Classifying shapes

Technical terms in geometry - part 2

This awareness of various ways of classifying numbers contributes to a greater confidence with number. The same is true of shapes. Just as with numbers, we might recognize an attribute common to certain shapes (such as having three sides), form them into a category, give the set a name (for example, the set of triangles) and then, if necessary, make the classification more explicit with a precise definition. This process of classifying and naming leads to a greater confidence in handling shapes and a better awareness of the shapes that make up the world around us.

So, to participate in this important process of classification of shapes, we need first a whole batch of mathematical ideas related to the significant properties of shapes that are used to put them into various categories. This will include, for example, reference to whether the edges of the shape are straight, the number of sides and angles, whether angles are equal or right-angled, and whether sides are equal in length or parallel. Second, we need to know the various terms used to name the sets, supported where necessary by a definition.

My experience is that many primary teachers and trainee-teachers have a degree of uncertainty about some of these terms that undermines their confidence in teaching mathematics. For their sake the following material is provided for reference purposes.

Remember

The role of a definition in teaching and learning is not to enable pupils to formulate a concept, but to sharpen it up once the concept has been formed informally through experience and discussion, and to deal with doubtful cases.