Encyclopedia of Mathematics Education

Living Edition
| Editors: Steve Lerman

Mathematical Representations

  • Gerald A. Goldin
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-77487-9_103-4


As most commonly interpreted in education, mathematical representations are visible or tangible productions – such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, written words, mathematical expressions, formulas and equations, or depictions on the screen of a computer or calculator – that encode, stand for, or embody mathematical ideas or relationships. Such a production is sometimes called an inscription when the intent is to focus on a specific instance without referring, even tacitly, to any interpretation of it. To call something a representation thus includes reference to some meaning or signification it is taken to have. Such representations are called external– i.e., they are external to the individual who produced them and accessible to others for observation, discussion, interpretation, and/or manipulation. Spoken language, interjections, gestures, facial expressions, movements, and postures may sometimes...


Cognitive configurations Concrete embodiments Diagrams External representations Gestures Graphs Imagery Inscriptions Interpretation Internal representations Language Manipulatives Meanings Models Neuroscience Productions Representational systems Semiotics Signification Symbols Symbolization Visualization 
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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Graduate School of EducationRutgers UniversityNew BrunswickUSA

Section editors and affiliations

  • Ruhama Even
    • 1
  1. 1.Department of Science TeachingThe Weizmann Institute of ScienceRehovotIsrael