Exploring students’ understanding layers in solving arithmagon problems

Abstract

Previous studies have reported that students' understanding is strongly influenced by their previous knowledge. Specifically, “don’t need” boundaries are students’ activities with ideas that are no longer bound to previous forms of understanding. Anchored by the importance of knowing such boundaries and students’ understanding layers, the present study was designed to explore the characteristics of “don’t need” boundaries of students in solving arithmagon problems using a qualitative descriptive approach. To collect the data, test and unstructured interviews were carried out. The test questions were administrated to 23 participants. They were recruited based on indicators of students’ written communication skills which appeared in the activity of solving the test questions. To triangulate the data, unstructured interviews were done. Findings suggest that S1 crossed the first “don’t need” boundaries when solving the addition and multiplication arithmagon problems. S2 crossed the first and second “don’t need” boundaries when solving the addition arithmagon problem and only crossed the first ‘don’t need’ boundaries in solving multiplication arithmagon problems. However, S3 crossed the second “don’t need” boundaries in solving arithmagon problem of addition and multiplication. Based on these findings, future research is encouraged to find and explore the third “don’t need’” boundaries in solving mathematical problems.