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

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Abstract

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.

Résume

Par l’examen des discours reflétant l’algèbre contenue dans trois collections populaires de manuels scolaires en Chine, cette étude traite des possibilités offertes aux élèves pour s’instruire sur le raisonnement et la preuve (RP). Dans la présente analyse, nous avons incorporé la subdivision de la conjecture de Davis dans le cadre de Stylianides. En fonction de ceci, nous avons analysé les composantes du RP (les motifs, les conjectures, les preuves et les arguments non probants) ainsi que les fins pour lesquelles ces composantes existent respectivement. Les résultats indiquent que la proportion des tâches de RP se situe sous la barre des 40% et qu’il n’y a aucune différence statistiquement significative selon le niveau scolaire en ce qui a trait au nombre de composantes de RP parmi les trois collections de manuels. Une différence statistiquement significative s’est cependant révélée dans les tâches de RP pour toute la gamme de sujets abordés. De plus, il n’y a eu que quelques occasions pour développer des précurseurs de conjectures et de preuves. Compte tenu de cet état de choses, nous avons traité de l’organisation et des caractéristiques des manuels scolaires chinois dans le but d’expliquer ces différences.

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  1. Faculty of Education, Beijing Normal University, XinJieKouWai St. Haidian District, No. 19, Beijing, 100875, China

    Yu Fu, Chunxia Qi & Jiayao Wang

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  1. Yu Fu
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Correspondence to Chunxia Qi.

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Fu, Y., Qi, C. & Wang, J. Reasoning and Proof in Algebra: The Case of Three Reform-Oriented Textbooks in China. Can. J. Sci. Math. Techn. Educ. 22, 130–149 (2022). https://doi.org/10.1007/s42330-022-00199-1

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