Teaching for abstraction: A model

Paul White*, Michael C. Mitchelmore

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)


    This article outlines a theoretical model for teaching elementary mathematical concepts that we have developed over the past 10 years. We begin with general ideas about the abstraction process and differentiate between abstract-general and abstract-apart concepts. A 4-phase model of teaching, called Teaching for Abstraction, is then proposed that is explicitly designed to promote abstract-general learning. Studies investigating the model with 4 different topics (angles, decimals, percentages, and ratios) are reported, and the 4 phases are further elucidated. The article concludes with a discussion of the effectiveness of the model and its applicability to other mathematical concepts.

    Original languageEnglish
    Pages (from-to)205-226
    Number of pages22
    JournalMathematical Thinking and Learning
    Issue number3
    Publication statusPublished - Jul 2010


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