Understanding in MathematicsThe concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding. |
Contents
| 1 | |
Components and Conditions of an Act of Understanding | 27 |
Processes of Understanding | 72 |
Good Understanding | 112 |
Developmental and Cultural Contraints of Understanding | 138 |
| 170 | |
| 183 | |
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Common terms and phrases
abstract act of understanding adolescence Ajdukiewicz arithmetic awareness Bachelard basis Bolzano child cognitive communication complexive thinking conceptual thinking concrete construction continuous functions culture curve defined definition domain elements ematics End of example epistemological obstacles equation Ethnomathematics experience explain expressions fact features of objects formal function given Greeno ibidem ical idea identification important integers kind knowledge learning Leibniz linear algebra linear independence linear operators logical math mathematical proofs mathematicians mathematics education meaning mental mental models metaphor metonymies mind notion object of understanding operations philosophers Piaget potential concepts problem process of understanding proof question real numbers reasoning relations representations role scientific sense sequence Sierpinska situation social solving speak statement structure symbolic syncretic synthesis teacher teaching theorem theory things thought tion understanding in mathematics understood variable vector space vectors Vygotski word