Patterns of problem‐solving in children's literacy and arithmetic

Patterns of problem‐solving among 5‐to‐7 year‐olds' were examined on a range of literacy (reading and spelling) and arithmetic‐based (addition and subtraction) problem‐solving tasks using verbal self‐reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the arithmetic (addition and subtraction) than literacy‐based tasks (reading and spelling). However, across all four tasks, the children showed a tendency to move from less sophisticated procedural‐based strategies, which included phonological strategies for reading and spelling and counting‐all and finger modelling for addition and subtraction, to more efficient retrieval methods from Years 1 to 2. Distinct patterns in children's problem‐solving skill were identified on the literacy and arithmetic tasks using two separate cluster analyses. There was a strong association between these two profiles showing that those children with more advanced problem‐solving skills on the arithmetic tasks also showed more advanced profiles on the literacy tasks. The results highlight how different‐aged children show flexibility in their use of problem‐solving strategies across literacy and arithmetical contexts and reinforce the importance of studying variations in children's problem‐solving skill across different educational contexts.     

Working memory and literacy as predictors of performance on algebraic word problems

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient (IQ), and reading ability. Regression results were consistent with findings from the arithmetic literature showing that a literacy composite measure provided greater contribution than did executive function capacity. However, a series of path analyses showed that the overall contribution of executive function was comparable to that of literacy; the effect of executive function was mediated by that of literacy. Both the phonological loop and the visual spatial sketchpad failed to contribute directly; they contributed only indirectly by way of literacy and performance IQ, respectively.     

From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving Across Mathematical Representations

This article reports on students’ problem-solving approaches across three representations—number lines, coordinate planes, and function graphs—the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a hierarchical representational narrative (HRN), a discursive narrative around a set of representations that model conventional mathematics in structurally consistent ways. A paper-and-pencil assessment was administered to students in grades 5 and 8 along with videotaped interviews with a subset of students. Results revealed students’ application of particular meta-rules, which reflect their attempts to find and make use of recurring patterns in mathematics discourse. One such meta-rule, consistent with the HRN, was characterized by students’ coordination of geometric and numeric properties of an axis, whereas alternate meta-rules reflected coordinations inconsistent with conventional mathematics. Detailed analyses of problem-solving strategies are reported, and implications for theory, curriculum, and instruction are discussed.     

The attributional norm of internality and depressive sensitivity to social information

Two studies examined the existence, within an achievement-related context, of a social norm favoring internal explanations for task performances. In the first study, we investigated the reactions of observers to an actor's high, moderate, or low self-attribution of causal responsibility for his negative performance outcome on an ostensibly standardized aptitude test. The results indicated that the actor was evaluated more positively to the degree that he accepted more personal responsibility for his performance. In the second study, we examined the reactions of depressed and nondepressed observers to an actor's high or low self-attributions of causal responsibility for his poor performance on a test of analytical ability. On the basis of the notion that the chronic lack of control and resultant uncertainty, presumably characteristic of depressed persons, motivates attributional information processing, we expected depressed observers to be more sensitive to the actor's violation of the norm of internality and to respond with more social disapproval than nondepressed observers. Results generally were consistent with this reasoning. Experimental findings are discussed in terms of the interpersonal implications of expressed attributions.     

Mathematical Knowledge for Teaching Fraction Multiplication

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers' explanations and responses to their students' reasoning over extended sequences of lessons led to a theoretical frame that emphasizes relationships between teachers' unit structures and pedagogical purposes for using drawings. In particular, the present study builds on the distinction made in past research between reasoning with two and with three levels of quantitative units and demonstrates that reasoning with three levels of units is necessary but insufficient if teachers are to use students' reasoning with units as the basis for constructing generalized numeric methods for fraction arithmetic. Teachers need also to assemble three-level unit structures with flexibility supported by drawn versions of the distributive property.     

Validity of college admission indices for Jews and Arabs in Israel

This study examines Israeli cultural group differences in scholastic aptitude and achievement indices as well as the differential construct and predictive validity of precollege admission indices for Jewish and Arab students in Israel. The sample was composed of 1778 Jewish and 1017 Arab student candidates applying for admission to a major university. The admission indices include five scholastic aptitude subtests appearing on both the Hebrew and Arabic versions of the college entrance test battery and matriculation certificate grades in three required subjects. The predictor battery shows comparable factor structure across cultural groups. The correlations between aptitude and achievement predictors and first-year college G.P.A. were homogeneous across the groups. A slight degree of intercept bias was evidenced with the predictive indices tending to over predict the scholastic achievement of Arab students and under predict that of their Jewish counterparts. The results are consistent with previous research in America showing negligible differences in the construct and predictive validity of college admission tests for different cultural and racial groups.     

Cross language learning disabilities and verbal versus spatial memory

The research reported in this talk involves comparisons of verbal and spatial memory tasks across groups of children (and adults) with different types of learning difficulties. The research focuses on children with literacy acquisition problems and investigates whether such problems are related to specific areas of deficit. In the first piece of research, children with dyslexia (literacy learning problems) and dyspraxia (motor deficits) were contrasted on measures of memory (for example, tasks that required the retention of sequences of verbal material or spatial movements) and additional measures of literacy (reading and spelling), phonological (awareness of sounds within words) and motor (fine and gross motor tasks) functioning. The data were consistent with a dissociation between tasks/groups such that dyslexics showed weak phonological processing but intact visuo-spatial processing, whereas children with dyspraxia showed weaknesses on task involving visuo-spatial information, but average levels of performance on tasks that required phonological processing. Similar results were identified amongst adult groups, consistent with a deviant level of functioning rather than a developmental delay. A second line of research contrasted children with or without literacy problems across language backgrounds (English, Arabic, Chinese and bilingual children). Consistent with the dyslexia data, children with poor English literacy skills showed weaknesses in verbal/phonological memory tasks but not in visuo-spatial memory. However, for Chinese-language children, visuo-spatial memory differed between good and poor literacy learners, but there was little evidence for verbal memory differences. In contrast, the Arabic and bilingual children showed differences in both verbal and visuo-spatial areas, although the evidence was consistent with enhanced visual/spatial skills amongst the good literacy groups, rather than poor literacy children showing weaknesses in those tasks. These data suggest that the influence of memory skills on learning may vary with the language of instruction. A final line of enquiry considers whether teaching strategies to children with learning difficulties may overcome some of the identified memory deficits and lead to better levels of learning. English language children with learning difficulties were taught visual and verbal strategies to support retention of materials in short-term memory tasks. In the majority of cases, learning was improved when it focused on visuo-spatial strategies but not when verbal strategies were used. These data support the relationship between learning difficulties and different aspects of short-term memory that may lead to poor levels of learning. It also presents evidence that memory (particularly those related to visuo-spatial) processes are influenced by the context within which learning is taking place, both in terms of the language of instruction and the strategies used to support learning. For some children with educational difficulties based around language-related deficits, visuo-spatial strategies may support acquisition.     

Sex differences in scholastic aptitude: The Israeli scene

The major goal of the present study is two-fold: (a) To assess the direction, magnitude and profile of sex differences in scholastic aptitude test performance among Israeli college student candidates and (b) to test for possible sex bias in the construct validity of aptitude test scores. The analyses are based on the college admissions aptitude test scores of 1088 female and 690 male college candidates, applying for admissions to a major Israeli campus. On the whole, the data are consistent with much previous research, generated mainly from the American scene, showing small but consistent sex differences in favor of male examinees for the test as a whole and for the quantitative subscale, in particular. Also, the sex difference profiles for varying ethnic groups in the sample are surprisingly similar. Furthermore, our data show little evidence for differential construct validity of ability test scores by gender. On the whole, our data lend a greater degree of generality and cross-cultural validity to the bulk of previous research negating the sex bias contention and pointing to negligible gender differences in scholastic aptitude.     

L’apport des tests d’aptitudes dans le recrutement : l’exemple de la NV5-R

From the observation of a limited use of aptitude tests in the recruitment process, this article attempts to illustrate the relevance of such tests from applied research on the recruitment of sales persons. Thus, 32 candidates have participated in the recruitment process that is traditionally practiced by the organization, to which we have added three of the subtests of the battery NV5-R. The comparison of the scores at this test and the results of the classical procedure of recruitment for each subject shows that similar information is obtained by these two methods of selection. The contribution of aptitude tests in selection procedures has been discussed in terms of these results while laying the limitations of this study.     

On the form of the forgetting function: the effects of arithmetic and logarithmic distributions of delays

Forgetting functions with 18 delay intervals were generated for delayed matching-to-sample performance in pigeons. Delay interval variation was achieved by arranging five different sets of five delays across daily sessions. In different conditions, the delays were distributed in arithmetic or logarithmic series. There was no convincing evidence for different effects on discriminability of the distributions of different delays. The mean data were better fitted by some mathematical functions than by others, but the best-fitting functions depended on the distribution of delays. In further conditions with a fixed set of five delays, discriminability was higher with a logarithmic distribution of delays than with an arithmetic distribution. This result is consistent with the treatment of the forgetting function in terms of generalization decrement.     

Stress and blood glucose in type II diabetes mellitus

Six adults with non-insulin dependent diabetes mellitus participated in a laboratory procedure to determine the effects of an acute Stressor, mental arithmetic, on blood glucose, cardiovascular, and subjective indices of stress. They then completed 12 days home monitoring of stressful events, subjective stress, and blood glucose. Diet and activity were controlled to evaluate the direct effects of stress on blood glucose in the natural environment. Laboratory results showed significant increases in blood glucose, cardiovascular (HR and SBP), and subjective stress ratings during the mental arithmetic task when compared to a resting condition. Home monitoring data were consistent with the laboratory findings; blood glucose range tended to be greater on high vs low stress days, especially when the difference between high and low stress was greatest. These findings suggest that the laboratory stress induction procedure was externally valid and that in the natural environment, stress has a hyperglycemic effect on blood glucose.     

Individual differences in digit span, susceptibility to proactive interference, and aptitude/achievement test scores

Individual differences in digit span, susceptibility to proactive interference, and various aptitude/achievement test scores were investigated in two experiments with adults. Susceptibility to proactive interference was estimated from performance in a position task in Experiment 1, and from the Brown-Peterson task in Experiment 2. In contrast to previous research, digit span was strongly correlated with many of the aptitude/achievement scores in both experiments, suggesting that the digit span task taps some important components of mental ability. The results of both experiments were also consistent in offering no support for the hypothesis that susceptibility to proactive interference is an important source of span differences. Finally, the results of Experiment 2 suggest that susceptibility to proactive interference is a source of individual differences in reading comprehension and knowledge of word meanings, but not in grammar and word usage skills, reading rate, or quantitative ability.     

Distinct Pathways From Parental Beliefs and Practices to Children’s Numeric Skills

It is imperative to identify contextual factors contributing to the development of early math skills, considering their role in later academic achievement. To pursue this goal, the present study investigated the paths connecting parental beliefs and practices during the preschool years to children’s numeric skills at the end of kindergarten (N = 98). Results were consistent with theoretical predictions of specific relations between particular types of parental input and different aspects of number knowledge. Direct math learning activities mediated the relation between parental beliefs and children’s number identification skills. Daily activities involving quantitative components mediated the relation between parental beliefs and children’s numerical magnitude understanding. Both types of activities predicted arithmetic skills that integrate the basic aspects of symbolic number knowledge. These findings contribute to developmental theory by specifying how characteristics of children’s environments are related to particular aspects of their development, which is critical for informing intervention work to improve early math skills.     

The utility of visuospatial mnemonics is dependent on visuospatial aptitudes

Classic studies in cognition have demonstrated that the use of appropriate memory mnemonics can reliably increase recall performance. However, is the facilitative effect of mnemonics consistent across all individuals? As some mnemonics explicitly contain a large visuospatial component, does normal variance in visuospatial aptitudes predict the effectiveness of such strategy usage? To explore this question, participants who varied in visuospatial ability were asked to recall several lists of words, and either did or did not use a visuospatial mnemonic. Results indicated that effective mnemonic usage was directly dependent on participants' visuospatial ability, and those lower in visuospatial aptitudes actually produced lower recall performance when asked to use such a mnemonic. Similarly, those lower in visuospatial aptitude also reported that mnemonic usage made the task significantly more difficult. These findings suggest that individual differences in relevant cognitive abilities can influence the effectiveness of memory strategies commonly used to enhance recall.     

Emotional Reactions to Health Status Changes and Emotional Well-Being Among HIV-Positive Persons with Limited Reading Literacy

People living with HIV-AIDS experience emotional distress in response to negative changes in their health status. The current study hypothesized that individuals with poorer health literacy skills would evidence greater emotional distress in response to negative changes in health status compared to persons with higher health literacy skills. HIV positive persons (N = 294) completed anonymous surveys that included measures of depression and social support and a subset of 98 participants completed two experimental vignettes depicting a person receiving test results showing an increase in HIV viral load (negative health changes) followed by a vignette suggesting decreased viral load (improved health changes). Responses to affective reactions and coping strategies indicated that persons with lower health literacy skills more strongly endorsed negative affective states and maladaptive coping strategies compared to persons with higher health literacy skills. In addition, lower health literacy was associated with greater symptoms of affective depression and poorer social support, whereas higher literacy was associated with greater negativistic thinking. Findings suggest the need for patient education and counseling regarding changes in health status among people living with HIV-AIDS, particularly persons with limited health literacy skills.     

Sexual Arousal and the Polarization of Perceived Sexual Attractiveness

It was predicted that sexual arousal would lead to polarized evaluations of the sexual attractiveness and desirability of those of the opposite sex. More specifically, sexual arousal was hypothesized to enhance the perceived sexual attractiveness of medium and highly attractive target persons but to decrease the perceived sexual attractiveness of unattractive target persons. Sexually aroused and nonaroused subject's of both sexes rated the sexual attractiveness, dating desirability, and marriage desirability of low, medium, and high attractive people of the opposite sex. As expected, sexually aroused subjects rated medium and high attractive targets as more sexually attractive but low attractive targets as less sexually attractive than did nonaroused subjects. The findings were interpreted as consistent with a two process evaluative polarization hypothesis but also discussed in terms of arousal misattribution and arousal transfer hypotheses.     

小学3-6年级学生解决比较问题的研究

本研究对465名小学3—6年级学生解决不同类型的比较问题进行了研究。结果表明：(1)小学生解决比较问题的成绩受问题类型及年级的交互影响。儿童在一致算术问题上的成绩都很好,且显著优于不一致算术问题。在不一致算术问题、一致代数问题及不一致代数问题上,存在年级差异。5、6年级学生优于4年级学生。(2)小学生在算术问题上的通过率高于代数问题,5、6年级学生的通过率高于3、4年级。除一致算术问题外,其它类型比较问题的通过率较低。(3)小学生解决比较问题的成绩无性别差异。     

An empirically feasible approach to the epistemology of arithmetic

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology.     

An evaluation of reciprocal peer tutoring across elementary school settings

The effects of a reciprocal peer tutoring (RPT) intervention on the arithmetic performance of 12 low-income, underachieving elementary school students across three elementary school settings were evaluated and a partial component analysis was conducted. The results indicated that merely teaming students and providing them with positive attention for constructive team activities had no clear effect on arithmetic performance. An RPT condition that involved peer-managed group contingencies yielded consistent increases in rate of accurate arithmetic performance to a level that was significantly above the rates of untreated control students. Attendance and maintenance data also supported the efficacy of the intervention.