Should I Learn Division Algorithm?: An Investigation of Elementary Students’ Solution Strategies on Division with Remainder (DWR) Problems

Abstract

The division with remainder (DWR) problems offer significant potential for students to make sense of the division operation. The purpose of the study is to investigate elementary school students' solution strategies for DWR problems. In particular, this study aims to compare the problem-solving strategies in DWR problems employed by second-grade students, who are versed in multiplication, but have not been introduced to division; with those of third and fourth-grade students who are familiar with division but have yet to engage with the interpretation of remainders. This qualitative research obtained data from 144 students in second, third, and fourth-grades in a public primary school. A total of six different DWR problems were presented to the students, including types as remainder divisible, remainder not divisible and remainder as a whole. The findings indicated that the strategies used by students in solving DWR problems differed. While second-grade students prefer strategies such as repetitive addition, repetitive subtraction, grouping, verbal explanation and using models, there is a noticeable tendency to use the division algorithm by fourth-grade students. However, it was noticed that students were unable to interpret the remainder in a meaningful way, especially from the third-grade, when they began to learn the division algorithm. According to the study, rather than moving immediately to the division algorithm, teachers should spend their time helping students understand division through contextual problems and representations.