An examination of reasoning and proof opportunities in three differently organized secondary mathematics textbook units

摘要

Students' struggles in learning reasoning and proof (RP) in mathematics are well known. Despite the instantiation of RP opportunities in mathematics textbooks in the USA and the important role that textbooks play in teachers' instructional decisions, little research has been conducted on analyzing student textbook tasks and narrative sections of mathematics textbooks in the USA. One polynomial functions unit located within a reform-oriented, conventional, and hybrid secondary mathematics textbook was examined for RP instances. RP tasks comprised 4, 9, and 22 % of the student tasks in the conventional, hybrid, and reform-oriented textbook units, respectively. The textbook exposition of all three textbook units promoted the presentation of proof building blocks (e. g., definitions) with no occurrences of conjecture development or testing. Overall, only 19 % of the learning objectives across the three textbook units were validated. The conventional and hybrid textbook units had the potential to promote an authoritative proof scheme in students while the reform-oriented textbook unit had the potential to promote an empirical proof scheme in students.