Reasoning and Proof in Algebra: The Case of Three Reform-Oriented Textbooks in China

Examining the narratives of algebra content of three popular series of mathematics textbooks in China, this study explored the opportunities for students to learn about reasoning and proof (RP). In this study, we incorporated Davis’s subdivision of conjecture into Stylianides’s framework. Based on this, we analysed the components of RP (patterns, conjectures, proofs and non-proof arguments), as well as the purposes of each component respectively. The results show that the proportion of RP tasks was less than 40% and there was no significant statistical difference in the number of RP components by grade among the three series of textbooks. On the other hand, across topic levels, there was a significant statistical difference in RP tasks. Furthermore, there were only a few opportunities for developing conjecture precursors and proof precursors. Based on them, we discussed the arrangement and features of Chinese textbooks to explain these differences.