Graduate Level Students’ Techniques and Difficulties in Proving Theorems of Abstract Algebra

Abstract

This paper has discussed different techniques of proving theorems of abstract algebra adopted by the students of graduate level followed by their difficulties revealed over there. For, three graduate students from the classroom of Master’s degree level in mathematics education of Tribhuvan University were selected by using purposive sampling technique. The difficulties as experienced by students were explored through interviews with the help of interview guidelines; and their responses were recorded by using mobile phone. These recorded responses were transcribed and analyzed by using general inductive approach. The findings reveal that students have felt more difficulty in the indirect approaches of proofs in comparison to direct approaches while learning theorems in abstract algebra. The major difficulties as they experienced are in the selection of appropriate techniques of proofs, connection of previous concepts for logical arguments in proofs and construction of examples and counter examples of the concepts related to theorems. These difficulties are expected to be reduced if the teacher of abstract algebra course in higher mathematics education focuses on conceptual understanding and critical thinking for their students’ learning.