, Volume 47, Issue 3, pp 483–496 | Cite as

Developing a network of and for geometric reasoning

  • Ami Mamolo
  • Robyn Ruttenberg-Rozen
  • Walter Whiteley
Original Article


In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known “open box problem”, we sought to enrich learners’ conceptual networks for optimisation and rate of change, and to explore these concepts vertically across curricula for a variety of grades. We analyse a network of physical, geometric spatial visual representations that can support new inferences and key understandings, and that scaffold these advanced concepts so that they could be meaningfully addressed by learners of various ages, from elementary to university, and with diverse mathematical backgrounds.


Input Space Task Design Spatial Reasoning Geometric Reasoning Conceptual Thinking 
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Copyright information

© FIZ Karlsruhe 2014

Authors and Affiliations

  • Ami Mamolo
    • 1
  • Robyn Ruttenberg-Rozen
    • 2
  • Walter Whiteley
    • 2
  1. 1.University of Ontario Institute of TechnologyOshawaCanada
  2. 2.York UniversityTorontoCanada

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