Strategy Transformations in Learning Disabled Children's Math Performance

Swanson, H. Lee; Rhine, Barbara

doi:10.1177/002221948501801007

Cited by 21 publications

(7 citation statements)

References 18 publications

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“…Put differently, they remain overly reliant on relatively slow counting strategies [Mazzocco et al, 2008]. Although children with MD can be taught reasoning strategies [e.g., Thornton et al, 1983;Torbeyns et al, 2004;Tournaki, 2003], they do not spontaneously invent the strategies-that is, the children fail to independently achieve Phase 2 [Swanson and Cooney, 1985;Swanson and Rhine, 1985]. They typically are unable to retain basic combinations, particularly larger combinations with sums over 10 [Smith, 1921;Kraner, 1980].…”

Section: Why Do Children Have Difficulty Learning the Basic Combinatimentioning

confidence: 99%

Why can't Johnny remember the basic facts?

Baroody

Bajwa

Eiland

2009

Dev Disabil Res Revs

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Memorizing the basic number combinations, such as 9 þ 7 5 16 and 16 2 9 5 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage View), memorizing a basic fact is a simple form of learning-merely forming and strengthening an association between an expression and its answer. The two primary reasons this simple form of learning does not occur are inadequate practice or, in cases where adequate practice has been provided, a defect in the learner. According to the number sense perspective (Active Construction View), memorizing the basic combinations entails constructing a well-structured or -connected body of knowledge that involves patterns, relations, algebraic rules, and automatic reasoning processes, as well as facts. In effect, fluency with the basic number combinations begins with and grows out of number sense. Aspects of number sense critical to such fluency begin to develop in the preschool years. According to the Active Construction View, the primary cause of problems with the basic combinations, especially among children at risk for or already experiencing learning difficulties, is the lack of opportunity to develop number sense during the preschool and early school years.

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Section: Why Do Children Have Difficulty Learning the Basic Combinatimentioning

confidence: 99%

Why can't Johnny remember the basic facts?

Baroody

Bajwa

Eiland

2009

Dev Disabil Res Revs

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“…Poor recall of arithmetic facts, of course, leads to difficulties executing calculation procedures and immature problem-solving strategies (Geary, 1993). For example, the literature suggests that children with MD do not show the shift from direct counting procedures to a memory-based production of the solution (e.g., Swanson & Rhine, 1985). That is, they do not remember that certain combinations of new numbers yield a certain result and they have difficulty accessing facts from longterm memory (LTM); as a result, they have difficulty engaging in labor-intensive calculations.…”

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confidence: 99%

Math Disabilities: A Selective Meta-Analysis of the Literature

Swanson

Jerman

2006

Review of Educational Research

299

262

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This article synthesizes published literature comparing the cognitive functioning of children who have math disabilities (MD) with that of (a) average-achieving children; (b) children who have reading disabilities (RD); and (c) children who have co-morbid disabilities (MD+RD). Average achievers outperformed children with MD on measures of verbal problem solving, naming speed, verbal working memory (WM), visual-spatial WM, and long-term memory (LTM). Children with MD outperformed co-morbid children on measures of literacy, visual-spatial problem solving, LTM, short-term memory (STM) for words, and verbal WM. Children with MD could be differentiated from children with RDonly on naming speed and visual-spatial WM. Differences in cognitive functioning between children with MD and average achievers were related primarily to verbal WM when the effects of all other variables (e.g., age, IQ, and other domain categories) were partialed out.

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“…For instance, analyses of problem solving in children with MD Geary, Brown, & Samaranayake, 1991) have shown that these students use less efficient strategies for retrieving information than their typically achieving peers. Children with MD are also less likely to retrieve answers related to math problems directly from memory and depend more on the use of fingers or verbal counting (Swanson & Rhine, 1985). One factor that has been overlooked in much of the research linking MD and working memory is children's declarative knowledge of strategies.…”

mentioning

confidence: 99%

Does Strategy Knowledge Influence Working Memory in Children with Mathematical Disabilities?

Keeler

Swanson

2001

J Learn Disabil

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This study investigated the relationship between working memory (WM), declarative strategy knowledge, and math achievement in children with and without mathematical disabilities (MD). Experiment 1 examined the relationship between strategy knowledge, verbal WM, and visual-spatial WM in children with MD as a function of initial, gain, and maintenance conditions. The results showed that after partialing the influence of reading, stable strategy choices rather than specific strategy knowledge was related to verbal and visual-spatial WM span in high demand (maintenance) conditions. Experiment 2 compared children with MD to a group of chronological age-matched children and a group of math ability-matched children on the same conditions as Experiment 1. Age-matched children's verbal and visual-spatial WM performance was superior to that of children with MD, whereas WM performance was statistically comparable between children with MD and younger children matched on math ability. The selection of expert strategies was related to high WM span scores in the initial conditions. After controlling for reading achievement in a regression analysis, verbal and visual-spatial WM, stable verbal strategy choices, and expert strategy choices related to visual-spatial processing all contributed independent variance to math achievement. Overall, these results suggest that WM and math achievement are related to strategy knowledge.

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Strategy Transformations in Learning Disabled Children's Math Performance

Cited by 21 publications

References 18 publications

Why can't Johnny remember the basic facts?

Why can't Johnny remember the basic facts?

Math Disabilities: A Selective Meta-Analysis of the Literature

Does Strategy Knowledge Influence Working Memory in Children with Mathematical Disabilities?

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