The Development of Numerical Understandings

Siegler, Robert S.; Robinson, Mitchell B.

doi:10.1016/s0065-2407(08)60072-5

Cited by 223 publications

(249 citation statements)

References 44 publications

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“…Moreover, the pattern of retrieval errors generally mirrored the pattern of counting errors. The first of these results supports the argument that strategy choices are influenced by the probability of retrieving the correct answer, and the second finding suggests that the distribution of associations between a problem and all potential answers to that problem develops based upon the execution of more basic numerical operations, such as counting (Siegler & Robinson, 1982;Siegler & Shrager, 1984;Siegler, 1986).…”

Section: Discussionmentioning

confidence: 67%

“…During the experimental session, the strategy used to solve each problem was recorded by the experimenter and each was classified as one of the four strategies described by Siegler and Robinson (1982): (a) counting fingers, (b) fingers, (c) verbal counting, or (d) no visible strategy (memory retrieval). The counting fingers and verbal counting trials were further classified in accordance with the specific algorithm used for problem solving.…”

Section: Methodsmentioning

confidence: 99%

“…Within the strategy choice model, four basic strategies for solving addition problems have been identified (Siegler, 1986;Siegler & Robinson, 1982;Siegler & Shrager, 1984). Of these four strategies, three are visible or audible, overt strategies, and are termed (a) counting fingerschildren use their fingers to physically represent the problem integers and then count their fingers to reach a sum; (b) fingers-children use their fingers to represent the integers but do not visibly count them before giving an answer; and (c) verbal counting-children count audibly or move their lips as if counting implicitly.…”

Section: Strategy Choice Modelmentioning

confidence: 99%

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A componential analysis of an early learning deficit in mathematics

Geary

1990

Journal of Experimental Child Psychology

227

280

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This study was designed to assess strategy choice and information-processing differences in normal and mathematically disabled first and second grade children. Twenty-three normal and 29 learning disabled (LD) children solved 40 computerpresented simple addition problems. Strategies, and their associated solution times, used in problem solving were recorded on a trial-by-trial basis and each was classified in accordance with the distributions of associations model of strategy choices. Based on performance in a remedial education course, as indexed by achievement test scores, the LD sample was reclassified into an LDimproved group and an LD-no-change group. No substantive differences comparing the normal and LD-improved groups occurred in the distribution of strategy choices, strategy characteristics (e.g., error rates), or rate of information processing. The performance characteristics of the LD-no-change group, as compared to the two remaining groups, included frequent counting and memory retrieval errors, frequent use of an immature computational strategy, poor strategy choices, and a variable rate of information processing. These performance characteristics were discussed in terms of the strategy choice model and in terms of potential long-term memory and working memory capacity deficits. In addition, implications for remedial education in mathematics were discussed. o 1990 ACademic Press, Inc.A learning disability in mathematics achievement is characterized by the failure to acquire grade appropriate knowledge and problem-solving skills (Schoenfeld, 1987a). While traditional achievement measures allow for the identification of learning disabled (LD) students, they do not

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Section: Discussionmentioning

confidence: 67%

Section: Methodsmentioning

confidence: 99%

Section: Strategy Choice Modelmentioning

confidence: 99%

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A componential analysis of an early learning deficit in mathematics

Geary

1990

Journal of Experimental Child Psychology

227

280

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“…If Barrouillet et al are correct, then when children with MD/RD or MD retrieve facts from long-term memory, their errors should reflect frequent intrusions of related associations. For simple addition problems, counting-string associates of the addends might be one form of intrusion for children of this age (Siegler & Robinson, 1982); for instance, the counting-string associates for 5 ϩ 2 would be 6 and 3, respectively, the numbers that follow 5 and 2 in the counting sequence. Of course, some children might show both forms of retrieval deficit.…”

Section: Arithmeticmentioning

confidence: 99%

Numerical and Arithmetical Cognition: A Longitudinal Study of Process and Concept Deficits in Children with Learning Disability

Geary

Hamson

Hoard

2000

Journal of Experimental Child Psychology

537

539

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Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade ϭ 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n ϭ 42), a group of children who showed variable achievement test performance across grades (n ϭ 16), and a control group of academically normal peers (n ϭ 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.

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“…Brown and Burton (1978) found in their study that the students forget the place they count after a while since they use immature strategies like finger counting, and therefore make this error. Geary (1990), Siegler and Robinson (1982) indicated that this error was particularly common in addition operations. Because students count as 4, 5, 6 instead of 5, 6, 7 in an addition operation of 4+3, they get the incorrect result.…”

Section: Discussion Conclusion and Suggestionsmentioning

confidence: 99%

Examination of Addition and Subtraction Performances of Students with and without Learning Disabilities

Kumaş¹,

Ergül²

2017

IOJES

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In this study, addition and subtraction performances of students experiencing learning disability, mathematics difficulties, and typical development were examined. The study group was consisted of 30 students with learning disability, 30 with mathematic difficulties, and 30 with typical development. All participants attended third grade. Relational screening model was utilized for research purposes. A tool including 14 addition and subtraction questions developed by the researcher was used to gather data. Obtained data was analyzed through one-way analysis of variance. Results showed that in written operations, students with learning disabilities and with mathematics difficulties performed more slowly, had lower scores, and made more errors compared to those with typical development. In terms of comparing the types of errors made by students in written, all students seemed to make similar errors. © 2017 IOJES. All rights reservedKeywords 1 : learning disability, mathematics difficulties, addition and subtraction, error patterns Extended SummaryA learning disability mostly appearing as academic failure is connected to the problems experienced in the processes of auditory and visual perception, attention, memory, language development and learning using the cognitive strategies and the information processing systems (Glago, Mastropieri and Scruggs, 2009). There is a significant difference between the academic achievement and the learning potential of the individuals with learning disabilities and the difference continues although the appropriate learning experiences are provided (Bateman, 1992).Several studies have focused on academic difficulties experienced by students with learning disabilities. However, most of these studies concentrate on students' reading and writing problems while their difficulties in mathematics-related skills are overlooked. Moreover, recent research suggests that students with learning disabilities suffer from difficulties not only in literacy, but in mathematics as well (Hanich, Jordan, Kaplan and Dick, 2001). Approximately 25% of the students with learning disabilities were reported to have difficulties in acquiring the mathematics abilities (Miller, Butler and Lee, 1998;Rivera, 1997). Students having difficulties in learning mathematics are described under the term mathematics learning disabilities. Although they are a heterogeneous group, they show similar difficulties in some areas. The most common difficulties they experience have been reported to be difficulty in time and place-direction concepts, failure to solve the problems requiring counting operation, using immature or inappropriate strategies, solving the operations 1 Corresponding author's address:

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The Development of Numerical Understandings

Cited by 223 publications

References 44 publications

A componential analysis of an early learning deficit in mathematics

A componential analysis of an early learning deficit in mathematics

Numerical and Arithmetical Cognition: A Longitudinal Study of Process and Concept Deficits in Children with Learning Disability

Examination of Addition and Subtraction Performances of Students with and without Learning Disabilities

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