# Mathematical Representations

**DOI:**https://doi.org/10.1007/978-3-319-77487-9_103-4

## Definitions

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...

## Keywords

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## References

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