Students' Errors in Learning Elementary Group Theory: A Case Study of Mathematics Students at Andalas University

Dr Yerizon,Sri Nita,Bukti Ginting,I Made Arnawa,Dr Yanita

doi:10.13189/ujer.2019.071216

Abstract

This paper will discuss level of conceptual understanding of 18 mathematics students in learning elementary group theory during abstract algebra course 2016-2017 academic year at Andalas University. Participants were asked to answer three proof tests in relation to group theory. Students' solutions to the proof test were taken as the key source of data used to: (i) classify students to one of the four levels of conceptual understanding and (ii) analyze students errors in learning elementary group theory. One student for each level was interviewed to provide additional information about common students' errors on the proof task and to aid the process of understanding the underlying cause of these errors. The finding shows that: (1) Students' achievement in proof task is still problematic; (2) Most students have difficulties in verifying the existence of identity and inverse element; (3) Factors that contribute to errors in proof task are: lack of conceptual understanding and that student treated binary operations on a group as a binary operations on real numbers.

Highlights

According to Baylis [1], proof is the heart of mathematics and thinking mathematically, so in evaluating the success of students in learning mathematics, especially in abstract algebra, should be assessed by the ability of the student in a proof task
Proof task makes mathematics unique and different from other disciplines [2], through the proof task, a lecturer can observe: (1) how the student's ability in arguing logically, (2) how students use examples or non-examples to support their argument, (3) what the weaknesses are experienced by students in reasoning, and (4) whatthe misconceptions that often experienced by college students are
In order to understand the abstract algebra, students are required to be able to understand every definition, lemma, theorem, and able to use them in proving some of the problems in abstract algebra.improving student understanding in abstract algebra can be done through improving the ability of students in proving, which is in line with what is suggested by Hanna [5] that the understanding in mathematics should be promoted through a mathematical proof

Summary

Introduction

According to Baylis [1], proof is the heart of mathematics and thinking mathematically, so in evaluating the success of students in learning mathematics, especially in abstract algebra, should be assessed by the ability of the student in a proof task. In order to understand the abstract algebra, students are required to be able to understand every definition, lemma, theorem, and able to use them in proving some of the problems in abstract algebra.improving student understanding in abstract algebra can be done through improving the ability of students in proving, which is in line with what is suggested by Hanna [5] that the understanding in mathematics should be promoted through a mathematical proof. Learning mathematics without accompanied by a proof does not reflect the theory and practice of mathematics

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