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PubMedDate not supplied

Role of cognitive theory in the study of learning disability in mathematics.

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.

Cognition↗
PubMedDate not supplied

Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities.

The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of mathematical problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher mathematical word-problem-solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images.

Demography↗
PubMedDate not supplied

Mathematics learning disabilities: a view from developmental psychology.

U.S. education suffers from shortcomings that put even children possessing adequate intellectual abilities at risk for low mathematics achievements. Consequently, identifying and understanding children whose academic failure is influenced by a genuine learning disability requires a complex "developmental" research agenda. This perspective suggests the use of sensitive research methods--clinical interviews, ethnographies--to examine the development of children's construction of knowledge in the context of schooling. Researchers should consider such factors as the adequacy of classroom instruction, the availability in children of informal knowledge, the role of motivation, the effects of specific interventions, the role and operation of different cognitive processes in constructing mathematical understanding, children's difficulties across different areas of mathematics, and the development of children's thinking throughout the school years.

Adolescent↗
PubMedDate not supplied

Cognitive strategy instruction in mathematics for students with learning disabilities.

This article provides a context for understanding and using cognitive strategy instruction to improve students' performance in mathematics. The theoretical and research base for strategy instruction is reviewed, and characteristics of students who have difficulties in mathematics are discussed from a developmental perspective. Then, a practical illustration of cognitive strategy instruction used to assess the teach mathematical problem solving to middle school students with learning disabilities is presented.

Achievement↗
PubMedDate not supplied

Cognitive arithmetic and problem solving: a comparison of children with specific and general mathematics difficulties.

This study examined problem-solving and number-fact skills in two subgroups of third-grade children with mathematics difficulties (MD): MD-specific (n = 12) and MD-general (n = 12). The MD-specific group had difficulties in mathematics but not in reading, and the MD-general group had difficulties in reading as well as in mathematics. A comparison group of nonimpaired children (n = 24) also was included. The findings showed that on both story and number-fact problems, the MD-specific group performed worse than the nonimpaired group in timed conditions but not in untimed conditions. The MD-general group, on the other hand, performed worse than the nonimpaired group, regardless of whether tasks were timed or not. An analysis of children's strategies in untimed conditions showed that both the MD-specific and the MD-general groups relied more on backup strategies than the nonimpaired group. However, children in the MD-specific group executed backup strategies more skillfully than children in the MD-general group, allowing them to achieve parity with children in the nonimpaired group when tasks were not timed. The findings suggest that children with specific MD have circumscribed deficits associated with fact retrieval, whereas children with general MD have more basic delays associated with problem conceptualization and execution of calculation procedures.

Achievement↗
PubMed1980

Sex differences in factorial dimension of verbal, logical, mathematical and visuospatial ability.

The factor structure of verbal, logical, visuospatial, and mathematical ability was compared for responses from 52 male and 54 female college students. Separate verbal, quantitative, and visuospatial factors were isolated among males while compound verbal-mathematical-visuospatial and verbal-logical-field dependence factors were isolated among females. The data supported the hypothesis of sex-related differences in the factorial organization of verbal, mathematical, reading, writing, and visuospatial ability.

Female↗
PubMed2002

Goal orientation, perceived task outcome and task demands in mathematics tasks: effects on students' attitude in actual task settings.

BACKGROUND: In earlier studies, it has been found that students' domain-specific cognitions and personal learning goals (goal orientation) influence task-specific appraisals of actual learning tasks. The relations between domain-specific and task-specific variables have been specified in the model of adaptive learning. In this study, additional influences, i.e., perceived task outcome on a former occasion and variations in task demands, were investigated. AIM: The purpose of this study was to identify personality and situational variables that mediate students' attitude when confronted with a mathematics task. Students worked on a mathematics task in two subsequent sessions. Effects of perceived task outcome at the first session on students' attitude at the second session were investigated. In addition, we investigated how differences in task demands influenced students' attitude. Variations in task demands were provoked by different conditions in task-instruction. In one condition, students were told that the result on the test would add to their mark on mathematics. This outcome orienting condition was contrasted with a task-orienting condition where students were told that the results on the test would not be used to give individual grades. SAMPLE: Participants were sixth grade students (N = 345; aged 11-12 years) from 14 primary schools. METHOD: Multivariate and univariate analyses of (co)variance were applied to the data. Independent variables were goal orientation, task demands, and perceived task outcome, with task-specific variables (estimated competence for the task, task attraction, task relevance, and willingness to invest effort) as the dependent variables. RESULTS: The results showed that previous perceived task outcome had a substantial impact on students' attitude. Additional but smaller effects were found for variation in task demands. Furthermore, effects of previous perceived task outcome and task demands were related to goal orientation. CONCLUSION: The resulting pattern confirmed that, in general, performance-oriented learning goals emphasised the negative impact of failure experiences, whereas task-oriented learning goals had a strengthening effect on how success experiences influenced students' attitude.

Attitude↗
PubMed2001

A mathematical evaluation of dose-dependent PpIX fluorescence kinetics in vivo.

The in vivo pharmacokinetics of protoporphyrin IX (PpIX) after administration of 5-aminolevulinic acid (ALA) cannot be described accurately by mathematical models using first-order rate processes. We have replaced first-order reaction rates by dose-dependent (Michaelis-Menten [MM]) reaction rates in a mathematical compartment model. Different combinations of first-order and dose-dependent reaction rates were evaluated to see which one would improve the goodness-of-fit to experimentally determined in vivo PpIX fluorescence kinetics as a function of concentration. The mathematical models that were evaluated are all based on a three-compartment model for drug distribution, conversion to PpIX and subsequent conversion to heme. Implementation of dose-dependent reaction rates improved the goodness-of-fit and enabled interpolation to other drug doses. For most data sets the time constant for delivery to the target cells turned out to be dose dependent. For all data sets the use of MM rates for the conversion of ALA to PpIX yielded better fits. The clearance of PpIX turned out to be a first-order process for all doses and types of administration. Fluorescence curves measured on a specific tissue type but obtained in different studies with different measurement techniques could be described with a single set of parameters.

Aminolevulinic Acid↗
PubMed1991

Assessment of threshold and saturation pressure in the baroreflex function curve: a new mathematical analysis.

The baroreflex function has been assessed with logistic function analysis, a mathematical model suitable for function curves of sigmoid shape. The nonlinear (sigmoid) relationship between carotid sinus pressure (CSP) and systemic arterial pressure (SAP) reflects threshold and saturation of the SAP responses to CSP changes. The threshold and saturation pressures (TP and SP) are often determined by gross inspection from the experimental recordings. Objective and accurate determination of TP and SP may be achieved by mathematical analysis. Kent et al. (Cardiology, Vol. 57, pp. 295-310, 1972) provided equations that estimated SP and TP to be +/- 1.317/k from the midrange CSP (k, the slope coefficient of a curve). Tan et al. (Circ. Res., Vol. 65, pp. 63-70, 1989) recently used an equation to calculate TP based on the consideration that it is about 95% of the maximal SAP. In this report, we elaborated new equations for the estimation of SP and TP, which approximate midrange pressure +/- 2/k. The accuracy of these new equations compared to other equations was tested using various sets of simulation data. In addition, experiments were conducted in anesthetized dogs with isolated carotid sinus. The open-loop CSP-SAP curves were obtained following various holding pressure (HPs) to demonstrate the phenomenon of baroreflex acute resetting. The effects of using different equations on the values of TP, SP, and delta TP/delta HP (extent of resetting) were analyzed. Both simulation and experimental data revealed that the equations of Kent et al. gave rise to values of TP and SP far different from the realistic values. The values of TP calculated by equation of Tan et al. were dependent on the maximal SAP and the slope of the function curve. The TP and SP (+/- 2/k from the midrange pressure of the sigmoid curve) obtained by our new equations were not significantly affected by the maximal SAP and the curve slope. The mathematical analysis may be particularly useful for comparison among various baroreflex curves with different maximal SAP and/or curve slope.

Animals↗
PubMed2000

Middle-school students of United Arab Emirates: effects of heterogeneous small group work on attitudes toward mathematics.

This study compared the effects of two instructional strategies, small heterogeneous cooperative learning experience versus lecture and discussion, on students' attitudes toward mathematics. 54 boys and 57 girls in Grade 8 of four middle-school mathematics classes participated. Two classes (57 students) were taught using a cooperative learning method and the other two classes (54 students) were taught using traditional lecture and discussion. Differences between attitudes of boys and girls were also investigated and discussed in the light of Arabic culture. The results suggested that cooperative learning might be a valuable method with which to teach mathematics concepts to boys.

Adolescent↗
PubMed1991

Bender-Gestalt developmental scores: predicting reading and mathematics achievement.

This study examined the relative importance of perceptual-motor processes and intelligence in predicting reading and mathematics achievement of children of low birthweight. Subjects were two groups of 153 children, ages 6 to 12 years, of either low (3 lb. or below, n = 72) or normal birthweight (n = 81) who participated in a comparative study on sequelae of children of low birthweight. To examine the utility of the Bender-Gestalt test in predicting academic achievement, Bender developmental scores, WRAT reading and mathematics scores, and WISC-R Full Scale IQs from both groups were compared and then intercorrelated separately. The mean comparisons indicated that children of low birthweight scored significantly lower on both Bender scores and reading achievement and had lower IQs than those of normal birthweight. Bender scores also appeared to have more utility for predicting reading and mathematics achievement for children of low birthweight than for those of normal birthweight.

Achievement↗
PubMed1995

A study of planning and mathematics instruction for students with learning disabilities.

The purpose of this study was to extend research in training the use of cognitive strategies or planning to mathematical computation for 4 students with specific learning disabilities. A cognitive education method utilized in previous research was duplicated. It was expected that students would find the instruction differentially effective based upon their initial scores on a measure of planning. Using the Planning, Attention, Simultaneous, Successive model as a base, a cognitive instruction which facilitated planning was provided to two students with low scores on planning, obtained using an experimental version of the Das-Naglieri Cognitive Assessment System, and two students with average planning scores. All students completed three sessions of baseline and seven sessions of cognitive instruction in addition and multiplication. During the cognitive instruction phase, 5-min. sessions of self-reflection and verbalization of strategies about the mathematics problems were conducted after each initial 10-min. session of mathematics. Scores on addition problems showed that all students improved. On multiplication, however, 2 students with low planning scores improved considerably but not 2 with higher planning scores. Implications are provided.

Child↗
PubMed2000

Conceptions of and approaches to learning mathematics.

Pearson correlation coefficients indicated a different relationship between conceptions of mathematics and approaches to learning mathematics to that reported in literature. It was concluded that the 154 students (82 women and 72 men) followed a strategic approach to learning mathematics.

Adolescent↗
PubMed2001

Psychometric characteristics of the conceptions of mathematics questionnaire.

This study describes the psychometric characteristics of the 19-item Conceptions of Mathematics Questionnaire for a total of 158 students (86 women and 72 men). The coefficient alpha of internal consistency reliability was .75. Principal components analysis with varimax rotation indicated a two-component solution could be extracted. The two theoretically meaningful dimensions were fragmented conceptions (alpha = .80) and cohesive conceptions (alpha = .80). The former entails seeing mathematics as number rules and formulae to be used to solve problems. Students who hold this conception use rote learning and memorization. In contrast, the latter entails seeing mathematics as a complex logical system for solving complex problems. Students with such a conception approach learning to attain, develop, and apply knowledge.

Adolescent↗
PubMed2001

University students' conceptions of first-year mathematics.

The 1998 Crawford, Gordon, Nicholas, and Prosser Conceptions of Mathematics scale was administered to 156 first-year university students at a large public university in the midwestern United States. The scale represented fragmented and cohesive conceptions of mathematics. The reliability estimated as internal consistency had a Cronbach alpha of .80 for the fragmented scale and .87 for the cohesive scale. Factor analysis of the intercorrelations indicated the same two factors of fragmented and cohesive as in the original and other replicating studies. Students' conceptions of mathematics in this study were comparable to those reported in the original study.

Adolescent↗
PubMed2003

A mathematics content course and teaching efficacy beliefs of undergraduate majors in education.

This study was designed to assess the mathematics teaching efficacy beliefs of undergraduates in elementary education through a manipulative-based course in mathematics. Responses of 106 university undergraduates to the 21-item Mathematics Teaching Efficacy Beliefs administered as pre- and posttest without a control group showed a significant immediate postcourse change in their efficacy beliefs using dependent t test.

Adolescent↗
PubMed2005

Attitudes of university precalculus students toward mathematics.

To investigate the attitudes of 200 university students (83% freshmen) toward mathematics, a questionnaire was administered to report on their attitudes toward mathematics. Analysis indicated that students studying precalculus had a somewhat positive attitude toward mathematics.

Adolescent↗
PubMed2005

Nigerian undergraduate education majors' conceptions of mathematics.

The Conceptions of Mathematics Questionnaire by Crawford, et al. was administered to 130 southwest Nigerian undergraduate education majors who took mathematics. Coefficient alphas of .86 and .84 for the Fragmented and Cohesive subscales were similar to prior values. There were no statistically significant mean differences between men and women or between undergraduates taking mathematics with science and nonscience topics.

Adolescent↗