Difficulties Experienced by Undergraduate Students in Proving Theorems of Real Analysis

Abstract

Developing proofs is a very important task of undergraduate mathematics students. However, proving theorems in real analysis is a challenging task for many undergraduate students. In this context, this research was conducted to explore difficulties experienced by undergraduate students in proving theorems of real analysis. Narrative research design under the interpretive research paradigm was used for the study. Three students (higher achiever, average achiever, and below-average achiever) were selected purposively from the sixth semester of B.Ed. programme of the central campus of Far West University. Radical constructivism was selected as the theoretical basis of the study. Interview guideline was prepared as a research tool and interviews of participants were taken based on the guideline. For the analysis and interpretation, interview data were transcribed, coded and then themes were generated. Four themes were constructed that are inability to link statements logically, lack of skill of applying definitions/theorems, lack of skill of selecting an appropriate path of proving, and inability to grasp language/symbols and lengthy proof. The conclusion is that students can have the above types of difficulties in understanding/constructing proof of theorems but the type and extents of the difficulty experienced by learners depend upon the context and ability of learners. This study indicates that beliefs and practices guided by modernism is one of the reasons behind the difficulties in proof construction. The findings of this study would help teachers to select the appropriate pedagogical approach of teaching proofs and students to understand/construct proofs of Real Analysis.