Journal of Mathematics Teacher Education

, Volume 20, Issue 1, pp 5–29

On mathematical understanding: perspectives of experienced Chinese mathematics teachers

Article

DOI: 10.1007/s10857-015-9325-8

Cite this article as:
Cai, J. & Ding, M. J Math Teacher Educ (2017) 20: 5. doi:10.1007/s10857-015-9325-8

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 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of DelawareNewarkUSA
  2. 2.Temple UniversityPhiladelphiaUSA