Preschoolers' Understanding of the Addition–Subtraction Inverse Principle: A Taiwanese Sample

Baroody, Arthur J.; Lai, Meng-Lung

doi:10.1080/10986060709336813

Cited by 46 publications

(34 citation statements)

References 44 publications

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“…In keeping with theories of concept development, some researchers (e.g., Baroody & Lai, 2007; have proposed that children develop understanding of inversion from experience and expertise in solving addition and subtraction problems. For example, Canobi suggests that "children may reach an understanding of the inverse relation between addition and subtraction after they become sufficiently experienced in problem solving to be able to reflect on the outcomes of the additions and subtractions they have carried out" p.…”

Section: Discussionmentioning

confidence: 99%

“…Social experience may play a role in this as children take part in give-and-take games with other children and adults (Klein & Bisanz, 2000). Children's experience with small quantities (e.g., 1, 2, 3) might allow children to infer localized informal knowledge of inversion, that becomes more general with experience of larger quantities (Baroody & Lai, 2007). Recent evidence also suggests that a system of approximate non-symbolic representation of number may play a role in children's developing understanding of quantitative inversion.…”

Section: Discussionmentioning

confidence: 99%

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Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Gilmore

Παπαδάτου-Παστού

2009

Mathematical Thinking and Learning

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Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual differences in the way this concept develops. To determine whether these differences are reliable and reflect alternative paths of development, we examined data from 14 studies of children's understanding of inversion. Cluster analyses and meta-analytic techniques were used to quantify the size of the inversion effect and examine factors influencing its size and to test the stability of patterns of individual differences across the studies. Evidence was found for reliable patterns of individual differences, which have implications for current theories of concept development. Individual Differences Meta-Analysis 3Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-AnalysisAn enduring question in mathematical cognition concerns how children develop understanding of mathematical concepts. This has attracted attention from researchers in both cognitive psychology and mathematics education. One of the key questions for both fields is how children's understanding of mathematical concepts develops in relation to their ability to perform mathematical procedures.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Gilmore

Παπαδάτου-Παστού

2009

Mathematical Thinking and Learning

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“…However, Allen then switched to count the total in the larger group (the mat in front of Allen) and counted on from the smaller group (the mat in front of Becka). This strategy was quite typical relative to the literature on algebraic reasoning development, as it seemed Allen was able to access the task additively before inversely considering the relations on both cupcake trays [19]. Regardless, these new strategies Allen was developing evidences of changes in his ability to access multiple reasoning strategies elicited through access of the mathematical concepts in the task.…”

Section: Examples Of Task Design That Allowed Allen Equal Access To Mmentioning

confidence: 99%

“…Also, young students struggle to comprehend relational terms (e.g., more, less, and the same) when solving inversion tasks [18]. To support early forms of algebraic development and support students' coordination of operations and numbers and use of relational terms, findings suggest that students begin with additive and subtraction experiences with simple expressions before students are required to combine multiple operations and numbers in more comprehensive expressions [19].…”

Section: Early Algebra and Mental Reversibilitymentioning

confidence: 99%

“…Recent findings suggest that young students are capable of constructing algebraic generalizations, paying attention to the explicit language and use of conjectures in solving operation problems [19][20][21][22]. Students as young as preschool-age have been found capable of transitioning their everyday experiences to mathematical experiences when developing an additive-subtractive inversion principle [19].…”

Section: Early Algebra and Mental Reversibilitymentioning

confidence: 99%

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Mathematics Intervention Supporting Allen, a Latino EL: A Case Study

2017

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This research discusses a single case study of a first-grade Latino English Learner (EL) student, Allen (pseudonym), from a larger inquiry-based intervention on inversion and mental reversibility development. The purpose of this case study was to develop a better understanding of the relationship between Allen's English language proficiency and his ability to solve inversion and compensation mathematics tasks. The integration of multiple paradigms confronting radical constructivism and sociocultural theory of learning via culturally relevant pedagogy provided us with a multi-faceted set of perspectives in understanding the interconnection between Allen's cultural and linguistic background and his development of algebraic reasoning. Through conceptual and retrospective analyses, we found that Allen's language features are highly correlated with the development of his thinking strategies and his ability to solve mathematics tasks. Implications of this study include the development of teaching strategies that address critical issues in mathematics, such as the individual differences of learners, specifically ELs from Latino background. We suggest further research is needed in the field of language acquisition and access to STEM related concepts.

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The Development of Mathematical Reasoning

Nuñes

Bryant

2015

Handbook of Child Psychology and Developmental Science

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Psychological research on the development of children's mathematical reasoning has focused either on their understanding of quantities or on their knowledge of number. A synthesis between these two different kinds of theory can be achieved by acknowledging that numbers have two meanings: a representational meaning, defined by their use as signs for quantities or relations between quantities, and an analytical meaning, defined by the conventions in the number system. In the introduction, this chapter introduces these two meanings of numbers and explores the vital connections between them. The subsequent sections analyze how children's mathematical knowledge develops by their increasing ability to use different numerical representations (e.g., from the use of fingers to represent quantities to the use of conventional signs), by their growing understanding of invariant relations between quantities (e.g., realizing that, given a fixed number of cookies, the more people sharing the cookies, the less each one receives) and by their increasing awareness of the relevance of specific concepts to different situations (e.g., understanding the relevance of division to the solution of situations more readily connected to multiplication). Throughout the chapter, the connection between the nature of quantities and their numerical representations is explored. The final substantive section focuses on the use of numbers to quantify space and relations between spatial dimensions, and argues that understanding relations between different dimensions in space (e.g., length, width, and area) is crucial to quantifying space. The chapter ends with a brief discussion of directions for future research.

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Preschoolers' Understanding of the Addition–Subtraction Inverse Principle: A Taiwanese Sample

Cited by 46 publications

References 44 publications

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Mathematics Intervention Supporting Allen, a Latino EL: A Case Study

The Development of Mathematical Reasoning

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