Abstract
Mathematically, most theorems can be seen as classifying those mathematical objects which satisfy certain properties, in terms of other, usually more manageable, properties. Thus Pythagoras’ theorem classifies right-angled triangles as those triangles for which the sum of the squares on two sides is the square on the third, while the law of cosines defines a property which holds for all triangles. Whenever a method is devised for solving a particular problem, there is an immediate challenge (and value) to classify all those problems which succumb to the same method. This is a fundamental process in mathematics, and a key aspect of learning mathematics in order to appreciate each technique and the concepts on which it draws. Classifying and characterising are natural powers which children display long before they get to school. They are also a core component of mathematical pedagogy. For mathematical thinking, it is important that learners are provoked to use their own powers to classify and characterise so that these are developed explicitly throughout their mathematical schooling, which means teachers being aware of and drawing attention to their use, whether actual or potential. This chapter elaborates on these claims.
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Mason, J. (2011). Classifying and Characterising: Provoking Awareness of the Use of a Natural Power in Mathematics and in Mathematical Pedagogy. In: Zaslavsky, O., Sullivan, P. (eds) Constructing Knowledge for Teaching Secondary Mathematics. Mathematics Teacher Education, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09812-8_3
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