# Children's understanding of probability: an intervention study

This project will examine 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 follows 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:

- To understand the nature of randomness.
- To be able to work out all the possible events in the context of the problem.
- To reason proportionally in order to calculate the probability of particular events.
- 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 - will assess 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 are also working closely with teachers who are using the materials with whole classes.

The researchers will also conduct 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.

**Researchers:**

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

**Funding programme:**

**Grant amount and duration:**

£232,986

1^{ }May 2011 – 31 October 2013

*Children's understanding of probability: a literature review*,

**Peter Bryant and Terezinha Nunes, July 2012**

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

**Literature review - Presentation by Peter Bryant**

**Intervention study - Presentation by Terezinha Nunes**

**Other presentations**

## See also

- Strategies for preparing pupils for Key Stage 2 maths tests
- School-university partnerships to support mathematics teachers
- When to teach what? Sensitive learning periods and adolescence
- Employment trajectories of STEM graduates
- Rethinking the Value of A Level Mathematics Participation
- Measuring conceptual understanding in mathematics
- Understanding mathematics anxiety