University of Edinburgh

Boosting Maths Skills in Deaf Children

Presented on 24 April 2008

Deaf children's informal knowledge of multiplicative reasoning

Terezinha Nunes, Peter Bryant, Diana Burman, Daniel Bell, Deborah Evans, Darcy Hallett
Department of Education, University of Oxford
Support: RNID

What is multiplicative reasoning?

Multiplicative reasoning is not the same thing as additive reasoning:
- Additive reasoning is about putting together or separating things of the same type.
- Multiplicative reasoning is about (at least) two variables in a fixed correspondence (ratio) to one another.

The importance of multiplicative reasoning

Two contexts in which multiplicative reasoning is used illustrate its importance:
- Counting complex units and place-value: in 23, the digit '2' is implicitly multiplied by 10.


- In problem solving: different types of situation that involve ratio (these prepare children for understanding proportions).

The origin of multiplicative reasoning

  • Young children can solve multiplicative reasoning problems using the scheme of action of correspondences before they are taught about multiplication in school.
  • Some can use this scheme more flexibly than others but most 6-year-olds can solve some multiplication problems.

The importance of multiplicative reasoning

Both types of task predict hearing children's mathematics achievement in school 14 months later after controlling for:

  • Age
  • Cognitive ability
  • Knowledge of numbers at school entry
  • Working memory.

Interventions with hearing children at risk for mathematics learning significantly improved their mathematics achievement (Nunes et al, 2007)

Deaf children's use of correspondence

Aim: to assess whether deaf children perform in correspondence problems as expected from their level of cognitive ability

28 deaf children; mean age 6y5m; SD=0.7 years (grades 1 and 2)
78 hearing children; mean age 6y2m; SD=0.3 years (grade 1)


British Abilities Scale – matrices sub-test

Correspondence problems

  • 6 presented with simultaneous information
  • 6 presented with successive information


Child's preferred in school (all schools use total communication); researchers passed BSL Level 2


British Abilities Scale: hearing children out-performed deaf children

Correspondence problems

  • No significant difference between simultaneous and successive and no interaction with hearing status
  • Hearing children out-performed deaf children

Scores in correspondence problems at the beginning of the year

Results of 79 hearing and 26 deaf children in the same age range.
The difference is significant even after controlling for differences in BAS Matrices scores. F=47.9; p<.0001).


Deaf children could profit from instruction on the use of correspondences to solve problems.

Aims of our teaching study

  • To test whether an effective method for improving hearing children’s use of correspondences could be adapted for deaf children.
  • To see whether they can catch up with hearing children in the same grade level in the use of correspondences to solve multiplicative reasoning problems.


  • 27 deaf children from 6 schools (7 schools for the deaf and mainstream schools with units); mean age=6y6m; SD=0.66 years
    - 12 profoundly deaf; 8 had CI; no documented learning disability
  • 33 hearing children (2 schools); mean age=5y7m; SD=0.31 years

Design of the teaching study

  • 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 correspondence and sharing
  • One group received teaching on visual analysis
  • Each group works as a comparison group for the other type of teaching because both work on reasoning tasks with an experimenter on a one-to-one basis.


  • British Abilities Scale – matrices subtest
  • Correspondence problems

Teaching Tasks

  • A series of tasks graded in difficulty was created
  • The tasks were presented with the help of materials
  • When the children did not immediately solve the problem, we prompted them
  • 20 problems were used in the intervention; two sessions on subsequent school days

Item 1

Materials needed:
3 Cut out lorries and a pile of unifix blocks (all of one colour)

The teacher is organising a party. Three lorries will bring tables to the school. Each lorry will carry 4 tables. How many tables did the teacher order?

lorry game

1. Cut out lorries and bricks to be the make-believe tables.
Three lorries were bringing tables to the school. Inside each lorry there are 4 tables. How many tables are they bringing to the school? (The children can make the row of lorries and put the bricks on top to try to solve this).

Materials needed:

Pile of cut out plates and pile of same colour unifix blocks
The teacher is putting biscuits on plates for the children. There are 8 children in her group. Each one is going to get 2 biscuits. How many biscuits does she need? (if child doesn’t take the right number of plates, T helps)

A teacher is putting biscuits on the plates for the children. There are 8 children in her group. Each one is going to get 2 biscuits. How many biscuits does she need?

Materials needed:

12 Cut out balloons

A boy was going to have a party. He had 12 balloons. He wants to give 2 balloons to each friend that comes to the party. How many friends can he invite?


This is hard because each group of balloons will mean that you can invite one boy. If the children cannot solve the problem just with the cut-out balloons, suggest that they use something to represent the boys.

Item 20

Materials needed:
Pile of same colour unifix blocks

The mayor of this city went to visit the children in a school. She brought 20 story books with her for the classes in Year 1. There are 5 year 1 classes. How many books can she give to each class?

Results – pre-test


There were no significant differences between the deaf and hearing children in the British Abilities Scale and the Multiplicative Reasoning Problems (the hearing children are younger and matched for cognitive ability). No differences between control and intervention groups.

Results – immediate post-test

post test

The intervention group made significantly more progress than the control group at the immediate post-test (F=10.65; p=.004)

The deaf children did not differ from the hearing children in the intervention group.


At the delayed post-test the difference between the taught and the control group was not significant.

The hearing children out-performed the deaf children.


  • The intervention was effective in improving the deaf children's use of correspondence and sharing to solve problems.
  • Their performance was lower (though not significantly so) at delayed post test.
  • Perhaps it is necessary to increase the amount of teaching for the gains to remain at delayed post-test.
  • The next step in this programme of research is to assess the effects of interventions on the children’s mathematics achievement.