## Boosting Maths Skills in Deaf Children

Presented on 24 April 2008

## Improving deaf children's counting and understanding of additive composition

The RNID Project
Department of Educational Studies, University of Oxford

Aims of our teaching study

• To test whether there are differences between deaf and hearing children when they start school.
• To identify the best methods to help the deaf children catch up if they are underperforming for their level of intelligence.
• To help them understand the logic of the counting system in order to count better and to use counting more efficiently.
• Additive composition: any number can be the sum of other numbers – to realise that 13 is the sum of 10 plus 3.

Design of the teaching studies

• Pre-test
• Two sessions of teaching
• Immediate post-test
• Delayed post-test (about 2 weeks later)

Design of Study

• Two groups
• One group received teaching on the logic of the counting system
• One group received teaching on the inverse relation between addition and subtraction
• Each group works as a comparison group for the other type of teaching because both work on mathematics tasks with an experimenter on a one-to-one basis

Participants

28 deaf children (mean age 6y1m) from 6 schools (2 schools for the deaf) and 40 hearing children from 2 schools.

When is learning to count easiest?

Regular and irregular counting systems

Learning to count in Japanese

• Some learning of the counting system is based on memory.
• Most of the learning must be based on understanding.
• What understanding of the counting system do deaf and hearing children show?

Deaf children are doing worse than expected from their intelligence.

The intervention
We observed how deaf and hearing children discover the idea of additive composition.

How can we help them understand the system?

Different types of knowledge needed

One 2p coin is the same as two 1p coin
- work with exchanges
- work with comparisons

Ladybird 2p spot game for two players

You will need:

A die
30 x 1p coins
16 x 2p coins

To play:
1. Children decide which ladybird they are going to try to fill with 2ps
2. First child throws die.
3. Child collects from central pile of 1ps the corresponding number of coins to that on the die and puts them on her 'waiting area' on board.
4. Second child throws die and does the same.
5. From now on, when a child has 2 x 1p they can exchange it for a 2p coin which they put on a 2p spot on their designated side of the ladybird.
6. Their target is to fill the 2p spots on their ladybird by exchanging the 1ps for 2ps.

Put out 1 x 2p and 2 x 1p coins

Point to the purse on the left and ask the child 'How much is in this purse?'
Ask them to show with fingers how much is there.

If not sure, look on the coins for the number '1' and say 'Look, here is 1p' and hold up 1 finger, 'and here is 1p' holding up another finger.
'How much is there altogether in the purse?'

Then point to the purse on the right and say 'How much is in this purse?' Ask the child to show with their fingers how much is there.
If they are unsure, ask them to look on the coin for the '2' and get them to hold up the correct number of fingers.

'So, how much was in the 1st purse?
How much is in the second purse?
Does one purse have more money in than the other purse or not?' (BSL: Are they the same or different?)

If child incorrect, repeat with number of fingers held up for each purse and get them to compare the 2 fingers on one hand and the two on the other.

'So, there is 2p in this purse, and 2p in that purse, but one has a 2p and the other has 2 x 1ps, but it is the same amount in each.'

Composing amounts

• Encourage the children who cannot do this to show 2p on their fingers then go on to count 1p
• With practice, the children count on – this is the aim of the addition task
• These tasks become more difficult – involving more coins and larger values (5p, 10p, 20p)

Butterfly 5p game for 2 players.

You will need:
8 x 5p coins
30 x 1p coins
Die or number cards 1 – 6

To play:
1. Put 5p coins and 1p coins on table as the 'bank'.
2. Ask child to choose which butterfly they want to fill.
3. Then with a second child or with teacher taking the other butterfly, start the game.
4. Roll the die and child collects the number of 1ps according to number they have thrown on their 'waiting area' on the board.
5. They collect the 1ps until they have enough 1ps to exchange with the bank for a 5p coin which they then place on a 5p spot on the butterfly.
6. Game continues with player 1 and 2 taking turns until the winner has completed 4 exchanges of 1p's for 5p and all 5p spots are covered on their butterfly.

Have available 1 x 10p, 3 x 5p, 4 x 1p, 1 x 2p

Say to the child:
'Joe has emptied his piggy bank and has found this much money inside (pointing to the 1 x 10p, 1 x 5p, 1 x 1p). Can you get out the same coins and then see how much money he has?
Can you write the amount in the box underneath?'

'Hannah has emptied her piggy bank and found this much money inside (pointing to the 3 x 1p, 1 x 2p, 2 x 5p). Can you get out the same coins and then see how much money she has?
Can you write the amount in the box underneath?'

If they are stuck, ask the child to start with the largest coin (5p or 10p) and count on either with 5p, 2p or with 1ps. Ask them to show the amounts with their fingers.

Ask them to tick which child has more money. (BSL: Who has biggest money?)

Find different ways of making 20 p
1 x 20p, 3 x 10p, 6 x 5p, 10 x 2p, 20 x 1p

The 20p challenge game

Put the following coins on the table and give child a copy of the base board. (1 x 20p, 3 x 10p, 6 x 5p, 10 x 2p, 20 x 1p)

Give them the challenge: 'Can you find 2 different ways of making 20p using only these coins on the table?'

Ask them to lay the coins on top of a bag and count on from the largest coin they have chosen as they do it.

'Now can you find a different way?' ask the child to leave the coins on top of each bag so that they do not use the same coins each time.

See if the child is able to find 5 different ways of making 20p, each time getting them to count on where appropriate. Discuss with them the fact that the same total can be made using different coins, that the totals are equivalent even though the coins used are different.

Have available on table 1 x 20p, 2 x 10p, 4 x 5p, 5 x 1p

Say to the child: 'Max wants to buy his favourite comic which costs 37p.
Which would be the least number of coins you could use to pay the shopkeeper?' (BSL: Small number of coins?)
If the child is stuck, ask them to identify the largest value coin(20p, or they may choose 2 x 10p to make 20) and then count on with the smaller coins.

If the child chooses 2 x 10p you might ask them about the comparison with 20p coin , same value but different coins, to see if they are seeing the equivalence.
Ask the child to cross with a coloured pencil which coins they chose to make the 37p.

Have available the following coins on table: 1 x 50p, 1 x 5p, 1 x 10p, 2 x 2p, 3 x 1p

Say to the child: 'Jeevan needs to buy a stamp to send a letter to his pen-friend in Australia.
The stamp will cost him 57p from the machine. He needs to put the exact money into the machine, which coins should he choose?'

If the child is stuck, get them to identify the largest value coin, then to count on to the amount they need with their fingers, relating this to the coins available.

'Tick the coins you choose with a coloured pencil.'

Analysis of the effects of the intervention

• All the analyses will control for the pre-test differences
• The results are presented on a scale that varies from -3 (worse than expected) to + 3 (better than expected); 0 is exactly what was expected if there are no group differences

Deaf children: results controlling for pre-test, age and BAS differences

Conclusions

• It is possible to improve deaf children's understanding of how the counting system works.
• It is expected that this will help them progress further in learning the counting system.
• Deaf children have difficulties with the logic of inversion and of additive composition when they start school.
• They can improve in their understanding through teaching that uses their visual skills.