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Topic: Children's understanding of probability - Report Available
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Jerry P. Becker

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Registered: 12/3/04
Children's understanding of probability - Report Available
Posted: Aug 16, 2012 1:11 PM
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The Nuffield Foundation (England) just launched a report that written
by Terezinha Nunes and Peter Bryant about children's understanding
of probability. It is a review of research with a broad coverage of
children's understanding and does not focus on teaching. The link to
the review is:
Information provided by Terezinha Nunes.
Children's understanding of probability

The Foundation has published Children's Understanding of Probability,
a literature review by Professors Peter Bryant and Terezinha Nunes
from the University of Oxford.

In this review, the authors identify four 'cognitive demands' made on
children when learning about probability, and examine evidence in
each of these areas: randomness, the sample space, comparing and
quantifying probabilities, and correlations.

They draw together international evidence, from the early years
through to adulthood, and highlight studies that are of particular
relevance to teaching. They also identify areas that have been
relatively neglected and would benefit from further research,
particularly from fully evaluated intervention projects.


Research using computer microworlds has shown that by the age of
about ten, many children realise that there is an association between
randomness and fairness, and that randomisation can be an effective
way of ensuring fair allocations.

Both children and adults find it particularly difficult to understand
the independence of successive events in a random situation. When
tossing a coin for example, people often predict that a run of heads
makes it more likely that the next toss will be tails (the 'negative
recency' effect), or that the previous run of heads makes it more
likely that heads will be the next result too (the 'positive recency'

Sample space

Children can have particular difficulty with problems where some
outcomes are equiprobable and others are not. For example, in
throwing two dice at the same time, there are 36 possible
equiprobable outcomes (1,1; 1,2; 1,3 etc.). But, if you record the
result in terms of the sum of the two numbers thrown, there are only
11 possible outcomes and they are not equiprobable.

Understanding the sample space means children have to construct an
exhaustive list of alternative, and uncertain, possibilities, but
there is currently no research on their ability to do this.

Quantifying probability

Children understand proportions as ratios before they understand them
as fractions, suggesting that children would learn about
probabilities more easily if they are initially introduced as ratios.

Children and adults are much more likely to work out conditional
probabilities correctly if the basic information is given as absolute
numbers rather than as decimal fractions.


Correlational thinking depends on children realising that the way to
work out whether an association is random or not is to consider the
relative amount of confirming and disconfirming evidence. When they
use simple intuitive reasoning they often fall prey to a confirmation
bias; they pay more attention to the confirming than to the
disconfirming evidence.

Recommendations for further research

The authors make two main recommendations in relation to further
research. Firstly that researchers should take advantage of research
designs that have been successful in research on other aspects of
children's intellectual development. In particular, the combined use
of intervention and longitudinal methods to study the links between
the four aspects of probability.

Secondly, they recommend that more attention is paid to the great
amount of related data that exists on other aspects of cognitive
development. Probability makes a number of different cognitive
demands and most of these demands are shared with other aspects of
cognitive development about which we know a great deal. Probability
is an intensive quantity, but so are density and temperature for
example. Many people doing research on probability have not paid
attention to research on these related topics, and have missed out on
potentially valuable information.

Intervention study

The Foundation is now funding the authors to undertake a large-scale
controlled intervention study of the teaching of probability to
9-to-10-year-olds [2].

See also at http://www.nuffieldfoundation.org/print/3626

Download Children's understanding of probability from the website

Summary report [3]

Full report [4]

Similar projects

Probability intervention study >> [2]

Mathematics education >> [5]

Source URL:

[1] http://www.nuffieldfoundation.org/news
[5] http://www.nuffieldfoundation.org/mathematics-education-0

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244
E-mail: jbecker@siu.edu

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