## The issue

Many young hearing children start school with an impressive amount of mathematical knowledge. They can place sets in correspondence – for example, dolls and candies – to make sure that each doll gets a piece of candy. Many can share items fairly, which is another correspondence task. They can even share items fairly if the recipients are not in sight – for example, if they see two rabbits going into each of three houses, they can put out two pieces of food in front of each house so that there is one piece for each rabbit. These are examples of thinking in action; the children do not need to say anything, but do have to understand about correspondences. Other examples of thinking in action involve understanding the relation between addition and subtraction: knowing that if you add some blocks to a set and take away the same number, the number in the set remains the same. The mathematical knowledge assessed by such tasks is a reliable predictor of how well children learn mathematics later in school.

Entering school, many more deaf and hard-of-hearing than hearing children show difficulties with such tasks. Adults may want children to learn to count to a high number before they engage in such mathematical reasoning tasks. Perhaps they believe that children need to learn the language of numbers to think about quantities. In fact, research about children’s mathematical reasoning shows that development works the other way around: children first learn to think in action; this reasoning forms the basis for understanding numbers, beyond learning to count.

## What we know

Psychologists disagree on many issues, but they agree that thinking starts before language. Toddlers solve problems in action: For example, if they want something which is out of reach on a table, they pull the table cloth. They use the tablecloth as a tool but could not put this in words. Toddlers also imitate actions that produce an outcome they want: For example, they take a key and try to open the door when they want to go out because they saw their parents doing this.

Young children succeed more in solving problems when all the relevant information is in sight at the same time. This is true of all children, but even more so of deaf children.

The figure below shows examples of activities we have used with 4- to 7-year olds to motivate their thinking in action. Series A shows a “tell me how many bricks now” game: A row of 6 red bricks is hidden under a cloth after the child counts them; 5 black bricks are added; then 5 black bricks are taken away; the children are asked how many bricks are in the row now. Most children realize that there are still 6 bricks. Series B builds on this reasoning. A mixture of series A and B questions builds up the child’s understanding of the relation between addition and subtraction.

Series C shows activities that require children to work with correspondences. They see two rabbits being put behind each of the houses. One pair of rabbits stays outside as a reminder of the number. The children need to get the right number of food pellets so that there is one for each rabbit. Section D shows drawings by slightly older children, when a similar problem was presented on paper and we asked for the solutions in drawing.

Pictures can be used to present information visually; the children can answer in action. Sections E and F show examples of activities that draw on children’s observation of visual patterns and on their thinking in action.

These examples were taken from our research with deaf and hard-of-hearing children. They were part of a program that used teaching through demonstration and problem solving in action. It promoted their mathematical achievement beyond that of children who did not participate in the program.

## What we don’t know

We don’t know how long lasting the effects of early interventions are. Our studies were short-term studies, confined to mathematical outcomes within the same year in which the teaching took place.

## Implications

The development of programs to promote deaf and hard-of-hearing children’s learning through observation, imitation, and thinking in action does not depend on expensive resources. Although there isn’t yet a full program for parents and teachers to use, there are many examples of activities that can promote children’s thinking in action, providing a basis for successful mathematics learning.

Posted on Oct 6, 2016 by

Terezinha Nunes

University of Oxford

terezinha.nunes {at} education.ox.ac.uk

## Further reading