Incomprehension of the Indonesian Elementary School Students on Fraction Division Problem

Abstract

The purpose of the study is to investigate the Indonesian students’ performance in solving fraction division case including the difficulties, relations, and implications for classroom instruction. This study employed a descriptive case study to achieve it. The procedures of data collecting were initiated by giving a context-based problem to 40 elementary school students and it then according to the test result was selected three students for semi-structure interviewed. The findings of the study showed that the tendency of students’ procedural knowledge dominated to their conceptual knowledge in solving the fraction division problem. Furthermore, it was found several mistakes. First, the students were not accurate when solving the problem and unsuccessful to figure out the problem. Second, students’ conceptual knowledge was incomplete. The last was is to apply the laws and strategies of fraction division irrelevant. These findings emphasized other sub-construct of fractions instead of part-to-whole in the teaching and learning process. Teaching and learning of fraction in the mathematics classroom should take both conceptual and procedural knowledge into account as an attempt to prevent faults and misconceptions. In conclusion, it was substantial to present context-based problems at the beginning of the lesson in order for students to be able to learn fraction division meaningfully.

Fraction Cipher: A Way to Enhance Student Ability in Addition and Subtraction Fraction

“…The uniqueness of its nature has made it difficult to understand (Braithwaite et al, 2018). This topic often occurs, there are four things that students often do when answering addition and subtraction fraction operation questions, namely systematic errors, random errors, negligence errors and not knowing how to answer fraction questions (Braithwaite et al, 2018;Loc et al, 2017;Purnomo et al, 2019;Salleh et al, 2013;Saparwadi et al, 2017;Tian & Siegler, 2017).…”

Prospective Teachers Understanding Fraction Division Using Rectangle Representation

“…However, fraction operation subjects still quite difficult in elementary school students, especially fraction division (Fitri & Prahmana, 2019;Purnomo et al, 2019;Widada et al, 2020;Yeo, 2019). They still assuming that if a number divided by another, it will be smaller than before (Ervin, 2017;Yeo, 2019).…”

“…They still assuming that if a number divided by another, it will be smaller than before (Ervin, 2017;Yeo, 2019). Besides that, they still using keep-change-flip algorithm to solve the fraction problems without understanding the meaning of fraction division and how that algorithm valid mathematically (Alenazi, 2016;Bentley & Bossé, 2018;Purnomo et al, 2019;Sahin et al, 2020;Whitehead & Walkowiak, 2017;Yeo, 2019).…”

“…Many things that can affect this problem, one of them is teacher habits that tends to give keep-change-flip algorithm directly to be memorized, remembered and implemented without telling them the concept of fraction division and how that algorithm valid mathematically (Apsari et al, 2020;Bentley & Bossé, 2018;Haji, 2013;Purnomo et al, 2019;Whitehead & Walkowiak, 2017). Fraction division also have the different meaning, so students still not properly understand the meaning of fraction division.…”

“…Fraction division also have the different meaning, so students still not properly understand the meaning of fraction division. Fraction division known as measurement concept usually done with repeated substraction until the number that are divided become zero (Purnomo et al, 2019;Stohlmann et al, 2020;Widada et al, 2020). Furthermore, fraction division also known as equal share, for instance there is a half of cake that will be divided into a quarter of cake, how many person that will get that cake (Purnomo et al, 2019;Stohlmann et al, 2020).…”