Comparison of Proof Characteristics of Mathematics Gifted Students and General Students in Algebra

Objectives The purpose of this study was to obtain educational implications for proof guidance by examining the recognition of proof types and the actual proof process using algebra questions for first-year high school math gifted students and general students who learned proof in the 2015 revised curriculum. Methods A questionnaire was provided to 10 gifted students from science high schools located in middle and small cities and 20 general high school students. We investigate the preference for the proof type. In addition, after comparing the type of proof that appeared in the actual proof process and the type of proof that they preferred, the satisfaction level was investigated, and the result was analyzed. Results Gifted students showed a higher rate of preference for deductive proof in algebra questions than general students. Gifted students with the perception that they prefer deductive proof types performed deductive proofs with sophisticated algebraic expressions even in actual proofs, and showed high satisfaction with their proofs. On the other hand, the type of empirical proof (40%) was investigated in recognition of the type of proof preferred by general students. They frequently failed to perform their preferred deductive proof, and in these cases, they expressed dissatisfaction with their proof for reasons such as ‘not showing generality of proof’ and ‘unable to use mathematical characters and symbols’. In addition, the preferred proof type and the actual proof type did not match. Conclusions It was found that step-by-step proof guidance was needed to provide appropriate proof tasks to students with excellent proof ability, and to progress to the level of deductive proof through idea generation and understanding such as empirical proof if not.