Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework

Martin A. Simon, Melike Kara, Nicora Placa, Arnon Avitzur

Research output: Contribution to journalArticle

Abstract

We discuss the theoretical framework of the Learning Through Activity research program. The framework includes an elaboration of the construct of mathematical concept, an elaboration of Piaget's reflective abstraction for the purpose of mathematics pedagogy, further development of a distinction between two stages of conceptual learning, and a typology of different reverse concepts. The framework also involves instructional design principles built on those constructs, including steps for the design of task sequences, development of guided reinvention, and ways of promoting reversibility of concepts. This article represents both a synthesis of prior work and additions to it.

Original languageEnglish (US)
Pages (from-to)95-112
Number of pages18
JournalJournal of Mathematical Behavior
Volume52
DOIs
StatePublished - Dec 2018

Keywords

  • Guided reinvention
  • Learning trajectory
  • Mathematical concept
  • Reflective abstraction
  • Reversibility
  • Task design

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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