Teacher Challenges and Strategies in Addressing Proof in Mathematics

Abstract

Mathematical proof is fundamental to mathematical reasoning and conceptual understanding, yet teaching proof remains challenging because learners must coordinate mathematical knowledge, logical reasoning, justification, and communication. This study investigated the challenges mathematics teachers encounter in addressing proof and the strategies they employ to respond to students’ misconceptions and learning difficulties. A mixed-method research design was used to integrate quantitative assessment of teachers’ perceived challenges with qualitative analysis of instructional strategies. The participants were 30 mathematics teachers in Region VI who were enrolled in graduate studies in mathematics or mathematics education. Data were collected through a researcher-developed questionnaire consisting of respondent profiles, 15 Likert-scale items on challenges in proof instruction, and open-ended questions concerning instructional strategies. Descriptive statistics, the Kruskal–Wallis H test, and the Mann–Whitney U test were used to analyze quantitative data, while thematic analysis was used for qualitative responses. The findings indicate a very high level of challenges across cognitive, affective, instructional, curricular, and structural dimensions, with the tendency of students to treat examples as proofs receiving the highest rating. Teachers report using multiple proof techniques, scaffolded instruction, guided questioning, collaborative learning, and engagement-oriented strategies. No significant differences are found across teacher profile variables. The findings support the need for progressive proof instruction, reasoning-focused professional development, improved instructional resources, and stronger curriculum alignment.