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.     

Deaf college students' comprehension of relational language in arithmetic compare problems

In this study of deaf college students' performance solving compare word problems, relational statements were either consistent or inconsistent with the arithmetic operation required for the solutions. The results support the consistency hypothesis Lewis and Mayer (1987) proposed based on research with hearing students. That is, deaf students were more likely to miscomprehend a relational statement and commit a reversal error when the required arithmetic operation was inconsistent with the statement's relational term (e.g., having to add when the relational term was less than). Also, the reversal error effect with inconsistent word problems was magnified when the relational statement was a marked term (e.g., a negative adjective such as less than) rather than an unmarked term (e.g., a positive adjective such as more than). Reading ability levels of deaf students influenced their performance in a number of ways. As predicted, there was a decrease in goal-monitoring errors, multiple errors, and the number of problems left blank as the reading levels of students increased. Contrary to expectations, higher reading skills did not affect the frequency of reversal errors.     

Structural variables affecting CAI performance on arithmetic word problems of disadvantaged and deaf students

Summary We have shown that it is possible to account for a substantial portion of variability in student responses to arithmetic word problems using variables that describe structural features of the problems. However, the results obtained at this stage in our investigations are situation-dependent. The greater variance in observed proportion correct compared with the variance in the predicted proportions, and the differing sets of variables contributing significantly to the regressions come as no surprise. First, the population for this study differed from that used in the pilot study. Second, it is clear that characteristics of the problem set, for example, the frequency of occurrence of exemplars for the range of values for each variable and the way variable values are combined in problem types, affect the weighting for each variable in the regression analysis. Thus, differences were expected because different problem sets were used for the pilot study and the present study.In the light of these differences, the similarity in performance of the two disadvantaged groups gains in significance, and deserves further study. We believe we can increase the generalizability of our results by redesigning the basic problem set to exemplify in a balanced fashion the full range of variables found to account for problem difficulty. Given, however, the difficulty of making accurate predictions about problem-solving results, the correctness of this belief needs to be explicitly tested.This research was supported by Office of Education Grant OEG-0-70-4797 (607) and NSF Basic Research Grant GJ-443X.     

Deaf and hearing students' morphological knowledge applied to printed English

The study examined the ability of deaf and hearing students at the college and middle school levels to discern and apply knowledge of printed word morphology. There were 70 deaf and 58 hearing participants. A two-part paper-and-pencil test of morphological knowledge examined subjects' ability to (a) perceive segmentation of morphemes within printed words and (b) recognize meanings associated with various printed morphemes. The hearing college students performed best on every dependent measure of the two-part test. The deaf college students scored significantly lower than the hearing college students but similarly to the hearing middle school students. Deaf middle school students consistently scored the lowest on both parts of the test. While all students' performance declined as the difficulty of the morphemic content increased within both tasks, the decline was greatest among middle school deaf students. Although segmentation and semantic analysis skills necessary to morphographic decoding were apparent in the deaf students, their mastery levels fell significantly below those of the hearing subjects.     

Deaf children's use of cognitive strategies in simple arithmetic problems

Research shows that deaf children have inferior achievement in simple arithmetic compared to their hearing agemates. The reported study investigates whether the reasons for deaf children's poor achievement can be sought in their strategy development. As this is a central issue, the strategies used by deaf children when solving symbolic addition and subtraction problems are identified, classified and compared to findings from earlier research, involving both deaf and hearing children. The effect of Sign Language in strategy invention and use is the main concern in this study. One result from the present study is that structural aspects of Sign Language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but instead to refined procedural competence. This is a development in simple arithmetic that is compatible with that of less able hearing children. The counting procedures used by the deaf children involve both oral counting and Sign Language counting. Due to the small sample size, and the shortcomings of the research design, the results are more suggestive than conclusive. Thus, further studies are needed in this area.This revised version was published online in September 2005 with corrections to the Cover Date.     

Working on arithmetic word problems when English is an additional language

There has been little research in the UK into how students learning English as an additional language (EAL) learn mathematics. This article reports results from a three‐year study of the participation of learners of EAL in Year 5 in an arithmetic word problem task. The research, drawing on ideas from discursive psychology, used discourse analysis to explore patterns of attention in students' interaction as they worked in pairs or threes. The article briefly describes four patterns of attention: to genre, to mathematical structure, to narrative experience and to written form. Further analysis explored how students used attention as part of the social activity involved in working on the task. The rest of the article illustrates how students used attention to narrative experience to make links between word problems and their own experience, as well as to negotiate their relationships with each other.     

Pathways to arithmetic: The role of visual-spatial and language skills in written arithmetic,arithmetic word problems,and nonsymbolic arithmetic

This study set out to develop and test a pathway model of the relations between general cognitive skills, specifically visual-spatial and spoken and written language skills, and competence in three forms of arithmetic that vary in modes of number representation. A total of 88 Chinese 4-year-olds participated and were tested first in kindergarten second grade (K2) and then in kindergarten third grade (K3). Language skills, including phonological, morphological, and visual-orthographic skills, and visual-spatial skills were measured at K2, and arithmetic outcomes, including written arithmetic, word problems, and nonsymbolic arithmetic, at K3. The results generally supported our model. Specifically, visual-spatial skills contributed to the prediction of all three types of arithmetic outcomes. Morphological skills predicted word problems, whereas phonological skills predicted written arithmetic. Finally, visual-orthographic skills contributed to both written and nonsymbolic arithmetic. These findings underscore the importance of delineating the specificity of cognitive processes in learning diverse forms of arithmetic.     

Realistic considerations in mathematical modeling of school arithmetic word problems

The aim of the present study was to collect in a systematic way empirical data about the (lack of) activation of real-world knowledge during elementary school pupils' understanding and solution of school arithmetic word problems. Ten pairs of word problems were collectively administered to 75 fifth-graders during a typical mathematics lesson. While the first item of each pair could be modeled and solved in a straightforward and unproblematic way by one or two simple arithmetic operations with the given numbers, the second problem could not be modeled and solved in such a way, at least if one seriously takes into account the realities of the context called up by the problem statement. An analysis of the pupils' reactions to these problematic word problems shows an alarmingly small number of realistic responses or additional comments based on realistic considerations.     

Comparing deaf and hearing college students' mental arithmetic calculations under two interference conditions

Deaf and hearing college students' mean reaction times (RTs) were compared on a mental calculation task in which they had to verify the accuracy of solutions to addition and multiplication problems. The deaf students were divided into higher and lower readers. Higher deaf readers and hearing students had similar RTs and accuracy on addition problems; their RTs were greater in the voicing interference mode than in the manual tapping interference mode. The lower deaf readers showed no RT differences between the two interference modes and had consistently lower RT performance and score accuracy across the verification tasks. On the verification task for multiplication problems, all participants showed a greater RT effect for manual tapping. The lower deaf readers were significantly less accurate on multiplication problems.     

Deaf and hard of hearing children and adolescents in China: their fears and anxieties

The study examined the fears and anxieties of Chinese deaf and hard of hearing children and adolescents, and the ability of parents and teachers to report the presence of these fears and anxieties. Chinese deaf youth are at risk due to a lack of trained teachers, an overemphasis on oral education in schools, negative stereotypes, and parental overprotectiveness. The deaf children and adolescents in the study reported significantly higher levels of total fears, total anxieties, fear of the unknown, fear of injury and small animals, fear of medical procedures, and concentration anxiety than their hearing counterparts. Girls reported more total fears, fear of the unknown, fear of minor injury and small animals, and fear of failure and criticism than boys. Parents showed a better ability than teachers to confirm these reports of fears and anxieties. Implications and directions for future studies are presented.     

Deaf and hard of hearing Americans' instant messaging and e-mail use: a national survey

An online survey of 884 deaf and hard of hearing adults asked about their current and past use of communication technologies, notably TTY, telecommunications relay services, e-mail, and instant messaging (IM). Results showed that respondents were using e-mail and IM far more than TTY and relay services. The study participants virtually all had e-mail and IM at home. In fact, about one quarter had a high-speed ("broadband") connection at home. While the vast majority also had and used e-mail at work, just 1 in 3 had IM at his or her place of employment. The findings have several implications. Most important for educators is that strong reading and writing skills are essential if adults who are deaf or hard of hearing are to take advantage of today's communications technologies. Another conclusion is that some workers who are deaf or hard of hearing appear to face discrimination in employment because office policies forbid the use of a highly effective reasonable accommodation, instant messaging.     

Reread-adapt and answer-comprehend intervention with Deaf and hard of hearing readers: effect on fluency and reading achievement

The researchers investigated the effect of the Reread-Adapt and Answer-Comprehend intervention (Therrien, Gormley, & Kubina, 2006) on the reading fluency and achievement of d/Deaf and hard of hearing elementary-level students. Children in the third, fifth, and sixth grades at a state school for d/Deaf and hard of hearing students received a fluency intervention that was supplemental to their regular reading instruction. Significant improvement was found on a generalized measure of reading fluency after intervention. Though the researchers found no significant improvement in performance on a generalized measure of comprehension after intervention, the students demonstrated consistently good comprehension on both literal and inferential questions during the intervention sessions. The findings support the importance of incorporating a comprehension monitoring strategy in fluency instruction.     

Deaf college students' perspectives on literacy portfolios

The study examined how literacy portfolios were used as tools in a college developmental English class in which deaf students assessed their reading comprehension as well as their writing processes and products. The students' reading and writing assignments involved reflective thinking and were grounded in authentic tasks. Immediate feedback was provided. The study was multidimensional, longitudinal, and ongoing. A variety of field research techniques were used to ascertain the uses and influences of portfolios in regard to students' reading, writing, and reflective thinking. The results support the idea that the use of literacy portfolios can positively influence students who are deaf when they assess their reading and writing abilities.     

Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study

2493 children aged from 5 to 15 years in 114 classes in 25 primary schools were asked to do a similar set of 22 arithmetic word problems. 1195 of the children were in Grades K through 6 in Victorian schools (Australia) and 1298 were in Grades 4 through 6 in Papua New Guinea (PNG) schools. For both samples the questions were posed in English. This was the first language for most children in the Victorian sample but, for the PNG sample, English was usually the second, third, or even fourth language (even though it is the language of instruction in PNG schools). While the test instrument was based on widely accepted information processing models of how children solve arithmetic word problems, the data obtained were not so much in accord with these models as with psycholinguistic theories on children's acquisition of polarised comparative pairs (like more and less). The data also indicate that children from the two samples used similar strategies and made similar errors, with the order of relative difficulty being the same for both samples, the main factor determining difficulty being the semantic structure of the questions. Differences in performance between corresponding grades from the two samples can be attributed to differences in the degree of English language competence rather than to numerical facility.     

Solving arithmetic word problems: an analysis of classification as a function of difficulty in children with and without arithmetic LD

This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c) position of the unknown quantity in the problem. Facet theory with multidimensional scaling techniques (MINISSA) was used to analyze the underlying dimensions in the responses of each group of participants. Our results indicate that although the word problem difficulty classifications for the 2 groups of children were different, the position of the unknown quantity had a greater influence on the level of difficulty of story problems than other variables. The noncanonical problems--specifically, those with the unknown term in the first place--although difficult for both groups of children, were the most difficult problems for children with ALD.