On mathematical understanding: perspectives of experienced Chinese mathematics teachers

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 underst...

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Bibliographic Details
Published in:Journal of mathematics teacher education 2017-02, Vol.20 (1), p.5-29
Main Authors: Cai, Jinfa, Ding, Meixia
Format: Article
Language:English
Subjects:
Cognition & reasoning
Cybernetics
Education
Experienced Teachers
Foreign Countries
Learning Strategies
Mathematical analysis
Mathematical Aptitude
Mathematical Concepts
Mathematics
Mathematics Achievement
Mathematics Education
Mathematics Teachers
Philosophy of Education
Studies
Teacher Attitudes
Teachers
Teaching and Teacher Education
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Summary: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.
ISSN:1386-4416
1573-1820
DOI:10.1007/s10857-015-9325-8