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An Approach to Facilitate Coherent Concept Image Formation via Guided Reinvention

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Abstract

This chapter presents an approach in mathematical teaching and learning that centers on facilitating student’s coherent concept image formation via guided reinvention. The key to forming a coherent concept image lies in the proper understanding of a particular concept. To do this effectively, instead of passively receiving a mathematical notion from a teacher, students take an active role to re-invent the mathematical notion for themselves. There are three general stages in this approach: (1) motivating; (2) investigative and exploring; and (3) reinventing. Three implementations of such an approach are presented in this chapter: (I) areas of closed figures and their formulas; (II) fractions addition and subtraction with different denominators; and (III) the rigorous definition of the limit of a sequence. Details and philosophy of the implementations will be summarized and discussed.

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, N.T., Hong Kong

    Kell Hiu-Fai Cheng & Siu Cheung Kong

Authors
  1. Kell Hiu-Fai Cheng
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  2. Siu Cheung Kong
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Correspondence to Kell Hiu-Fai Cheng .

Editor information

Editors and Affiliations

  1. Centre for Learning, Teaching and Technology, The Education University of Hong Kong, Tai Po, Hong Kong

    Siu Cheung Kong

  2. Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, Hong Kong

    Tak Lam Wong

  3. Department of Curriculum and Instruction, The Education University of Hong Kong, Tai Po, Hong Kong

    Min Yang

  4. Department of Science and Environmental Studies, The Education University of Hong Kong, Tai Po, Hong Kong

    Cheuk Fai Chow

  5. Department of Chinese Language Studies, The Education University of Hong Kong, Tai Po, Hong Kong

    Ka Ho Tse

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Cheng, K.HF., Kong, S.C. (2017). An Approach to Facilitate Coherent Concept Image Formation via Guided Reinvention. In: Kong, S., Wong, T., Yang, M., Chow, C., Tse, K. (eds) Emerging Practices in Scholarship of Learning and Teaching in a Digital Era. Springer, Singapore. https://doi.org/10.1007/978-981-10-3344-5_15

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  • DOI: https://doi.org/10.1007/978-981-10-3344-5_15

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3342-1

  • Online ISBN: 978-981-10-3344-5

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