Encyclopedia of Mathematics Education

Living Edition
| Editors: Steve Lerman

Visualization and Learning in Mathematics Education

  • Norma PresmegEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-77487-9_161-4

Definitions and Background

Visualization in mathematics learning is not new. Because mathematics involves the use of signs such as symbols and diagrams to represent abstract notions, there is a spatial aspect involved, that is, visualization is implicated in its representation. However, in contrast with the millennia in which mathematics has existed as a discipline, research on the use of visual thinking in learning mathematics is relatively new. Such research has been growing in volume and depth since the 1970s, initiated by Bishop (1973, 1980) and later Clements (1981, 1982), who investigated preferences of individual learners with regard to visualization in mathematics and how spatial abilities interacted with these preferences. Visualization has internal and external forms (Goldin 1992), which may be designated as visual mental imagery and inscriptions, respectively (Presmeg 2006). Presmeg defined a visual image as a mental sign depicting visual or spatial information and...


Signs Symbols Diagrams Spatial aspect Representation Preferences of individual learners Spatial abilities Visual mental imagery Inscriptions Visual image Ana-vis scale Logic Strength of mathematical processing Type Verbal-logical Visual-pictorial Analytic geometric and harmonic types Reluctance to visualize Pedagogy Abstraction Generalization One-case concreteness Prototype Uncontrollable image Compartmentalization Dynamic imagery Pattern imagery Metaphor Mnemonic advantages Interactive dynamic geometry software Gestures Conversion processes Registers Connections Idiosyncratic visual imagery Reification Computer technology Overarching theory of visualization 
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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsIllinois State UniversityMaryvilleUSA

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA