New light on old horizon

Constructing mathematical concepts, underlying abstraction processes, and sense making strategies

Thorsten Scheiner*

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Citations (Scopus)


The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students’ ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical approaches and abstraction-from-objects theoretical approaches. Acknowledging and building on research on knowing and learning processes in mathematics, this article presents a theoretical framework that provides a new perspective on the underlying abstraction processes and a new approach for interpreting individuals’ ways of constructing concepts on the background of their strategies to make sense of a mathematical concept. The view taken here is that the abstraction-from-actions and abstraction-from-objects approaches (although different) are complementary (rather than opposing) frameworks. The article is concerned with the theoretical description of the framework rather than with its use in empirical investigations. This article addresses the need for more advanced theoretical work in research on mathematical learning and knowledge construction.

Original languageEnglish
Pages (from-to)165-183
Number of pages19
JournalEducational Studies in Mathematics
Issue number2
Publication statusPublished - 1 Feb 2016
Externally publishedYes


  • Cognition
  • Learner types
  • Reflective abstraction
  • Reflectural abstraction
  • Sense making strategies
  • Structural abstraction
  • Theory development

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