University of Edinburgh

Boosting Maths Skills in Deaf Children

Presented on 24 April 2008

Deaf children's understanding of the inverse relation between addition and subtraction

Terezinha Nunes, Peter Bryant, Diana Burman, Daniel Bell, Deborah Evans, Darcy Hallett and Laura Montgomerry Department of Educational Studies University of Oxford
Support: RNID

The development of the understanding of the inverse relation

Putting something on and taking it off.

Identity trials

identity trials

Inversion trials

inversion trials

  • Bryant et al (1999) showed that identity trials are significantly easier for children aged 5 and 6 years
  • They also showed that if the number added or taken away was not exactly the same in inversion trials, the problem became even more difficult.

The connection between children's logic and mathematics learning

  • Hearing children's understanding of the inverse relation between addition and subtraction predicts their mathematics achievement more than one year later (Nunes et al, 2007).
  • For children at risk for difficulties in learning mathematics, improving their understanding of logical principles, including the inverse relation, improves their mathematics learning.

Study 1

Aim: To assess deaf children's understanding of the inverse relation between addition and subtraction in their first year in school.


  • 130 hearing children (mean age 5y8m) and 23 deaf children (mean age 6y7m) in their first year in primary school.
  • Loss of hearing was at least severely-profound; all attending special schools or mainstream schools with units.

Assessing the understanding of inversion

3 problems with blocks

3 story problems




For age and inversion problems score, r=.25; p<.001.
Mean (out of 6)
HC: 2.18
DC: 1.12
F 1,150 5.40; p=.02
Cohen’s d=0.6 SD


In this sample of deaf children, who show no intellectual deficits or visual deficits, there is a delay in the understanding of the inverse relation between addition and subtraction.

It would be important to design effective training to improve their understanding of the inverse relation.

Study 2


To test whether methods that were effective with hearing children would also be effective with deaf children.

The teaching starts with visual and identity cues and eliminates these cues as training proceeds.

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
  • The intervention group received teaching on the logic of inversion
  • The control group received teaching to enhance their understanding of the counting system
  • Children in both groups worked with an experimenter on a one-to-one basis

27 deaf children from 6 schools (2 schools for the deaf, 4 mainstream schools with units).

Pre- and post-test measures

6 inversion items (x + a – a = ?), 3 using bricks and 3 using story problems displayed with cards
6 inversion plus decomposition items [x + a – (a +1) = ?]
6 control items (x + x – a = ?)

Measures for control - BAS matrix score

BAS matrix

The intervention

  • Items with blocks
  • Items with objects
  • No story problems with cards were used during the intervention

Using identity and colour to help understand inversion

using colour

no colour change

An inversion item with objects: the child sees 9 cards being put in, then 6 are added, and 6 of the original ones are taken out.

inversion item

Analysis of the effects of the intervention

  • All the analyses will control for the pre-test differences in BAS matrix and pre-test performance
  • The graphs are presented on a scale that varies from -3 (worse than expected from pre-test performance) to + 3 (better than expected from pre-test performance)

Results controlling for pre-test, BAS and age – intervention group performed significantly better.


  • The intervention was effective in helping deaf children understand the inverse relation between addition and subtraction.
  • There was no significant difference between the groups in the items that involved decomposition.
  • These most difficult items continued to cause problems for the children.
  • Significant results after such a short training (2 sessions of about 20 minutes each) are very encouraging, particularly with such large effect sizes.
  • The items were then included in a larger scale intervention programme.