# 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.

## Keywords

Mathematical understanding Achieving mathematical understanding Experienced teachers Chinese teachers Perspective of classroom practitioners## Notes

### 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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