Multiplicative reasoning is required in different contexts in mathematics: it is necessary to understand the concept of multipart units, involved in learning place value and measurement, and also to solve multiplication and division problems. Measures of hearing children's multiplicative reasoning at school entry are reliable and specific predictors of their mathematics achievement in school. An analysis of deaf children's informal multiplicative reasoning showed that deaf children under-perform in comparison to the hearing cohorts in their first two years of school. However, a brief training study, which significantly improved their success on these problems, suggested that this may be a performance, rather than a competence difference. Thus, it is possible and desirable to promote deaf children's multiplicative reasoning when they start school so that they are provided with a more solid basis for learning mathematics. The aim of this investigation was to analyze the development of multiplicative reasoning in young deaf children. In the first section of this paper, we define multiplicative reasoning and its importance for children's mathematics learning. In the second section, we review studies with hearing children that investigate the schemas of action that constitute children's informal knowledge of multiplicative reasoning used in solving multiplication and division problems before they are taught about these arithmetic operations in school. The third section provides an overview of research on deaf students’ performance in tasks that involve multiplicative reasoning. Two new empirical studies are then presented. The first compares the performance of deaf and hearing children on multiplicative reasoning problems at the beginning of primary school, before they have been taught about multiplication and division. This study established that deaf children under-perform, in comparison to hearing children, and therefore could benefit from instruction that supports their ability to use their informal mathematics knowledge to solve such problems. The second study reports a brief intervention that was relatively successful in promoting this ability.

This paper analyzes the reliability and validity of a questionnaire designed by Archbold, Lutman, Gregory, O'Neil, and Nikolpoulos (2002) for the assessment of pediatric cochlear implantation. Parents of 61 youngsters (age range 5 to 16 years), who had the implant for at least 3 years, responded to the questionnaire and to an interview. The alpha reliability of the 11 questionnaire scales varied between .41 and .74. Content validity was assessed by comparison with parents' responses to an interview. In general, there was agreement between parents' concerns and views expressed in the interview and as assessed by the questionnaire. However, extra issues were identified in the interview, which suggest the need for increasing the breadth of the questionnaire. Criterion validity was assessed by identifying contrasting cases, with very low or very high scores in each scale, and analyzing the descriptions obtained in the interviews. For nine scales this analysis provided support for the validity of the questionnaire; two scales did not produce positive results. Correlations with interview scores were calculated for only four scales: two were positive and significant whereas two were not significant. A factor analysis of the questionnaire scales identified four components, interpreted as the child's functioning in social situations, attitudes to the process of implantation, support required in the long term, and effective use of the implant. Suggestions for further research and descriptive comments provided by parents are included. The aim of this investigation was to carry out an independent assessment of a parent outcome questionnaire from pediatric cochlear implantation designed by Archbold, Gregory, Lutman, O'Neil, and Nikolpoulos (2002). Their instrument is presently titled “Parent outcome profile from pediatric cochlear implantation” but was originally named “Parents' views and experiences with pediatric cochlear implant questionnaire.” It will be referred to here as the PVECIQ. In their previous work, the authors obtained data to show that the questionnaire is robust and repeatable. The questionnaire was given twice, with a 1-month interval, to a random sample of parents from a list of children who had received implants in one implant center. The children were all either born deaf of had been deafened before the age of 3 and had been using the implant for at least 2 years. Twenty parents were approached; 100% responses were obtained on both occasions, after reminder letters were sent out. The authors reported the test-retest correlation by item. Of the 103 test-retest correlations, only 8 were not significant; the majority (68) was above .60. Archbold et al. also considered the value of the standard deviation of the difference between the first and the second responses. The range of possible differences when the second response was subtracted from the first was −4 to +4. For all the items, the mode for the difference between the responses on the two occasions was equal to zero and the absolute value of the mean was less than one; the majority of the items (73) had standard deviations with values under 0.5. This indicates that the most likely answer on retest was the same answer given previously; for the 73 items with standard deviations under 0.5, the same answer is likely to be observed in 95% of the cases. Thus Archbold et al. showed that the PVECIQ is robust and the evaluation of the PVECIQ carried out here will not consider test-retest reliability. It will use other aspects of psychometric theory to analyze the internal consistency of the scales that compose the questionnaire, and the content, criterion, and construct validity of the questionnaire.

Our past research identified two aspects of deaf children's functioning that places them at risk for underachievement in mathematics. The first is their reduced opportunities for incidental learning, and the second is their difficulty in making inferences involving time sequences. This article examines the effectiveness of an intervention program to promote deaf children's numeracy that was designed to deal with these two factors. The design involved a comparison of 23 deaf pupils participating in the project with a baseline group formed by 65 deaf pupils attending the same schools in the previous year. The project pupils were tested before and after the intervention on the NFER-Nelson Age Appropriate Mathematics Achievement Test. The intervention was delivered by the teachers during the time normally scheduled for mathematics lessons. The project pupils did not differ from the baseline group at pretest but performed significantly better at posttest. They also performed at posttest better than expected on the basis of their pretest scores, according to norms provided by the NFER-Nelson Age Appropriate Mathematics Test for assessing the progress of hearing pupils. We conclude that the program was effective in promoting deaf pupils’ achievement in numeracy.

Arguments supporting the integration of deaf pupils in mainstream schools are often based on possible cognitive gains, but it has been suggested that integration should also be assessed in terms of its social consequences for pupils. If deaf pupils are rejected or feel isolated in mainstream schools, their education may ultimately suffer. We investigated the social adaptation of nine deaf pupils in two mainstream schools using three methods: peer ratings, sociometric status and interviews. The average peer ratings received by deaf pupils were not significantly different from those of hearing pupils. Thus these deaf pupils were not more disliked by their peers. However, they were significantly more likely to be neglected by their peers and less likely to have a friend in the classroom. Hearing pupils who were friends of deaf pupils described their friendship as involving pro-social functions whereas many who had no deaf friends found communication an obstacle to friendship. We conclude that, although deaf pupils are not rejected in mainstream schools, they may feel isolated. It is possible that schools can have a proactive role in helping hearing pupils learn how to overcome communication barriers and develop more positive attitudes towards deaf pupils.

Deaf children consistently lag behind their hearing cohorts in mathematics achievement tests. It has been hypothesized that their difficulty is a consequence of their lack of covert counting strategies and reliance on memorized verbal facts. We investigated the acquisition of an alternative method to solve sums, the signed algorithm, by six profoundly deaf primary school children. Similarly to the acquisition of the written algorithm by hearing children, deaf children’s calculation errors with the signed algorithm were found to be systematic and related to the structure of the numeration system in British Sign Language. These results can be used to examine better ways of teaching arithmetic to deaf children and illustrate in a novel way the role of systems of signs in mathematical cognition.