Children's understanding of probability: an intervention study

This project examined the most effective ways to teach children about probability. This is an important concept in education and daily life but can be difficult for both children and adults to understand. It followed two previous Nuffield-funded reviews by the same researchers, Key Understandings in Mathematics Learning, and a literature review of research on children’s understanding of probability

Learning about probability makes four kinds of demand on children’s cognitive skills:

  1. To understand the nature of randomness.
  2. To be able to work out all the possible events in the context of the problem.
  3. To reason proportionally in order to calculate the probability of particular events.
  4. To understand correlations, which are crucial for understanding risk.

Psychological research has provided evidence about how children can learn and can be taught to satisfy each of these demands. This project - a randomised controlled trial - assessed the effectiveness of applying this evidence to the teaching of probability to nine- and ten-year-old children. In the first phase of the project, children were allocated to three groups: those who received the probability intervention, those who had no intervention (passive control), and an active control group which received a (non-probabilistic) quantitative reasoning intervention. The researchers also worked closely with teachers using the materials with whole classes.

The researchers also conducted a small supplementary project to examine the effectiveness of teaching children about quantitative reasoning. Primary school children typically have difficulty with problems where they must operate on relations without knowing the quantities (e.g. "Kate, Donna, and Jamie have together 22 stickers. Donna has 3 stickers more than Kate and Jamie has 4 more than Kate. How many stickers does each have?"). They also find it difficult to identify and represent relations numerically, when the relations are not stated. For example, in the problem "I use 4 spoons of flour and 6 of milk to make 4 pancakes; how much flour and milk should I use for 10 pancakes?" the relations between quantities are not described, only the quantities.

Project details



Professor Terezinha Nunes, Professor Peter Bryant, Ms Deborah Evans, University of Oxford

Grant amount and duration:


1 May 2011 – 31 March 2015

Publications and presentations


Teaching mathematical reasoning: Probability and Problem solving in Primary School (2015). 

Children's understanding of probability: a literature review,
Peter Bryant and Terezinha Nunes, July 2012

Summary report

Full report

Presentations made at Nuffield Foundation seminar on 5th July 2012:

Literature review - Presentation by Peter Bryant

Intervention study - Presentation by Terezinha Nunes

Other presentations

Presentation at a DfE seminar on 14th November 2012