University of Edinburgh

Boosting Maths Skills in Deaf Children

Presented on 24 April 2008

Improving logic in order to promote deaf children's mathematics learning

Department of Education, University of Oxford
Support: RNID

The team
Terezinha Nunes
Peter Bryant
Diana Burman
Daniel Bell
Deborah Evans
Darcy Hallett
Laura Montgomery

Schools, teachers and children
The Nuffield Foundation


  • On average, deaf children are about three and a half years behind hearing children in mathematics achievement.
  • Many deaf children never make much progress in mathematics.
  • Very wide individual differences with about 15% performing at average or above average (but think that for hearing children this percentage would be 50%).
  • Traxler (2000): norming of the Standford Achievement Test for deaf children
  • 80% of pupils at age 14 performed in Problem Solving at levels considered below basic or basic
  • 90% performed in Procedures at the level below basic
  • More than half of the 9 year olds and 90% of the 15 year olds could not be given the test appropriate for their age level.

What could be the cause of this delay?

  • Non-verbal IQ results do not show significant differences between hearing and deaf children – so deaf children are not less intelligent.
  • Are deaf children inherently behind in number representation?
  • Or do they fall behind because of other factors?

Zafarty, Nunes, & Bryant (2004)

  • Deaf and hearing children aged 3 or 4 years
  • Number reproduction task in the absence of the model
  • Set sizes did not require counting (from 2 to 4)
  • Two conditions: sequential and simultaneous presentation
  • Two modes of presentation: by animation or with a person presented on the screen


  • Number of bricks in the array did not affect performance
  • Mode of presentation (with or without puppet) did not affect performance
  • Deaf and hearing children did not differ in successive presentations
  • Deaf children performed significantly better than hearing children in simultaneous presentation.


  • Deaf children are not inherently behind in number representation.
  • They differ in how well they can process simultaneous and successive information and this affects their performance in number representation tasks.
  • But what happens when the set size requires counting?

What time is it?
Your most likely reaction is to look at your watch in order to answer.

  • Our knowledge of time is organised by a cultural tool - the watch - and the knowledge that is part of using a watch.
  • Much of our mathematical knowledge is organised by culturally developed systems of signs.
  • These systems of signs are taught in school.
  • But in order to use the cultural tools, we have to be able to use the logic embedded in them.

Learning and teaching mathematics involves helping children coordinate their understanding of the logic of quantities with the representation of quantities.

Mathematics teaching in English primary schools currently gives more attention to representational systems and how to use these systems.

It is necessary to pay more attention to the development of children's understanding of the logic of quantities and its coordination with the systems of representation.

The connection between logic and mathematics learning

  • For hearing children, logical understanding at the start of school is a good indicator of how well they will learn mathematics.
  • Logical understanding is NOT the same as general intelligence in the traditional sense measured by IQ tests because IQ tests involve many different things.
  • Logical-mathematical thinking develops from children’s reasoning in many situations in everyday life: stimulation is crucial.
  • Children who do not do well in assessments of their logico-mathematical reasoning are at risk for difficulties in learning mathematics.
  • Interventions that help them develop this logical understanding results in better mathematics learning.

Teaching hearing children about logic

  • Our study involved 25 children who were at risk for mathematics difficulties
  • Half were assigned to a teaching group and half to a comparison group
  • We carried out small group interventions where one researcher worked with 3-5 children
  • Once a week during one numeracy hour for 12 weeks

Results on mathematics achievement: SATS-Maths


A comparison with the results for England

  • At the start of Year 1, all the children in the control and experimental group were below the 25th percentile in our logical reasoning assessment
  • At the end of Year 2, in the SATS-Maths
    - the mean for the control group was at the 28th percentile according to national results
    - the mean for the experimental group was just above the national average (i.e. Above the 50th percentile)

The logico-mathematical schemas in the teaching sessions

  • The inverse relation between addition and subtraction
  • Additive composition of number
  • One-to-one and one-to-many correspondence

Deaf children presently lag behind hearing children in these tasks when they start school.

In our RNID project, we adapted the methods we had used with hearing children for teaching deaf children.

We then assessed whether the methods we developed were effective in improving deaf children's understanding of logic.

The studies we carried out investigated separately whether we could improve deaf children's understanding of each of the three logical aspects of reasoning

  • Inverse relation between addition and subtraction
  • Additive composition
  • One-to-many correspondences
  • We also developed teaching to improve the use of their skills in visual analysis
  • The outcome measure in each of these studies was an assessment of what the children had been taught
  • The teaching was effective in all cases.
  • We then prepared a set of materials for teachers to use with their children.
  • The question we asked in this third year is: if the children use these materials, do they help the children learn mathematics in school?
  • So the outcome measure now is not their learning of the logic but their learning of mathematics.

If deaf children develop their logical reasoning, do they improve in mathematics learning?

  • 57 deaf children from 12 schools participated in the study
  • Mean age 6y7m, range 4y1m to 9y
  • Hearing loss: 6 moderate, 6 moderate-severe, 13 severe, 4 severe-profound, 10 profound
  • Cochlear implant: 18
  • Waiting list model: all children had the opportunity to participate in the intervention but some started in November and others in April
  • Those starting in April form the comparison group to assess the effect of the intervention
  • 26 participated in the intervention which started in November and 22 were in the comparison group

A short-term intervention study

  • Pre-test:
    Cognitive ability (BAS matrices), working memory, counting range and an assessment of mathematics achievement that correlates well with SATS-Maths
  • Intervention
    The children were taught about the logical relations and also visual analysis by their teachers in their schools
  • Post-test:
    Mathematics achievement – our assessment
    PIPS – developed by the University of Durham, totally independent from our research team

Difficulties for the analysis

  • Teachers use the materials differently and at different pace
  • The children work up to different parts of the programme
  • There were some real problems faced by teachers in school
  • Only a robust intervention can show positive results under these real-life circumstances

Pre-test scores


Results on our mathematics assessment


Results on the PIPS



  • Research on children's reasoning has led to the identification of the logical-mathematical principles that are at the basis of children's mathematics learning.
  • Some hearing children show poor performance on these tasks but their understanding of these logical principles can be improved through instruction.
  • This instruction has a positive and significant impact on their mathematics learning.
  • Deaf children at the start of primary school do not perform as well as hearing children on these logical tasks.
  • It is possible to promote their understanding of these principles through instruction.
  • When they receive this instruction, they profit more from the mathematics teaching.
  • Instruction on logical reasoning about mathematical principles has a positive impact on deaf children's mathematics learning.