Research-based guidance and classroom activities for teachers of mathematics

Misconceptions

Misconceptions is a theme within reasoning about uncertainty. Links to relevant activities and resources are on the right hand side of this page. 

The constructivist movement, informed by the work of Piaget, led to the notion that students’ ideas must be challenged in order to promote accommodation through reflective abstraction.

The psychological literature on probabilistic understanding is in fact replete with catalogues of human fallibility, reported as misconceptions. The heuristics (that is to say, intuitive rules-of-thumb) that people of all ages use when making judgements of chance have been catalogued. For example, there is the availability heuristic, by which people make judgements of chance by evoking from long-term memory similar events.

Another example is the representativeness heuristic, in which people expect the actual outcomes to represent closely the perceived sample space. Thus, in Roulette, one might expect the ball to land with regular occurrence on red and black numbers since red and black (ignoring the zero) make up the sample space. We consider how such heuristics might be regarded as starting points for teaching rather than obstacles to be overcome.