Abstract
The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.
| Original language | English |
|---|---|
| Pages (from-to) | 3743-3756 |
| Number of pages | 14 |
| Journal | Synthese |
| Volume | 197 |
| Issue number | 9 |
| Early online date | 4 Dec 2018 |
| DOIs | |
| Publication status | Published - 1 Sept 2020 |
Keywords
- mathematical cognition
- enculturation
- scaffolding
- algebra
- notations
- diagrams
- Geometry