This paper reports on combining semiotic and discursive approaches to reification in classroom interactions. It focuses on the discursive characteristics and semiotic processes involved in the teaching and learning of square roots in a ninth grade classroom in Japan. The purpose of this study is to characterize the development of mathematical…

Preparation is an effective and necessary activity; however, most students do not prepare for future lessons. The present study addressed this problem and examined how learners' motives, beliefs, and perceptions affected their strategy use during preparation for future lessons. Participants were 219 Japanese junior high school students who…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…