Approaches sto Proof in Geometry Textbooks: Comparing Texts from the 1980s and 2000s

Abstract

Eight American textbooks were studied, four each from the 1980s and the 2000s, with the purpose of identifying differences between the two groups of textbooks in their approaches to teaching proof and proof writing. All of the exercises in each text were coded using parameters established by the author for proofs, types of proof, and other justification and reasoning tasks. Additionally, numbers of proofs in the exposition of each textbook were determined. Thematic analyses of attention to form, presentation of theorems, and introduction to proof and proof writing were also included in the research design. Results suggest both quantifiable and qualitative differences in students' opportunities to engage in and practice proof writing as found in the exercises. Other differences in the newer textbooks include a conjecture-based approach to theorems, greater attention to placing proof in the context of mathematical reasoning, and emphasis on alternatives to the two-column form.