Abstract
Reflecting on the learning process of topologist Stephen Smale, certain properties and characteristics of that process are selected and analysed: the question and anticipation of future mathematics, the generalising potential thereof, and the shift from after-image or 'model of ...' to pre-image or 'model for ...'. These features are explored for the benefit of the design of learning-teaching sequences in mathematics education, and are illustrated in a variety of examples.
| Original language | English |
|---|---|
| Pages (from-to) | 37-62 |
| Number of pages | 26 |
| Journal | Educational Studies in Mathematics |
| Volume | 54 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2003 |
Keywords
- Equations
- Estimation
- Formulas
- Fractions
- Graphs
- Mathematicians' and students' learning processes
- Mathematization
- Measurement
- Models of and models for
- Number
- Ratio and scale
- Sine functions