The Teaching and Learning of Geometric Proof

Geometric proof-writing is a widely known cause of stress for secondary school students and teachers alike. As the textbook is the primary curricular tool utilized by novice teachers, a two-part qualitative study was conducted to determine (a) the types of proofs presented in a typical high school geometry textbook and (b) teachers’ preparedness and confidence to teach proof and proving. I conducted a qualitative analysis of the selected textbook based on its presentation of proofs and proof tasks, and then used said analysis to inform the creation of a five-question content assessment on proof, which was administered to 29 preservice and in-service secondary mathematics teacher participants. During the administration of the assessment, I interviewed each participant regarding their thought processes, as well as their knowledge, beliefs, and preparedness to teach proof and proving. The data were analyzed using a qualitative coding system to categorize participants’ responses to the interview questions according to their beliefs and attitudes, as well as issues with mathematical language and content that they encountered. The qualitative analyses indicated that the selected textbook largely underemphasizes the role of proof in the secondary school geometry curriculum, and that most participants are largely underprepared to teach proof at the secondary level. Participants expressed sentiments about the nature of proof and proving, verifying trends from the literature and providing the impetus for future study. The findings support that more studies are needed to analyze the intersection between curricular knowledge and content knowledge for secondary mathematics teachers.