstrated representative error patterns and were able to clearly communicate their reasoning were selected as key informants for in-depth analysis. The findings reveal three dominant types of errors: (1) errors related to place value, particularly failure to maintain the positional structure of digits in the quotient; (2) omission of zero digits in the quotient; and (3) incorrect use of approximation strategies in determining quotient digits. These errors indicate that students tend to rely on instrumental understanding rather than relational understanding. The weakest conceptual aspects include students’ understanding of place value, the role of zero in division, and the relationship between division and multiplication. This study highlights the importance of strengthening relational understanding in teaching porogapit division to reduce procedural errors.

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