Beliefs,Difficulties and Enhancement in Proving of Pre-Service Mathematics Teachers

Abstract

This study explored the beliefs, difficulties, and enhancement in mathematical proving among pre-service mathematics teachers. Using a multiple method of research, data were gathered through surveys and interviews to examine the perception of the participants in making mathematical proofs and the common challenges they encounter, and to the performance of the participants in the proving test based on the developed intervention program as a strategy to improve their proving skills. Findings revealed the existence of both negative and positive beliefs affecting their engagement in proof-making. Negative beliefs included perceptions of proving as abstract, impractical, intimidating, overly logical, and time-consuming to teach, while positive beliefs viewed proving as a means for deeper understanding, creativity, collaboration, and critical thinking. The study also identified key difficulties such as struggles with abstract reasoning, communication anxiety, fear of making mistakes, and limited practice in using mathematical symbols and representations. To address these challenges, an intervention program through the use of developed instructional material was developed and implemented. Results from a comparative analysis of pretest and posttest scores showed a significant improvement in the participants’ performance across various types of proofs such as counterexample, direct, indirect, and mathematical induction which demonstrated the effectiveness of the intervention.