Mathematical proof is one of the major themes of university mathematics courses, yet it is not prevalent in many secondary mathematics courses. Many advanced university mathematics classes are taught in the definition–theorem–proof tradition (Thurston, 1995). Even in courses not taught strictly in this tradition, mathematical proof plays an important role, reflective of the importance of proof in the discipline of mathematics. Proof is the way in which the validity of mathematical claims is established; as such, it is the cornerstone of mathematical activity. Many university programs now employ a “transition to proof” course to ease students’ transition from the calculus sequence to more advanced courses in which proof plays a pivotal role. Proving and justifying has been identified as an important mathematical process by the National Council of Teachers of Mathematics (NCTM, 2000). However, it is questionable how often formal proof may be seen in secondary mathematics classrooms outside geometry or courses for “more advanced” students. For example, Knuth (2002a) found that the teachers in his study thought proof was only appropriate in upper-level classes for advanced students and conceived of proof as a topic in mathematics rather than a tool for doing mathematics. The relative difference in emphasis on proof and proving at the secondary and college levels despite its recognized importance raises a question regarding how a secondary mathematics teacher’s conception of proof and proving influences his or her teaching practice. 

اثبات ریاضی یکی از موضوعات اصلی دوره های درسی دانشگاهی است، که هنوز هم در بسیاری از دوره های درسی دبیرستانی ریاضی رایج نشده است. بسیاری از کلاس های ریاضی دانشگاهی پیشرفته، سبک متداول تعریف-قضیه-اثبات را تدریس می کنند ( ثارستون، 1995). حتی در دوره های درسی که دقیقا در سبک سنتی تدریس نمی شوند، اثبات ریاضی نقشی مهم را بازی می کند، بازتابی از اهمیت اثبات در نظم و ترتیب ریاضی. بسیاری از برنامه های دانشگاهی یک درس انتقال به اثبات را برای تسهیل کردن انتقال دانش آموزان  از سبک محاسباتی به دوره های درسی پیشرفته تر، که در آن ها اثبات نقشی اساسی را ایفا می کند، در نظر می گیرند.