Reasoning and Proof Vol.2-395 DOES PROOF PROVE?: STUDENTS ’ EMERGING BELIEFS ABOUT GENERALITY AND PROOF IN MIDDLE SCHOOL

This paper presents results from a multi-year research study1 that examined the development of middle school students ’ competencies in mathematical reasoning and proof. Written assessment data collected from 78 middle school students over a period of three years shows that while improvement occurs from 6th to 8th grades, results indicate that competencies needed to generate mathematical proof remain to be developed. Proof has always been a central aspect of the discipline of mathematics and the practice of mathematicians, but it is a relatively recent aspect of mathematics education for students at all grade levels. Traditionally, students ’ first encounters with proof occurred during high school geometry courses, where the formal two-column proof was often the only method of proving students encountered, and explorations of proving general mathematical statements in other mathematics courses such as algebra were typically not supported. However, researchers such as Schoenfeld (1994) and Wu (1996) assert that proof cannot be separated from mathematics and it is an essential part of the process of doing and communicating mathematics in all content areas. From its inclusion in the 2000 Principles and Standards for School Mathematics (NCTM), reasoning and proof has gained increased attention as a central part of mathematics education fo