The Profile of Structure Sense in Abstract Algebra Instruction in an Indonesian Mathematics Education

Junarti*, Y.,Nur Karomah,Mulyono Mulyono,Y. L.

doi:10.12973/eu-jer.8.4.1081

Abstract

<p>The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of abstract algebra course from two individual assignments given to the students. The students who could provide the best answers from the first and second individual assignments were chosen to be the respondents. The data from the second assignment, then, was analyzed through presentation, interpretation, coding, making a pattern, leveling and continued with clarification through an interview. The results of the study show that there were six patterns of structure sense answers and five levels of structure senses made by the students as the profile of structure sense. The conclusion is the inability to recognize the structure of the set elements, operation notations, and binary operation properties is one of the causes of the constraints in structuring the proof construction of the group. Thus, a thinking of mathematics connection is needed in structure understanding as a connection between symbol in learning and the symbol of abstract.</p>

Highlights

A proof is the center of Mathematics
Understanding of abstract algebra can influence the teaching of structure in early algebra (Wasserman, 2017) so that the proof structure is the part that must be possessed by a Mathematics pre-service teacher like the students of Mathematics Education Study Program as a teacher candidate in secondary school
Some studies on the structure sense that have been studied for algebra in high school (Hoch & Dreyfus, 2006), for algebra in university (Novotna, Stehlikova, & Maureen, 2006; Novotna & Hoch, 2008; Wasserman, 2016; Oktac, 2016), like a study that includes the theory of algebraic structures, Groups, Ring and Field by Durand-Guerrier, Hausberger & Spitalas (2015) and other difficulties due to the lack of consistency of the concept in the construction of evidence (Alcock et al, 2011), so it is reasonable that this study is of particular concern for further investigation

Summary

Introduction

A proof is the center of Mathematics. The difficulties in teaching and learning proof are internationally recognized (Miyazaki, et al 2017). Understanding of abstract algebra can influence the teaching of structure in early algebra (Wasserman, 2017) so that the proof structure is the part that must be possessed by a Mathematics pre-service teacher like the students of Mathematics Education Study Program as a teacher candidate in secondary school. Some studies on the structure sense that have been studied for algebra in high school (Hoch & Dreyfus, 2006), for algebra in university (Novotna, Stehlikova, & Maureen, 2006; Novotna & Hoch, 2008; Wasserman, 2016; Oktac, 2016), like a study that includes the theory of algebraic structures, Groups, Ring and Field by Durand-Guerrier, Hausberger & Spitalas (2015) and other difficulties due to the lack of consistency of the concept in the construction of evidence (Alcock et al, 2011), so it is reasonable that this study is of particular concern for further investigation

Objectives

Methods

Conclusion