TEACHING MULTIPLICATION FACTS TO STUDENTS WITH LEARNING DISABILITIES

Multiple baseline designs were used to examine the effects of an instructional package on accuracy of performance in solving multiplication facts by 3 students with learning disabilities. The instructional package included the following components: (a) a modified instructional sequence in which multiplication facts were grouped into the zeros, ones, doubles, fives, and nines categories, and those remaining; (b) identification of the category in which each fact belonged; (c) mnemonic strategies associated with solving facts in each category; and (d) steps to be completed for solving facts in each category. Results indicated that the instructional package produced substantial and immediate effects. After receiving instruction, a participant's accuracy was often 100%, and this was maintained throughout the evaluation even as other strategies were introduced. Comparable results occurred across students, demonstrating replication of the effects of the instructional package.     

The Role of Apparent Constraints in Normative Reasoning: a Methodological Statement and Application to Global Justice

The assumptions that are made about the features of the world that are relatively changeable by agents and those that are not (constraints) play a central role in determining normative conclusions. In this way, normative reasoning is deeply dependent on accounts of the empirical world. Successful normative reasoning must avoid the naturalization of constraints and seek to attribute correctly to agents what is and is not in their power to change. Recent discourse on global justice has often come to unjustified conclusions about agents obligations due to a narrow view of what is changeable and by whom.I would like to thank for their helpful comments Christian Barry, Rudiger Bittner, Darrel Moellendorf and Thomas Pogge.     

Sex differences in the relation between math performance, spatial skills, and attitudes

Sex differences have been previously found in cognitive and affective predictors of math achievement, including spatial skills and math attitudes. It is important to determine whether there are sex differences not only in the predictors themselves, but also in the nature of their relation to math achievement. The present paper examined spatial skills and math attitudes as predictors of curriculum-based measures of math performance in middle-school students, specifically comparing the patterns of these predictive relations for boys and girls. The results of the current study showed that, despite similar levels of math performance for boys and girls, the significance of particular predictors varied as a function of sex. Specifically, spatial skills predicted math performance in boys, but not in girls. We suggest that sex differences in spatial reasoning in conjunction with the differential involvement of spatial reasoning in math problem solving may lead to later sex differences in math outcomes.     

A Comparison of Taped-Problem Interventions to Increase Math Fact Fluency: Does the Length of Time Delay Affect Student Learning Rates?

An alternating treatments design with a control condition was used to evaluate and compare the effects of two taped-problem interventions on addition fact fluency. Both taped-problem interventions were identical with the exception of the time delay between the auditory cue of the problem and the answer. One condition used a 2-s delay and the other condition used no delay. Results showed that both taped-problem conditions showed growth in student digits correct per minute scores and that the no-delay condition was slightly more efficient as the taped-problem no-delay procedure took approximately 33% less time. Discussion focuses on using comparative intervention designs to detect nuances in procedures to improve our understanding of math fact interventions that result in the highest learning rates.     

Investigating the predictive roles of working memory and IQ in academic attainment

There is growing evidence for the relationship between working memory and academic attainment. The aim of the current study was to investigate whether working memory is simply a proxy for IQ or whether there is a unique contribution to learning outcomes. The findings indicate that children’s working memory skills at 5 years of age were the best predictor of literacy and numeracy 6 years later. IQ, in contrast, accounted for a smaller portion of unique variance to these learning outcomes. The results demonstrate that working memory is not a proxy for IQ but rather represents a dissociable cognitive skill with unique links to academic attainment. Critically, we find that working memory at the start of formal education is a more powerful predictor of subsequent academic success than IQ. This result has important implications for education, particularly with respect to intervention.     

Comparison of a math fact rehearsal and a mnemonic strategy approach for improving math fact fluency

The current study used a randomized controlled trial to compare the effects of a practice-based intervention and a mnemonic strategy intervention on the retention and application of single-digit multiplication facts with 90 third- and fourth-grade students with math difficulties. Changes in retention and application were assessed separately using one-way ANCOVAs in which students' pretest scores were included as the covariate. Students in the practice-based intervention group had higher retention scores (expressed as the total number of digits correct per minute) relative to the control group. No statistically significant between-group differences were observed for application scores. Practical and theoretical implications for interventions targeting basic multiplication facts are discussed.     

The mathematical abilities of children with cochlear implants

Research has shown that cochlear implants give rise to improvements in speech recognition and production in children with profound hearing loss but very few studies have explored mathematical abilities in these children. The current study compared the mathematical abilities of 24 children with cochlear implants (mean age 10 years 1 month) to a control group of 22 hearing children (mean age 9 years 8 months). The math questions were categorized into questions that tapped into arithmetic or geometrical reasoning. It was predicted that the cochlear implant group would perform below the hearing group on the arithmetic questions but not the geometrical reasoning questions. Unexpectedly, the results showed that the cochlear implant group performed significantly below the hearing group on both types of math questions, but that this difference was mediated by language skill as assessed by vocabulary knowledge. The clinical implications of these results and possible future research results are considered.     

The Idea of an Exact Number: Children's Understanding of Cardinality and Equinumerosity

Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one‐to‐one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) linked children's understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood.     

Investigating the Relationship Between Attention and Working Memory in Clinical and Community Samples

The first aim of the present study was to investigate whether differences in core deficits in ADHD subtypes lead to dissociable working memory profiles. The second aim was to compare the working memory profiles of inattentive students with those identified as having poor working memory, as they exhibit very similar behavioral profiles. Finally, the relationship between working memory and academic attainment in these groups were also of interest. Four groups of 9-year-olds were recruited: a community sample of children with inattentive symptoms, a clinically diagnosed group of children with ADHD-Combined, children with low working memory, and a healthy comparison group. They were assessed on measures of working memory, IQ, academic attainment, and sustained attention. The findings indicated that the combined and inattentive subtypes could not be distinguished on the basis of their working memory profile. In contrast, those with inattentive symptoms did better on the short-term memory tasks than the low working memory group. The majority of all three atypical groups performed very poorly in reading and math. This pattern can be interpreted as reflecting the link between working memory and academic attainment, even in those with attention problems.     

Test anxiety and metacognitive skillfulness: Availability versus production deficiencies

Abstract

This paper focuses on the role of metacognition in test anxiety. In two experiments, the metacognitive skillfulness of high vs. low test-anxious secondary school students was contrasted. Low test-anxious subjects exhibited a superior metacognitive skillfulness during math performance relative to high test-anxious subjects. Furthermore, differences in metacognitive skillfulness were performance related. In order to unravel causality in the relation between metacognition and test anxiety, two types of test-anxious students may be distinguished analogous to Naveh-Benjamin (1991). Type-1 students would lack metacognitive skills (availability deficiency), through which they experience failure and develop test anxiety. Type-2 students would experience task irrelevant thoughts, which causes cognitive interference with available metacognitive skills (production deficiency). Results of Study 1 reveal that metacognitive cueing may represent an adequate method for the identification of both types. Due to time-constraints, metacognitive cueing in Study 2 failed to do so.