MỘT NGHIÊN CỨU THỰC NGHIỆM VỀ CÁC KHÓ KHĂN LIÊN QUAN ĐẾN VIỆC HỌC KHÁI NIỆM ĐẲNG CẤU NHÓM

Abstract

In this paper, we present the result of an experimental research about three difficulties that students face in learning the concept of group homomorphism and group isomorphism: (1) Not realize the basic element that “Domain and codomain are groups”; (2) Not understand the nature of the property that "operations of two groups are preserved"; (3) Not understand the nature of the property that “the map is one-to-one”. These difficulties originate from the epistemological obstacles and are influenced by the pedagogical obstacles due to institutional relations of university mathematics to the concept of group homomorphism and group isomorphism. The purpose of this research is to find out difficulties of students in learning the concept of group homomorphism and group isomorphism and help the trainers understand exactly the sources of student mistakes and thence be able to design optimal lectures to help students overcome these difficulties.