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On mathematical understanding: perspectives of experienced Chinese mathematics teachers

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Abstract

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers’ views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result of continuous connection making. However, in contrast to the popular view which separates understanding into conceptual and procedural, Chinese teachers prefer to view understanding in terms of concepts and procedures. They place more stress on the process of concept development, which is viewed as a source of students’ failures in transfer. To achieve mathematical understanding, the Chinese teachers emphasize strategies such as reinventing a concept, verbalizing a concept, and using examples and comparisons for analogical reasoning. These findings draw on the perspective of classroom practitioners to inform the long-debated issue of the meaning of mathematical understanding and ways to achieve mathematical understanding.

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Notes

  1. The survey was conducted by the workshop organizers about 3 weeks before the actual workshops. One of the authors conducted the workshops, and these teachers did not know the author. There were 63 Chinese teachers who participated in this workshop. However, two of them were beginning teachers and thus not included in this study.

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Acknowledgments

The research reported in this paper was supported by a grant from the Spencer Foundation and a grant from the University of Delaware’s Center for Global and Area Studies and the Center for the Study of Diversity. Any opinions expressed herein are those of the authors and do not necessarily represent the views of the Spencer Foundation and the University of Delaware. We gratefully acknowledge the feedback and editorial assistance from Stephen Hwang, Margaret Walshaw, and reviewers, which contributed to the paper’s improvement. Of course, any errors remain solely the responsibility of the authors.

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  1. University of Delaware, 523 Ewing Hall, Newark, DE, 19716, USA

    Jinfa Cai

  2. Temple University, Philadelphia, PA, USA

    Meixia Ding

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  1. Jinfa Cai
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  2. Meixia Ding
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Correspondence to Jinfa Cai.

Appendix 1

Appendix 1

See Table 4.

Table 4 Topics involved in Chinese teachers’ given examples and non-examples
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Cai, J., Ding, M. On mathematical understanding: perspectives of experienced Chinese mathematics teachers. J Math Teacher Educ 20, 5–29 (2017). https://doi.org/10.1007/s10857-015-9325-8

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