Using cognitive conflict to promote precision of definitions

Students' understanding of mathematical terms may be restricted to iconic (i.e., typical) representations.

For example, students may understand a rectangle to be a shape where one pair of sides is clearly longer than the other pair, although the mathematical definition of a rectangle does not involve mention of side lengths.

It is important that students' understanding is broadened to identify non-iconic representations (e.g. a square is a special case of a rectangle, even though students might initially think of a square as being different to a rectangle).

Sometimes one class of things (e.g. squares) is a subset of another class of things (e.g. rectangles), and students need help to recognise when this occurs.

Understanding this strategy

In this strategy, the teacher promotes "cognitive conflict" by having students predict which of the shapes drawn by the teacher matches their expectations (i.e., the shape they have already drawn).

The strategy below continues with the example of understanding rectangles.

Examples of using this strategy in the classroom

Teacher asks the class to draw a shape (e.g. a rectangle), expecting that many students will draw an iconic shape (e.g. rectangle with one pair of sides clearly longer than the other pair). 

Teacher draws several shapes on the board, including:

  • (correct) iconic shape (in usual orientation) (A below)
  • (correct) iconic shape (after it has been rotated) (B and C below)
  • (correct) non-iconic shape (e.g. square) (E below)
  • some incorrect shapes (D and F below)

Students discuss and decide which of the teacher's drawings are correct and which are not by reference to a source (e.g. using an online mathematics dictionary). 

Cognitive conflict occurs when students are presented with examples which cause them to question their incomplete understanding of a rectangle.

Shapes used in the above example
Shapes used in the above example

Curriculum link for the above example: VCMMG293.