Children’s Counting and Concepts of Number

Fuson, Karen C.

doi:10.1007/978-1-4612-3754-9

Cited by 985 publications

(1,057 citation statements)

References 4 publications

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“…Ideally, such a training of phonological awareness should be combined with training basic numerical skills to facilitate the differentiation and manipulation of single words in the number-word sequence (cf. Fuson, 1988). The fact that correlations between literacy and math development in school as well as in preschool were found to be substantial in our study further confirms this position.…”

Section: Discussionsupporting

confidence: 86%

“…Because phonological awareness reflects the ability to differentiate between meaningful segments of the language and to manipulate them, it should facilitate the differentiation and manipulation of single words in the number-word sequence. Accordingly, the number-word sequence should not be used as a string level anymore ("onetwothreefourfive", see Fuson, 1988), but conceived of as separated number words in a fixed order ("one two three four five "; see Fuson: unbreakable list), an order that even can start without the first elements ("three four five"; see Fuson: breakable list). One major goal of the present study was to explore this assumption in more detail.…”

Section: Relationships Among Literacy and Math Competencies: The Rolementioning

confidence: 99%

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Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

Krajewski

Schneider

2009

Journal of Experimental Child Psychology

431

358

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This longitudinal study explored the importance of kindergarten measures of phonological awareness, working memory, and quantity-number competencies (QNC) for predicting mathematical school achievement in third graders (mean age 8;8 years). It was found that the impact of phonological awareness and visual-spatial working memory, assessed at five years of age, was mediated by early QNC, which predicted math achievement in third grade. Importantly, and confirming our isolated number-words hypothesis, phonological awareness had no impact on higher numerical competencies (i.e., when number words had to be linked with quantities; QNC Level II and above), but predicted basic numerical competencies (i.e., when number words were isolated from quantities; QNC Level I), which explained the moderate relationship between early literacy development and the development of mathematical competencies.

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Section: Discussionsupporting

confidence: 86%

Section: Relationships Among Literacy and Math Competencies: The Rolementioning

confidence: 99%

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

Krajewski

Schneider

2009

Journal of Experimental Child Psychology

431

358

View full text Add to dashboard Cite

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“…The sequence of number words "one", "two", "three", etc. is known children before they start to learn the words' numerical meanings (Fuson, 1988). In this formal model, this means that the sequential structure of the count list of number words should be available to the learner via some primitive operations.…”

Section: Recursion (L S)mentioning

confidence: 99%

“…One particularly interesting example of this is the acquisition of number words. Children initially learn the count list "one", "two", "three", up to "six" or higher, without knowing the exact numerical meaning of these words (Fuson, 1988). They then progress through several subsetknower levels, successively learning the meaning of "one", "two", "three" and sometimes "four" (Wynn, 1990(Wynn, , 1992Sarnecka & Lee, 2009).…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping in a language of thought: A formal model of numerical concept learning

Piantadosi¹,

Tenenbaum²,

2012

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In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a recursive system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful representational system. We provide an implemented model that is powerful enough to learn number word meanings and other related conceptual systems from naturalistic data. The model shows that bootstrapping can be made computationally and philosophically well-founded as a theory of number learning. Our approach demonstrates how learners may combine core cognitive operations to build sophisticated representations during the course of development, and how this process explains observed developmental patterns in number word learning.

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“…With the use of either the counting fingers strategy or the verbal counting strategy, the child can execute one of several alternative counting procedures (Carpenter & Moser, 1984;Fuson, 1988;Groen & Parkman, 1972). According to Groen and Parkman, all counting algorithms involve the manipulation of an internal incrementing device, which in fact likely involves implicit counting (Ashcraft.…”

Section: Strategy Choice Modelmentioning

confidence: 99%

A componential analysis of an early learning deficit in mathematics

Geary

1990

Journal of Experimental Child Psychology

228

281

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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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Children’s Counting and Concepts of Number

Cited by 985 publications

References 4 publications

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

Bootstrapping in a language of thought: A formal model of numerical concept learning

A componential analysis of an early learning deficit in mathematics

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