The Influence of Proof Understanding Strategies and Negative Self-concept on Undergraduate Afghan Students’ Achievement in Modern Algebra

Oct 15, 2026

Uploaded by Aditya

This study investigates how proof understanding strategies and negative self-concept affect undergraduate Afghan students’ achievement in modern algebra. Using structural equation modeling with data from 139 sophomore students across three classes over two consecutive years (2016–2017), the analysis tests relationships among the variables and academic performance. Results show negative self-concept significantly and negatively predicts achievement, while proof understanding strategies significantly and positively predict it. Negative self-concept also negatively influences proof understanding strategies, and the SEM model fits very well.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Abstract

Introduction

Proof Understanding Strategies

Research Background and Evidence

The Influence of Proof Understanding Strategies and Negative Self-concept on Undergraduate Afghan Students’ Achievement in Modern Algebra Ahmad Khalid Mowahed 1*, Naiqing Song 1, Yang Xinrong 1, Pei Changgen 1 1 School of Mathematics and Statistics, Southwest University, Chongqing, CHINA * CORRESPONDENCE: [khalid. mowahed@gmail.com](khalid. mowahed@gmail.com) ABSTRACT This study explored the influence of proof understanding strategies and negative self-concept on undergraduate Afghan students’ achievement in modern algebra1 . To examine the relationships among proof understanding strategies, negative self-concept and achievement in modern algebra1, we used structural equation modeling on data collected from three classes of students taking modern algebra in two consecutive years of 2016 and 2017. Participants of this study included 139 sophomore Afghan students, 40.29% male and 59.71% female. Conducting SEM analysis resulted the following findings: firstly, negative self-concept had significant negative influence over students’ achievement in modern algebra1; secondly, proof understanding strategies had significant positive influence over students’ achievement in modern algebra1; thirdly, negative self-concept had significant negative influence over proof understanding strategies; finally, the data fitted very well the SEM model, implying that proof understanding strategies and negative self-concept significantly influence students’ achievement in modern algebra1 . Keywords: achievement in modern algebra, negative self-concept, proof understanding strategies INTRODUCTION Proof Understanding Strategies Advanced mathematics typically consist of definition, theorem, proof (Davis & Hersh, 1981) . Poofs are given in textbooks of undergraduate mathematics to explain why a mathematical result is true and how one can achieve the result following the process of mathematical reasoning. Indeed, modern algebra is an advanced mathematics course in which the definitions are solely made of a collection of axioms or self-evident statements that derive the whole body of concepts, theorems, and proofs. A typical introductory modern algebra course will start off by preliminaries such as sets, mappings, relations, and continues to discuss groups, group properties, subgroups, cyclic groups, cosets, factor groups, and a brief of rings and fields. Usually the course of action in teaching such a course is to follow the sequence of “theorem-proof-application” (Dreyfus, 1991) . The frequently practiced way of sharing and discussing these complex ideas of modern algebra is that the professor of the course presents proofs of theorems to students who are observing the process. Professor of the course expects students understand the theorem and every step in its proof so that they will be able to reproduce or produce proofs for theorems and problems posed throughout the assessment process as a main contributing factor to their achievement in modern algebra. Teaching experience as well as literature (Conradie & Frith 2000; Porteous 1986; Rowland 2001) shows that students and their educators struggle to comprehend as they read proofs of theorems. As a supporting evidence, it has been observed that students are struggling to comprehend the statement of some theorems in modern algebra, let alone to understand its proof. In many instances of teaching theorems of group theory in the class of modern algebra, before starting to state the theorem and its proof, we usually ask students to read the theorem in at least three minutes and elaborate what they understood after reading the theorem. It has been observed that there was an ‘aha’ moment when we explained every part of the theorem to students when they could not grasp it at the first reading. This is not only the case in the context of Afghanistan, several other empirical researches (Alcock & Weber, 2005; Ko & Knuth 2012) also show that undergraduate mathematics students have diffic

FAQs

What does the study examine regarding students’ performance in modern algebra?

It examines how proof understanding strategies and negative self-concept relate to undergraduate Afghan students’ achievement in modern algebra.

How was the data collected and analyzed?

Data were collected from 139 sophomore Afghan students across three classes over two consecutive years (2016 and 2017) and analyzed using structural equation modeling (SEM).

What are the key findings about negative self-concept and proof understanding strategies?

Negative self-concept significantly negatively influences achievement and also negatively influences proof understanding strategies, while proof understanding strategies significantly positively influence achievement. The SEM model shows a very good fit.

Oct 15, 2026

Uploaded by Aditya