The signed algorithm and its bugs

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.     

Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities?

Counting abilities have been described as determinative precursors for a good development of later arithmetic abilities. Mastery of the stable order, the one–one-correspondence and the cardinality principles can be seen as essential features for the development of counting abilities. Mastery of the counting principles in kindergarten was assessed in a large group of children with a broad range of arithmetic abilities (N = 423). Not all children mastered the counting principles by the end of kindergarten. Mastery of the counting principles in kindergarten was predictive for arithmetic abilities one year later in first grade, especially for scores on arithmetic achievement tests. Children sharing a common educational background tend to have more similar scores on arithmetic tests, yet the importance of mastery of the essential counting principles in the prediction of later arithmetic achievement was the same for all classrooms.     

Deaf and hard of hearing students' problem-solving strategies with signed arithmetic story problems

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e., modeling, counting, and fact-based strategies), they showed an overwhelming use of counting strategies for all types of problems and at all ages. This difference may have its roots in language or instruction (or in both), and calls attention to the need for conceptual rather than procedural mathematics instruction for deaf and hard of hearing students.     

Strategy development in children with mathematical disabilities: insights from the choice/no-choice method and the chronological-age/ ability-level-match design

This study investigated the strategy characteristics and development of children with mathematical disabilities (MD) in the domain of simple addition and subtraction, in terms of Lemaire and Siegler's model of strategic change, using the choice/no-choice method and the combined chronological-age (CA)/ability-level (AL)-match design. Four groups of children, matched on either CA or mathematical AL, solved a series of 36 problems with the bridge over 10 in four conditions. In the choice condition, children could choose between retrieval, decomposition to 10, and counting on to solve each problem. In the retrieval, decomposition, and counting conditions, they had to answer the same 36 problems using retrieval, decomposition to 10, and counting on, respectively. The results revealed clear differences in the frequency, efficiency, and adaptiveness with which the CA-matched children applied the available strategies. In contrast, we observed no differences in strategy frequency, efficiency, and adaptiveness between the AL-matched children. These results support the hypothesis that the strategy development of children with MD is marked by a delay rather than a specific deficit. Moreover, this study further documents the value of the methodology used to study children's strategy use and development in the domain of simple arithmetic.     

Working memory and hearing impairment

Abstract

Some children, particularly those who are hearing impaired, experience difficulties in developing spoken language. Such difficulty typically results in reduced literacy skills and academic achievement. Research suggests that short‐term memory problems are a contributing factor to those language difficulties. Specific training strategies are discussed which may improve the short‐term memory ability of a child with impaired hearing.     

Teaching sign language to hearing children as a possible factor in cognitive enhancement

We describe an educational experience designed to teach Italian Sign Language (LIS) to a group of hearing children. The hypothesis underlying this experience was that learning a visual-gestural language such as LIS may improve children's attentional abilities, visual discrimination, and spatial memory. To examine this hypothesis, we conducted two studies. The first involved an educational experience lasting two years with a group of hearing children attending a Sign Language class from first to second grade. The Raven PM 47 TEST was administered at the beginning and at the end of each school year to children attending the LIS classes and to a control group of children enrolled in the same school but not exposed to LIS. The second study involved an educational experience in first grade. The Raven PM 47 and Corsi's block tapping tests were administered at the beginning and at the end of the school year to the children attending the LIS classes, to children enrolled in the same school but at tending an English class, and to children not exposed to a second language. We found that in both studies the LIS group performed better than the other groups. These results suggest that learning a sign language may lead to a cognitive advancement in hearing children.     

The modes of communication used by children with cochlear implants and the role of sign in their lives

In a mixed-methods study, which included surveys of 247 parents and 151 teachers, the researchers investigated the modes of communication used by children with cochlear implants and the role of signed communication in the children's lives. Findings indicated that 15%-20% of the children in the parent surveys and approximately 30% of the children in the teacher surveys were using some form of signed communication. Qualitative findings from interviews with parents, teachers, and children with cochlear implants elaborated on the quantitative findings. While the development of spoken-language communication was the main aim of their children's cochlear implantation for the large majority of parents, many valued the use of either Signed English or Australian Sign Language, which they felt supported their children's personal, social, and academic development. Young people who used sign switched comfortably between communication modes according to their communication partners, topics, and settings.     

The development and psychometric properties of the American sign language proficiency assessment (ASL-PA)

We describe the procedures for constructing an instrument designed to evaluate children's proficiency in American Sign Language (ASL). The American Sign Language Proficiency Assessment (ASL-PA) is a much-needed tool that potentially could be used by researchers, language specialists, and qualified school personnel. A half-hour ASL sample is collected on video from a target child (between ages 6 and 12) across three separate discourse settings and is later analyzed and scored by an assessor who is highly proficient in ASL. After the child's language sample is scored, he or she can be assigned an ASL proficiency rating of Level 1, 2, or 3. At this phase in its development, substantial evidence of reliability and validity has been obtained for the ASL-PA using a sample of 80 profoundly deaf children (ages 6-12) of varying ASL skill levels. The article first explains the item development and administration of the ASL-PA instrument, then describes the empirical item analysis, standard setting procedures, and evidence of reliability and validity. The ASL-PA is a promising instrument for assessing elementary school-age children's ASL proficiency. Plans for further development are also discussed.     

Language codes and sense-making among deaf schoolchildren

There are at least two languages (American Sign Language [ASL], English) and three modalities (sign, speech, print) in most deaf individuals' lives. Mixing of ASL and English in utterances of deaf adults has been described in various ways (pidgins, diglossia, language contact, bilingualism), but children's mixing usually is treated as the 'fault' of poor input language. Alternatively, how might language mixing serve their communication goals? This article describes code variations and adaptations to particular situations. Deaf children were seen to exhibit a wide variety of linguistic structures mixing ASL, English, Spanish, signing, and speaking. Formal lessons supported a recoding of English print as sign and speech, but the children who communicated English speech were the two who could hear speech. The children who communicated ASL were those who had deaf parents communicating ASL or who identified with deaf houseparents communicating ASL. Most language produced by the teacher and children in this study was mixed in code and mode. While some mixing was related to acquisition and proficiency, mixing, a strategy of many deaf individuals, uniquely adapts linguistic resources to communication needs. Investigating deaf children's language by comparing it to standard English or ASL overlooks the rich strategies of mixing that are central to their communication experience.     

Approaching sign language test construction: adaptation of the German sign language receptive skills test

There is a current need for reliable and valid test instruments in different countries in order to monitor deaf children's sign language acquisition. However, very few tests are commercially available that offer strong evidence for their psychometric properties. A German Sign Language (DGS) test focusing on linguistic structures that are acquired in preschool- and school-aged children (4-8 years old) is urgently needed. Using the British Sign Language Receptive Skills Test, that has been standardized and has sound psychometric properties, as a template for adaptation thus provides a starting point for tests of a sign language that is less documented, such as DGS. This article makes a novel contribution to the field by examining linguistic, cultural, and methodological issues in the process of adapting a test from the source language to the target language. The adapted DGS test has sound psychometric properties and provides the basis for revision prior to standardization.     

Neural correlates for numerical processing in the manual mode

This paper reports a study designed to examine the neuronal correlates for comprehending the signs of American Sign Language representing numerals in deaf signers who acquired Japanese Sign Language as their first language. The participants were scanned by functional magnetic resonance imaging (fMRI) twice on the day of the experiment. The results of the measurements revealed that upon learning that the signs actually have numeric meaning, a network of brain areas is activated immediately. Many of these areas have been previously implicated in numerical processing. The similar neural network of brain regions responsible for numerical processing exists on a nonlinguistical basis and works to retrieve arithmetic facts from presented linguistic material regardless of the mode of the language.     

Head start children''s conceptions of and expectations for their future schooling

This study examined children's conceptions of and expectations for their future schooling, determined whether participation in a Transition Demonstration could affect these, and explored how these are related to children's academic achievement. Two cohorts, 151 former Head Start children completing kindergarten, and 171 children completing Head Start, were assessed. Two major themes in children's conceptions of school emerged: play and the cognitive or learning environment. Children realistically talked about the work of school becoming less play centered, more difficult, and more centered on academics as they moved from grade to grade. Children in the Demonstration group in both cohorts gave significantly more responses to the questions than those in the Comparison. Children's expectations for their future schooling were optimistic. There were several small but significant correlations between children's conceptions and expectations for school and their academic achievement as measured by subtests of the Wood-cock-Johnson-R.     

Siblings and theory of mind in deaf native signing children

We report a study designed to examine the basis of "theory of mind" (ToM) reasoning in deaf children who are native signers of British Sign Language. The participants were 20 native signers (aged 4-8 years) and their siblings. The children were given a measure of the quality of sibling relations together with a referential communication test concerning physical representations of objects and people. Sibling quality as perceived by siblings predicted children's ToM scores over and above age and referential communication. We conclude that the process of ToM understanding is linked to positive sibling relations that may permit access to knowledge about the inner worlds of beliefs and other mental states.     

Subtypes of mathematical learning disability and their antecedents: A cognitive diagnostic approach

Using cognitive diagnostic modeling (CDM), this study identified subtypes of mathematics learning disability (MLD) based on children's numerical skills and examined the language and spatial precursors of these subtypes. Participants were 99 MLD children and 420 low achievers identified from 1839 Finnish children (966 boys) who were followed from preschool (age 6) to fourth grade (2007–2011). Five subtypes were identified: the arithmetic fluency deficit only subtype, the counting deficit subtype, the pervasive deficit subtype, the symbolic deficit subtype, and the counting and concept deficit subtype. Different subtypes depended on different constellations of language and spatial deficits. Findings highlight the effectiveness of CDM in identifying MLD subtypes and underscore the importance of understanding the specific deficits and antecedents of the subtypes.     

Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge

Utilizing a longitudinal sample of Finnish children (ages 6–10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number‐related knowledge.     

What Counts? Sources of Knowledge in Children’s Acquisition of the Successor Function

Although many U.S. children can count sets by 4 years, it is not until 5½–6 years that they understand how counting relates to number—that is, that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½- to 6-year-olds (N = 136) may leverage to acquire this “successor function”: (a) mastery of productive rules governing count list generation; and (b) training with “+1” math facts. Both productive counting and “+1” math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from “+1” math facts.     

Language development in deaf children's interactions with deaf and hearing adults: a Dutch longitudinal study

The language development of two deaf girls and four deaf boys in Sign Language of the Netherlands (SLN) and spoken Dutch was investigated longitudinally. At the start, the mean age of the children was 3;5. All data were collected in video-recorded semistructured conversations between individual children and deaf and hearing adults. We investigated the lexical richness and syntactic complexity of the children's utterances in SLN and spoken Dutch, as well as language dominance and interactional participation. Richness and complexity increase over time, as well as children's participation. An important outcome is that syntactic complexity is higher in utterances with both sign and speech. SLN does not have higher outcomes on richness or complexity, but is dominant in terms of frequency of use.     

The relative difficulty of signed arithmetic story problems for primary level deaf and hard-of-hearing students

This study determines the relative difficulty and associated strategy use of arithmetic (addition and subtraction) story problems when presented in American Sign Language to primary level (K-3) deaf and hard-of-hearing students. Results showed that deaf and hard-of-hearing students may consider and respond to arithmetic story problems differently than their hearing peers, with the critical dimension in problem difficulty being based on the operation typically used to solve the problem, not the story within the problem. The types of strategies used by the students supported the order of problem difficulty. The visual-spatial nature of the problem presentation appeared not to assist the deaf and hard-of-hearing students in solving the problems. Factors that may have contributed to this pattern of problem difficulty are discussed so that educators can better align mathematics instruction to the thinking of the deaf child.