The importance of additive reasoning in children’s mathematical achievement: A longitudinal study.

Ching, Boby Ho-Hong; Nuñes, Terezinha

doi:10.1037/edu0000154

Cited by 44 publications

(30 citation statements)

References 113 publications

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“…Yet the relation between mathematical symbol understanding and mathematical competence has seldom been investigated—until recently, when researchers obtained promising results. For instance, in one study, children's understanding of commutativity and inversion predicted their growth in mathematical competence across 1 year (Ching & Nunes, 2017). Likewise, another study observed similar predictions based on children's understanding of equivalence (McNeil et al, 2019).…”

Section: Understanding Mathematical Symbols and Their Relevant Princimentioning

confidence: 99%

“…Fortunately, the correlation between mathematical symbol understanding and mathematical competence has captured researchers’ attention in recent years (Ching & Nunes, 2017; McNeil et al, 2019). Furthermore, new measures developed to assess the ability to identify the schema behind mathematical problems (Wong & Ho, 2017; Yip et al, 2020) have allowed more detailed investigations into situation comprehension and mathematization.…”

Section: The Next Step: Examining the Unique Roles Of The Three Compomentioning

confidence: 99%

“…While numerical magnitude knowledge is undoubtedly an important factor in mathematics learning, it is probably not the only important factor. Based on the aforementioned review, the mathematical symbol factor (Ching & Nunes, 2017) and the situation comprehension and mathematization factor (Wong & Ho, 2017) may also play important roles in developing mathematical competence. Having deficits in these domains may also cause difficulties in learning mathematics (Andersson, 2010; Yip et al, 2020).…”

Section: The Next Step: Examining the Unique Roles Of The Three Compomentioning

confidence: 99%

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Components of Mathematical Competence in Middle Childhood

Wong

2020

Child Dev Perspectives

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Mathematical competence in middle childhood predicts socioeconomic status in adulthood. Therefore, it is important to understand the components that constitute mathematical competence from kindergarten to sixth grade. Using an analytical approach, in this article, I identify three components: understanding numbers, understanding mathematical symbols and their relevant principles, and converting problems into mathematical expressions. Evidence suggests that all three components significantly predict children's mathematical competence. However, the interrelations of the three components, as well as their unique contributions to overall mathematical competence, remain largely unexaed, with most studies focusing on only one of the three components. Exploring such issues can give researchers and educators a more comprehensive view of mathematical competence in childhood, and can lead to reconsiderations of important theoretical issues. The three‐component framework of mathematical competence may also give educators insights on how to improve the mathematical competence of future generations.

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Section: Understanding Mathematical Symbols and Their Relevant Princimentioning

confidence: 99%

Section: The Next Step: Examining the Unique Roles Of The Three Compomentioning

confidence: 99%

Section: The Next Step: Examining the Unique Roles Of The Three Compomentioning

confidence: 99%

See 1 more Smart Citation

Components of Mathematical Competence in Middle Childhood

Wong

2020

Child Dev Perspectives

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“…The commutative principle (part a + part b = part b + part a)-that is, the irrelevant order of the addends-is one of the essential properties of the part-whole relationship of numbers (Kilpatrick et al, 2001). In addition to facilitating learners' computational fluency, the commutative principle is integral to part-whole reasoning (Ching & Nunes, 2017) such as understanding that the relation among three quantities, for example 5/4/1, can be expressed with symbols (e.g., 1 + 4 = 5; 4 + 1 = 5) and that both equations describe the same part-whole relation. Previous research has shown that children acquire informal knowledge of commutativity before entering school.…”

Section: Mathematical Principles Linked To Part-whole Relationshipsmentioning

confidence: 99%

Different Learning Possibilities from the Same Activity—Swedish Preschool Teachers’ Enactment of a Number Relation Activity

Ekdahl

2020

Scandinavian Journal of Educational Research

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In this paper, differences in the implementation of a number activity called the snake game are studied. Nine Swedish preschool teachers worked in collaboration with a research team, enacting the same activity with their groups of 5-year-old children over a 3-month period. Variation theory forms the basis for the analysis of 67 videorecorded enactments. The results suggest that an activity such as the snake game can bring various aspects of numbers to the fore through differences in enactment. The activity became mathematically richer when the teacher compared children's different finger patterns and used systematically varied examples of number relations. This study's results contribute knowledge about characteristics of teaching that foregrounds numbers' part-whole relations.

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“…It is critical that children enter kindergarten and first grade prepared to embark on formal math learning, however, there is wide variation in the level of math skill children acquire during the preschool years (Jordan et al, 2006 ). Conceptual knowledge of addition and subtraction is an especially important skill for children at the beginning of formal math education (Nunes et al, 2007 ; Ching and Nunes, 2017 ). Therefore, improving early conceptual knowledge of arithmetic is an important way to enhance math readiness in preschool children.…”

Section: Introductionmentioning

confidence: 99%

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

Szkudlarek

Brannon

2018

Front. Psychol.

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Recent studies suggest that practice with approximate and non-symbolic arithmetic problems improves the math performance of adults, school aged children, and preschoolers. However, the relative effectiveness of approximate arithmetic training compared to available educational games, and the type of math skills that approximate arithmetic targets are unknown. The present study was designed to (1) compare the effectiveness of approximate arithmetic training to two commercially available numeral and letter identification tablet applications and (2) to examine the specific type of math skills that benefit from approximate arithmetic training. Preschool children (n = 158) were pseudo-randomly assigned to one of three conditions: approximate arithmetic, letter identification, or numeral identification. All children were trained for 10 short sessions and given pre and post tests of informal and formal math, executive function, short term memory, vocabulary, alphabet knowledge, and number word knowledge. We found a significant interaction between initial math performance and training condition, such that children with low pretest math performance benefited from approximate arithmetic training, and children with high pretest math performance benefited from symbol identification training. This effect was restricted to informal, and not formal, math problems. There were also effects of gender, socio-economic status, and age on post-test informal math score after intervention. A median split on pretest math ability indicated that children in the low half of math scores in the approximate arithmetic training condition performed significantly better than children in the letter identification training condition on post-test informal math problems when controlling for pretest, age, gender, and socio-economic status. Our results support the conclusion that approximate arithmetic training may be especially effective for children with low math skills, and that approximate arithmetic training improves early informal, but not formal, math skills.

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The importance of additive reasoning in children’s mathematical achievement: A longitudinal study.

Cited by 44 publications

References 113 publications

Components of Mathematical Competence in Middle Childhood

Components of Mathematical Competence in Middle Childhood

Different Learning Possibilities from the Same Activity—Swedish Preschool Teachers’ Enactment of a Number Relation Activity

Approximate Arithmetic Training Improves Informal Math Performance in Low Achieving Preschoolers

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