There are many ways of going about concept formation.  Sometimes students need a clear understanding of an abstraction and we use a Frayer model.  But at other times we are exploring concepts that have inherent properties we can readily detect by grouping.

A great example of this comes from Lucy Twigger’s mathematics classroom.  For her Grade 9 she wanted students to identify types of decimal, and understand what kinds of fractions produce them, in order to support students in being able to move between the two forms of the number, and form generalisations about which types of fractions produce which type of decimals.  This requires that students identify what kinds of decimals exist.

She asked students to use integers to ten to make fractions, then produce decimals from these fractions and group them.

Students rapidly started creating their own, but completely meaningful conceptual categories for decimals  such as ‘terminating’, ‘recurring’, ‘non-terminating, not recurring’, etc.  This kind of grouping provides a powerful concept formation activity, and can be used with any examples whose attributes are clearly and distinctly identifiable (types of animal, energy sources, literary genres etc would work equally well).  The strategy is called ‘Open Sorting’.  One of the boards the students produced is below.