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Learning to teach mathematics through problem posing: teachers’ beliefs and performance on problem posing

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Abstract

Any effort to integrate problem-posing instruction in school mathematics must attend to teachers’ beliefs about the advantages of teaching through problem posing and especially their beliefs about the challenges of teaching in this way. This study investigated teachers who were learning how to teach mathematics through problem posing. The primary foci were the teachers’ beliefs about teaching through problem posing and their problem-posing performance. The findings demonstrate that the participating teachers were able to engage successfully in problem-posing tasks and that they held a number of different beliefs about the advantages and challenges of teaching through problem posing. After participating in three workshops, a sample of teachers showed gains in problem-posing performance and in the scope and specificity of their beliefs about teaching through problem posing.

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Notes

  1. The six steps in a typical solution to this problem are: (1) calculate Shasha’s driving distance, (2) calculate Jiajia’s driving distance, (3) calculate Xiaobing and Shasha’s driving distance, (4) calculate the total driving distance, (5) calculate the difference between the distance driving by Xiaobing and Jiajia, and (6) calculate the ratio.

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Authors and Affiliations

  1. Southwest University, Chongqing, China

    Xinlian Li & Naiqing Song

  2. University of Delaware, Newark, DE, 19716, USA

    Stephen Hwang & Jinfa Cai

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  1. Xinlian Li
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  2. Naiqing Song
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  4. Jinfa Cai
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Correspondence to Jinfa Cai.

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APPENDIX

APPENDIX

Table 6 Teachers’ beliefs about the advantages of teaching through problem posing after the first and third workshops
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Table 7 Teachers’ beliefs about the challenges of teaching through problem posing after the first and third workshops
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Li, X., Song, N., Hwang, S. et al. Learning to teach mathematics through problem posing: teachers’ beliefs and performance on problem posing. Educ Stud Math 105, 325–347 (2020). https://doi.org/10.1007/s10649-020-09981-0

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