Research-based guidance and classroom activities for teachers of mathematics

Intuitions

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

It has been suggested that the emphasis of the school curriculum on causality at the expense of the stochastic, has resulted in a failure to nurture young children's intuition of relative frequencies. 

Research has tried to respond to this challenge, especially in the light of opportunities offered by digital technology. For example, it has been reported that young students may have expert-like perceptions of randomness as unpredictable, uncontrollable and irregular, but may not recognize the limitations of these perceptions to the short-term. Similarly they may not recognize that even unfair situations might be random.

When such naïve conceptions are over-generalized, the pedagogic challenge is to introduce the student to the limitations of the idea, rather than to seek to eradicate the conception. On the other hand, students may not appreciate the power of their idea. For the student, it is perhaps surprising when the proportion of sixes on the die is equal to the proportion of each of the other numbers, but for him or her this may be a generalization about dice.

The pedagogic challenge is to seek to introduce the student to the power of the naïve conception, so that the result about the die has its equivalent result for coins, spinners and many other contexts, until eventually it can be seen by the student as general, the Law of Large Numbers.