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.     

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.     

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.     

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.     

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.     

Deaf college students' reading comprehension and strategy use

Two comprehension studies were conducted with 46 deaf college students. In the first, 20 deaf college students representing higher and lower reading-ability levels were tested for correctly stating the main idea of a passage, answering content questions, indicating their understanding of the words and phrases, and recognizing a topically incongruent sentence embedded in the passage. The results suggest that deaf students profess a better understanding of what they read than they are able to demonstrate. The students' inability to identify a topically incongruent sentence in the passage further suggests a need for them to more carefully and accurately evaluate their understanding of what they are reading. A second study investigated the effect of strategy review instruction on deaf college students' comprehension of short reading passages. Students reading at a higher level showed improved comprehension on the posttraining passage, but students reading at a lower level did not. Similarly, the control group of deaf students comparable to the higher-level readers did not show improved comprehension.     

Deaf college students' perceptions of their social-emotional adjustment

This study examined differences between deaf and hearing students' perceptions of their social emotional adjustment as they transition to college. The 16PF-Adolescent Personality Questionnaire Life Difficulties Scale was completed by 205 deaf students and 185 hearing students. A multivariate analyses of variance and subsequent univariate tests found that deaf students rated themselves as experiencing significantly higher home life difficulties than hearing students, and deaf students rated themselves as having fewer coping difficulties than hearing students. Results also revealed a hearing status by gender interaction with deaf females rating themselves significantly higher on worry than deaf males, hearing females, and hearing males. An exploratory factor analysis of the Life Difficulties subscales yielded three factors of life difficulties for deaf college students but only two factors for hearing college students. These findings suggest that there are differences between deaf and hearing students who are transitioning to college with regards to their social-emotional adjustment.     

Solving story-based arithmetic problems: achievement of children with hearing impairment and their interpretation of meaning

This article considers how a sample of Norwegian school children, ages 6 through 10 with hearing impairment, master three different types of elementary arithmetic problems presented in a nonreading format. The article outlines the effect of task-specific factors on the level of difficulty, as well as the children's understanding of problem structures. The results showed that semantic structure of the problems affected the level of difficulty. The problems were not solved significantly better by students from grade 4 than students from grade 1. Qualitative analyses revealed that the children interpreted the meaning of the imposed problems in three different ways: (1) as numbers and procedures, (2) as take-away situations, and (3) as part-part-whole relations.     

Promoting vocabulary learning in young children who are d/Deaf and hard of hearing: translating research into practice

Vocabulary knowledge is strongly associated with reading achievement and becomes increasingly predictive of overall reading proficiency as children progress through the elementary grades. Children who are d/Deaf and hard of hearing often begin schooling with small meaning vocabularies, a disadvantage that puts them at risk of struggling to learn to read. Recent research on vocabulary intervention with young children who have typical hearing demonstrates the effectiveness of targeted, contextualized instruction on children's word learning and provides insights for early childhood educators of young d/Deaf and hard of hearing children. In the present essay, which is grounded in the qualitative similarity hypothesis (Paul, 2010, in press; Paul & Lee, 2010) and sociocultural theories of learning, the author argues for evidence-based vocabulary interventions for young d/Deaf and hard of hearing children that are rooted in the contemporary research literature.     

基于组合度的汉语分词决策算法研究

提出了汉字组合的组合度概念,讨论了组合度与组合的成词能力之间的关系,利用决策树的方法挖掘了组合度与分词模板的关系．在此基础上得出了一种新的分词算法．实验表明组合度对组合成词能力的影响远远大于组合频率的影响．这种分词方法对汉语分词的歧义问题、人名、地名识别问题;新词识别问题等都有一定的作用．     

Through a glass darkly: A naturalistic study of students' understanding of mathematical word problems

A father is now 20 years older than his son. In 8 years, the father's age will be 5 years more than twice the son's age. Find their present age.Word problems, such as this one, are a perennial source of difficulty for students of school mathematics. Unfortunately, very little is known about why they are problematic, mainly because so little is known about how students understand such problems or the strategies they use in their efforts to solve them. Traditional research into word problems has shed precious little light on this question owing, in no small part, to its almost singular preoccupation with results of pupils' activities—as expressed in some sort of test score, and to its tendency to all but ignore what students actually do when confronted with problems of this kind.This study was carried out as one facet of a larger research project designed to gain more insight into some of the ways in which students understand school mathematics. It focuses on the efforts of one pupil, a twelve-year-old girl in grade seven, to come to terms with solving word problems using an algebraic approach. Strategies associated with both the structured and the unstructured clinical interview were used in order to reveal what was involved in her attempts to make sense of the word problems in her grade seven mathematics textbook.Based on the information gained in the interview, a rational reconstruction of the student's problem-solving strategy is proposed, and compared with the strategies normally prescribed in contemporary school mathematics textbooks. What emerges from this comparison is the finding that, while there appear to be systematic and fundamental differences between the procedures prescribed by the text and those actually used by the pupil in working through certain problems, these differences are undetectable in the finished product; either in the answer itself or in the rough or finished work. What this suggests, among other things, is that if, as educators and/or researchers, we limit our attempts to understand how students go about learning to solve word problems (or how they approach any other part of the school mathematics curriculum, for that matter) to examining what they commit to paper, we are apt to be seriously misled concerning what they genuinely understand and what they fail to understand. In short, if we are to learn more about why pupils experience difficulties with word problems we must begin to pay serious attention to what they say and do as they work their way through them.This study was supported by a Research and Development Grant from the Faculty of Education, Queen's University.     

Deaf college students' perceptions of communication in mainstream classes

Fifty deaf and hard-of-hearing students who were mainstreamed in postsecondary classes rated their classroom communication ease with hearing instructors, hearing peers, and deaf peers. A subgroup of these students participated in an in-depth interview that focused on perceptions of communication ease, support services, and attitudes of teachers and students toward deaf students in mainstreamed classes. Quantitative analyses indicated that students more comfortable in using speech in this setting reported being able to receive and send a greater amount and a higher quality of information than did students who were less comfortable in using speech. Both quantitative and qualitative results indicated that students varied considerably in their communication with hearing peers and professors, in their relations with deaf peers, and in their concerns about access. It is a challenge for interpreting and other support services to serve these various needs, especially when it is not unusual for these variations to occur in the same classroom.     

Inquiry-based science instruction and performance literacy for students who are deaf or hard of hearing

Deaf and hard of hearing students, who cannot successfully access and utilize information in print, experience various difficulties in conventional science instruction, which heavily relies on lectures and textbooks. The purpose of the present review is threefold. First, an overview of inquiry-based science instruction reform, including the so-ciohistorical forces behind the movement, is presented. Then, the author examines the empirical research on science education for students who are deaf or hard of hearing from the 1970s to the present and identifies and rates inquiry-based practice. After discussing the difficulty of using science texts with deaf and hard of hearing students, the author introduces a conceptual framework that integrates inquiry-based instruction and the construct of performance literacy. She suggests that this integration should enable students who are deaf or hard of hearing to access the general education curriculum.     

Deaf and hearing individuals' beliefs about the capabilities of deaf people

The study explored the beliefs of 100 residents of Greece about the capabilities of deaf people living in that country. Participants included deaf adults who communicated in Greek Sign Language (GSL), deaf adults who communicated orally, hearing adults who attended GSL courses, and hearing adults who did not attend such courses. Beliefs were explored through the ODP (Opinions About Deaf People) scale (Berkay, Gardner, & Smith, 1995) and an open-ended interview. All participant groups viewed deaf people's capabilities positively, but Deaf users of GSL expressed the most positive beliefs. The findings suggest that less positive beliefs reflect diverse ideological views toward GSL and Deaf culture or an awareness of the obstacles preventing deaf people from developing their potential. The Deaf community's role in empowering deaf people and the role of GSL courses in promoting awareness regarding deaf people are also discussed.