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Tablet computers (tablets) are positioned to be powerful, innovative, effective, and motivating research and assessment tools. We addressed two questions critical for evaluating the appropriateness of using tablets to study number-line estimation, a skill associated with math achievement and argued to be central to numerical cognition. First, is performance with paper and pencil comparable with performance on a tablet? Second, is comparability affected by students' preference for one method of presentation? Thirty-two students in Grade 6 estimated targets on a number line; half estimated with paper and pencil and half with a tablet. For both presentation methods, students' performance was comparable. Students liked both presentation conditions equally but, when asked to choose, most students preferred the tablet. Preference did not influence comparability of results across presentation methods. Finally, students' reasons for their preferences were explored, along with implications for using tablet applications in research and educational assessment.

The principle of "inversion," that a + b - b "must" equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.

The goal of this study was to examine the relation between mathematics and working memory in young children with Fetal Alcohol Spectrum Disorders (FASD). Children with FASD and comparison children (4 to 6 years old) completed standardized tests of mathematics and working memory. Children with FASD showed impairments on mathematics (applied problems and quantitative concepts) as compared to comparison children. The FASD group also performed less well than the comparison group on measures of phonological working memory. Math performance was highly correlated with phonological working memory in both groups and with central executive working memory only in the FASD group. The mathematics deficits in children with FASD appear to be associated with underlying working memory impairments. (Contains 3 tables.)

Most children who are older than 6 years of age apply essential counting principles when they enumerate a set of objects. Essential principles include (a) one-to-one correspondence between items and count words, (b) stable order of the count words, and (c) cardinality--that the last number refers to numerosity. We found that the acquisition of a fourth principle, that the order in which items are counted is irrelevant, follows a different trajectory. The majority of 5- to 11-year-olds indicated that the order in which objects were counted was relevant, favoring a left-to-right, top-to-bottom order of counting. Only some 10- and 11-year-olds applied the principle of order irrelevance, and this knowledge was unrelated to their numeration skill. We conclude that the order irrelevance principle might not play an important role in the development of children's conceptual knowledge of counting. (Contains 1 figure and 1 table.)

Children's failure on equivalence problems (e.g., 5 + 4 = 7 + __) is believed to be the result of misunderstanding the equal sign and has been tested using symbolic problems (including "="). For Study 1 (N = 48), we designed a nonsymbolic method for presenting equivalence problems to determine whether Grade 2 children's difficulty is due to the presence of symbols or to a more fundamental misunderstanding of equivalence. Children's superior performance on nonsymbolic versus symbolic problems suggests that children fail to map their understanding of equivalence onto problems presented with the symbols of arithmetic. For Study 2 (N = 32), we implemented a within-subject design to assess whether experience with nonsymbolic problems would facilitate performance on symbolic problems. This hypothesis was confirmed. Exposure to nonsymbolic problems may have enabled children to map their successful concepts and strategies to symbolic equivalence problems. (Contains 6 figures and 1 table.)

The authors explored the relationship between measures of self-belief, behavioural development, and academic achievement in Canadian Aboriginal children. Standardized measures of intelligence are unable to consistently predict academic achievement in students from indigenous populations. Exploring alternative factors that may be both predictive and amenable to improvements with interventions is therefore important in order to address the growing educational disparity in Canadian Aboriginal children. In this study, significant correlations were found between the Self-Perception Profile for Children rating of behavioural conduct and close friendships, the Behavior Assessment Scales for Children ratings of leadership and study skills, and the Wechsler Individual Achievement Test measures of academic achievement. A school environment that provides opportunities for developing social skills and creating friendships as well as culturally appropriate interventions that support the development of leadership and study skills may provide Canadian Aboriginal children with the tools they need to achieve academically. (Contains 4 tables and 3 notes.)

Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor multiplication fact mastery and calculation fluency and general working memory discriminated children with MLD from typically achieving age-matched peers. Furthermore, children with MLD were slower in executing backup procedures than typically achieving age-matched peers. The performance of children with MLD on multiple measures of multiplication skill and knowledge was most similar to that of ability-matched younger children. MLD may be due to difficulties in computational skills and working memory. Implications for the diagnosis and remediation of MLD are discussed. (Contains 6 tables and 3 notes.)

The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the inversion principle relates to other mathematical or numerical skills remain unclear. Two possibilities were explored in 3-year-olds by adapting a method used previously with older children involving the addition and subtraction of blocks differing in length. These children were significantly more accurate on inversion than standard problems, this difference was observed even in children who did not count well, and performance did not differ between formats that afforded qualitative or quantitative solutions. Thus, 3-year-olds appear to develop an early sensitivity to quantitative inversion. (Contains 2 figures and 1 table.)

Presented preschoolers and first graders with 3-term inversion problems such as 3 + 2 - 2 and similar standard problems to examine whether children used the inversion principle and if use was based on qualitative identity, length, or quantity. Found that both age groups showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal mathematics instruction. (Author/KB)

Describes some recent advances in the study of differential group performance and illustrates some of the ways that substantive analyses can be integrated with multidimensional, bundles-based statistical methods using test specifications to organize the analyses. Highlights some future directions for the analysis of differential item functioning. (SLD)

College students judged the credibility of specially constructed news briefs about science. Their credibility ratings were influenced by area of research, plausibility of conclusions, and quality of research methods, but not by the social context of the research. Students justified their judgments with information in reports, prior knowledge, and prior beliefs. Contains 53 references and sample test materials. (Author/SV)

Examines the types of requests for information made by university students (N=60) as they evaluate scientific news briefs. Student requests most often focus on how research is conducted and why results might occur. Contains 47 references. (DDR)

Children's activities related to science, nature, and technology were studied via structured interviews of parents and students in pre-school through upper-elementary grades. Interviews can be used to construct profiles of students to be used as a platform upon which to build instruction. Describes how interviews were developed, what type of information the research obtained, and lessons learned. (Author/DKM)

Chinese-speaking children have been shown to have an advantage over English-speaking children in a variety of mathematical areas, including counting. One possible explanation for the advantage in counting is that the Chinese number-naming system is relatively transparent, compared to English, in that number names typically are directly indicative of base-10 structure (e.g., 12 is named 'ten-two' rather than 'twelve'). To determine whether the transparency of the Chinese number-naming system influences counting in bilingual children, we tested 25 Chinese-English bilingual children between the ages of 3 and 5 years, both in English and in Chinese. Children were asked to count as high as they could (abstract counting) and also to count objects in small, medium, and large arrays (object counting). No evidence was found for transparency or for transfer from one language to the other. Instead, relative proficiency in the two languages influenced counting skill. These results are discussed in terms of linguistic and cultural variables that might account for cross-linguistic differences in counting. Nous savons que les enfants d'expression chinoise ont un avantage sur les enfants d'expression anglaise dans divers domaines des mathematiques, y compris l'aptitude a compter. L'avantage des enfants d'expression chinoise peut s'expliquer par le fait que le systeme chinois de denomination des nombres est plus ou moins transparent, comparativement au systeme anglais, en ce sens que, generalement, le nom des hombres se rapporte directement a la structure en base 10 (par ex., le chiffre 12 se nomme [??] dix-deux [??] et non pas [??] douze [??]). Afin d'etablir si la transparence du systeme chinois de denomination des nombres a un effet sur l'aptitude a compter chez les enfants bilingues, nous avons teste, en utilisant l'anglais et le chinois, 25 enfants bilingues (chinois-anglais) de 3 a 5 ans. Les enfants etaient invites 'a compter le plus loin possible (numeration abstraite) et compter les objets appartenant a des petits, des moyens et des grands ensembles (comptage d'objets). Nous n'avons observe aucun element probant mettant en evidence la transparence ou le transfert d'une langue a l'autre. Au contraire, nous avons constate que la maitrise relative des deux langues agissait sur l'aptitude a compter. Nous analysons les resultats h la lumiere des variables linguistiques et culturelles qui peuvent prendre en compte les differences interlinguistiques touchant l'aptitude a compter.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jecp.2005.01.004 Byline: Carmen Rasmussen, Jeffrey Bisanz Keywords: Working memory; Arithmetic; Mental model; Representation Abstract: Working memory has been implicated in the early acquisition of arithmetic skill, but the relations among different components of working memory, performance on different types of arithmetic problems, and development have not been explored. Preschool and Grade 1 children completed measures of phonological, visual-spatial, and central executive working memory, as well as nonverbal and verbal arithmetic problems, some of which included irrelevant information. For preschool children, accuracy was higher on nonverbal problems than on verbal problems, and the best and only unique predictor of performance on the standard nonverbal problems was visual-spatial working memory. This finding is consistent with the view that most preschoolers use a mental model for arithmetic that requires visual-spatial working memory. For Grade 1 children, performance was equivalent on nonverbal and verbal problems, and phonological working memory was the best predictor of performance on standard verbal problems. For both age groups, problems with added irrelevant information were substantially more difficult than standard problems, and in some cases measures of the central executive predicted performance. Assessing performance on different components of working memory in conjunction with different types of arithmetic problems provided new insights into the developing relations between working memory and how children do arithmetic. Author Affiliation: Centre for Research in Child Development, Department of Psychology, University of Alberta, Edmonton, Alta., Canada T6G 2E9 Article History: Received 7 July 2004; Revised 10 January 2005

Using multiplication facts, this experiment demonstrated an interference effect in the number-matching task. Here, subjects verified the presence of a target number (e.g., 8) in a previously presented cue (e.g., 5 x 8) that was masked after 60 ms. The SOAs between cue and target were 100, 120, 220, and 350 ms. Subjects were slower to reject targets that were the product of the cue (e.g., 40) than to reject unrelated targets (e.g., 42), but this was true only at the 100- and 120-ms SOAs (i.e., the interference effect). This pattern is consistent with the interference effect found by LeFevre and colleagues using addition facts. Furthermore, the present result supports the interpretation that the interference effect previously found with addition facts was due to obligatory activation and not to automatic counting.

Researchers have assumed that adults solve simple arithmetic problems by retrieving answers from a network of stored facts. In 2 studies, undergraduates described their solutions of single-digit multiplication problems. They reported direct retrieval on approximately 80% of trials, but also reported rules (e.g., anything times 0 is 0), repeated addition (e.g., 2 x 4 = 4 + 4), number series (e.g., 3 x 5 = 5, 10, 15), and derived facts (e.g., 6 x 7 = [6 x 6] + 6). Participants were slower to retrieve problems that were most likely to be solved by nonretrieval procedures and faster to retrieve problems that were usually solved by retrieval. These results indicate that direct-retrieval models are incomplete accounts of adults' performance and support a continuing influence of learning and experience on the mental representation of simple multiplication problems.

Adults' solution times to simple addition problems typically increase with the sum of the problems (the problem size effect). Models of the solution process are based on the assumption that adults always directly retrieve answers to problems from an associative network. Accordingly, attempts to explain the problem size effect have focused either on structural explanations that relate latencies to numerical indices (e.g., the area of a tabular representation) or on explanations that are based on frequency of presentation or amount of practice. In this study, the authors have shown that the problem size effect in simple addition is mainly due to participants' selection of nonretrieval procedures on larger problems (i.e., problems with sums greater than 10). The implications of these results for extant models of addition performance are discussed.

The influence of school- and age-related variables was examined separately on 2 tasks involving elementary quantitative skills: conservation of number and mental addition. Performance on these tasks was compared by using a cutoff design with 3 groups of kindergarten and Grade I children who differed in age but not amount of schooling (grade), in schooling but not age, or in both age and schooling. The effects of age and schooling were distinct. On conservation of number, performance improved as a function of age but not schooling. On mental arithmetic, accuracy improved with schooling rather than age, but children's use of various solution procedures (e.g., retrieval, counting) was not influenced by schooling. Thus, in the domain of elementary mathematical skills, the influence of schooling can be very specific, and age-related variables other than schooling play an important role in the development of elementary mathematical skills. Results illustrate the utility of the cutoff design for investigating instructional and developmental influences on cognitive development.

Children in grades 3 through 5 and adults performed a number-matching task in which they were required to verify the presence of a target digit (i.g., 7) in a previously presented pair (e.g., 2 + 7). For adults, targets that were the sum of the initial pair (e.g., 9) and targets that were close to the initial pair (e.g., 6) were rejected more slowly than unrelated digits. Activation of sums is consistent with models of arithmetic knowledge in which addition facts are stored in a network representation. Activation of close targets (the distance effect) may reflect the counting-based origins of number representations. Consistent with these hypotheses, 8- to 10-year-old children showed minimal effects of sum activation, but large effects of distance. Even at this age, however, distance effects were smaller for subjects with higher levels of arithmetic skill. Thus, changes in the strength of arithmetic connections occurred with development and accounted for individual differences among adults. For children, however, individual differences were related to changes in the strength of number-line connections.