Objects, Actions, and Images: A Perspective on Early Number Development

Gray, Edward Martin; Pitta, Demetra; Tall, David

doi:10.1016/s0732-3123(00)00025-0

Cited by 32 publications

(26 citation statements)

References 15 publications

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“…Then counting the added units gives the answer, or, by keeping track of the number of words added/counted on the smaller given quantity (addend). Gray, Pitta and Tall (2000) conclude from multiple observations that children who are less able to solve arithmetic problems seem to rely extensively on counting procedures. Children who are skilled arithmetic problem solvers, on the other hand, seem to find plausible procedures almost intuitively (like the inverse relation between subtraction and addition).…”

Section: Strategies In Arithmetic Problem Solvingmentioning

confidence: 99%

Structuring versus counting: critical ways of using fingers in subtraction

Björklund

Kullberg

Kempe

2018

ZDM Mathematics Education

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The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4-5-yearolds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children's finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

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Section: Strategies In Arithmetic Problem Solvingmentioning

confidence: 99%

Structuring versus counting: critical ways of using fingers in subtraction

Björklund

Kullberg

Kempe

2018

ZDM Mathematics Education

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“…Studies focused on imagery and arithmetic have indicated that students who recognise the structure of mathematical processes and representations acquire deep conceptual understanding (Pitta-Pantazzi, Gray & Christou, 2004;Gray, Pitta, & Tall, 2000;Thomas & Mulligan, 1995). Students with lower numerical achievement reported descriptive and idiosyncratic images; they focused on non-mathematical aspects and surface characteristics of visual cues.…”

mentioning

confidence: 99%

Awareness of pattern and structure in early mathematical development

2009

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“…Successful Nonverbal Calculation gives insight into the child's quantitative representations without the intervening variables of language (as occurs in Story Problems) and Number Combinations which may have been developed by rote (see below); it is an ability that typically precedes both (Levine, Jordan, and Huttenlocher 1992). Nonverbal Calculation is an important achievement because it marks some understanding of 'counting-on' and 'counting-back' and an appreciation of counting as an abstract activity (Gray, Pitta, and Tall 2000).…”

Section: Nonverbal Calculationmentioning

confidence: 99%

“…Modelling may begin with manipulatives or pictorial referents to represent quantities (Lesh, Post, and Behr 1987) through 'seeing' quantities in one's head (Gray, Pitta, and Tall 2000) to principle-based reasoning where repeated opportunity to derive new number knowledge allows learners to construct their own rules and generalisations Baroody, Bajwa, and Eiland 2009;Palm 2008). A child at an early representational stage of modelling with manipulatives may find it difficult to simultaneously consider the relationship (Thompson 1993) indicated in the particular Story Problem's structure (Riley, Greeno, and Heller 1983).…”

Section: Story Problemsmentioning

confidence: 99%

Number Sense: The Underpinning Understanding for Early Quantitative Literacy

Maclellan¹

2012

Numeracy

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The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early QL develops comprises interdependent dimensions: Number Knowledge, Counting Skills and Principles, Nonverbal Calculation, Number Combinations and Story Problems -summarised as Number Sense. In order to derive the findings for this manuscript, a realist synthesis of recent Education and Psychology literature was conducted. The findings are of use not only when teaching very young children, but also when teaching learners who are experiencing learning difficulties through the absence of prerequisite numerical knowledge. As well, distilling fundamental quantitative knowledge for teachers to integrate into practice, the review emphasises that improved pedagogy is less a function of literal applications of reported interventions, on the grounds of perceived efficacy elsewhere, but based in refinements of teachers' understandings. Because teachers need to adapt instructional sequences to the actual thinking and learning of learners in their charge, they need knowledge that allows them to develop their own theoretical understanding rather than didactic exhortations.

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Objects, Actions, and Images: A Perspective on Early Number Development

Cited by 32 publications

References 15 publications

Structuring versus counting: critical ways of using fingers in subtraction

Structuring versus counting: critical ways of using fingers in subtraction

Awareness of pattern and structure in early mathematical development

Number Sense: The Underpinning Understanding for Early Quantitative Literacy

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