scholarly journals Cognitive mediators of US—China differences in early symbolic arithmetic

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255283
Author(s):  
John E. Opfer ◽  
Dan Kim ◽  
Lisa K. Fazio ◽  
Xinlin Zhou ◽  
Robert S. Siegler
Keyword(s):  
Standardized Tests ◽  
Number Line ◽  
Chinese Children ◽  
Numerical Magnitude ◽  
Magnitude Comparison ◽  
Cognitive Mediators ◽  
Number Line Estimation ◽  
Mathematics Knowledge ◽  
Us Children ◽  
Symbolic Number

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

scholarly journals Numerical Magnitude Skills in 6-Years-Old Children: Exploring Specific Associations with Components of Executive Function

2016 ◽  
Vol 6 (1) ◽  
pp. 157 ◽  
Author(s):  
Venera Gashaj ◽  
Yoann Uehlinger ◽  
Claudia M. Roebers
Keyword(s):  
Executive Function ◽  
Number Line ◽  
Individual Characteristics ◽  
Numerical Magnitude ◽  
Spatial Updating ◽  
Magnitude Comparison ◽  
Performance Differences ◽  
Symbolic Number

<p>Little is known about how children learn to associate numbers with their corresponding magnitude and about individual characteristics contributing to performance differences on the numerical magnitude tasks within a relatively homogenous sample of 6-year-olds. The present study investigated the relationships between components of executive function and two different numerical magnitude skills in a sample of 162 kindergartners. The Symbolic Number Line was predicted by verbal updating and switching, whereas the Symbolic Magnitude Comparison was predicted by inhibition. Both symbolic tasks were predicted by visuo-spatial updating. Current findings suggest that visuo-spatial updating underlies young children’s retrieval and processing of numbers’ magnitude.</p>

scholarly journals Digit identity influences numerical estimation in children and adults

2017 ◽  
Author(s):  
Maxine Lai ◽  
Alexandra Zax ◽  
Hilary Barth
Keyword(s):  
Developmental Change ◽  
Mental Representations ◽  
Number Line ◽  
Effect Sizes ◽  
Numerical Magnitude ◽  
Numerical Estimation ◽  
Target Values ◽  
Number Line Estimation ◽  
Digit Identity ◽  
Symbolic Number

Learning the meanings of Arabic numerals involves mapping the number symbols to mental representations of their corresponding, approximate numerical quantities. It is often assumed that performance on numerical tasks, such as number line estimation (NLE), is primarily driven by translating from a presented numeral to a mental representation of its overall magnitude. Part of this assumption is that it is the overall numerical magnitude of the presented numeral, not the specific digits that comprise it, that matter for task performance. Here we ask whether the magnitudes of the presented target numerals drive symbolic number line performance, or whether specific digits influence estimates. If the former is true, estimates of numerals with very similar magnitudes but different digits (such as 399 and 402) should be placed in similar locations. However, if the latter is true, these placements will differ significantly. In two studies (N = 262), children aged 7-11 and adults completed 0-1000 NLE tasks with target values drawn from a set of paired numerals that fell on either side of “Hundreds” boundaries (e.g. 698 and 701) and “Fifties” boundaries (e.g. 749 and 752). Study 1 used an atypical speeded NLE task, while Study 2 used a standard non-speeded NLE task. Under both speeded and non-speeded conditions, specific hundreds digits in the target numerals exerted a strong influence on estimates, with large effect sizes at all ages, showing that the magnitudes of target numerals are not the primary influence shaping children’s or adults’ placements. We discuss patterns of developmental change and individual difference revealed by planned and exploratory analyses.

Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations

2019 ◽  
Vol 46 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Stephanie Morano ◽  
Paul J. Riccomini
Keyword(s):  
Middle School Students ◽  
Effective Area ◽  
Number Line ◽  
Students With Learning Disabilities ◽  
School Students ◽  
National Assessment ◽  
Circular Area ◽  
Magnitude Comparison ◽  
Number Line Estimation

The present study examines the features and quality of visual representations (VRs) created by middle school students with learning disabilities and difficulties in mathematics in response to a released fraction item from the National Assessment of Educational Progress (NAEP). Relations between VR quality and scores on other measures of fraction knowledge are also investigated. Results show that students used circular area models most frequently to represent the NAEP item, but used bar models most accurately. Based on results, bar models may be the most efficient and effective area model VRs for use in fractions instruction. Representation quality was associated with problem-solving accuracy, as well as with performance on fraction number line estimation and fraction magnitude comparison. Implications for practice are discussed.

scholarly journals How the Abstract Becomes Concrete: Irrational Numbers are Understood Relative to Natural Numbers and Perfect Squares

2018 ◽  
Author(s):  
Purav Patel
Keyword(s):  
Teaching And Learning ◽  
Number System ◽  
Number Line ◽  
Natural Numbers ◽  
Comparison Task ◽  
Irrational Numbers ◽  
Magnitude Comparison ◽  
Number Systems ◽  
Number Line Estimation ◽  
Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root of 2, is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers – specifically, the radicands of radical expressions – as natural numbers. Strategy self-reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task-specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.

scholarly journals Narrowing the early mathematics gap: A play-based intervention to promote low-income preschoolers’ number skills

2018 ◽  
Vol 3 (3) ◽  
pp. 559-581 ◽  
Author(s):  
Nicole R. Scalise ◽  
Emily N. Daubert ◽  
Geetha B. Ramani
Keyword(s):  
Low Income ◽  
Numerical Magnitude ◽  
Card Game ◽  
Middle Income ◽  
Early Mathematics ◽  
Magnitude Comparison ◽  
Number Representations ◽  
And Gender ◽  
Symbolic Number ◽  
Numerical Knowledge

Preschoolers from low-income households lag behind preschoolers from middle-income households on numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s numerical knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a numerical magnitude comparison or a numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early numerical knowledge.

scholarly journals The hierarchical symbol integration model of individual differences in mathematical skill

2019 ◽  
Vol 5 (3) ◽  
pp. 262-282
Author(s):  
Chang Xu ◽  
Feng Gu ◽  
Katherine Newman ◽  
Jo-Anne LeFevre
Keyword(s):  
Cardinal Number ◽  
Ordinal Number ◽  
Number Line ◽  
Integration Model ◽  
Word Problem Solving ◽  
Mathematical Performance ◽  
Number Line Estimation ◽  
Mathematical Skill ◽  
Symbolic Number ◽  
Number Knowledge

Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in China (n = 71) and had substantially higher levels of mathematical skill compared to the other group who was educated in Canada (n = 68). Both groups completed a variety of symbolic number tasks, including measures of cardinal number knowledge (number comparisons), ordinal number knowledge (ordinal judgments) and arithmetic fluency, as well as other mathematical measures, including number line estimation, fraction/algebra arithmetic and word problem solving. We hypothesized that Chinese-educated individuals, whose mathematical experiences include a strong emphasis on acquiring fluent access to symbolic associations among numbers, would show more integrated number symbol knowledge compared to Canadian-educated individuals. Multi-group path analysis supported the hierarchical symbol integration hypothesis. We discuss the implications of these results for understanding why performance on simple number processing tasks is persistently related to measures of mathematical performance that also involve more complex and varied numerical skills.

scholarly journals Domain-specific and domain-general training to improve kindergarten children’s mathematics

2017 ◽  
Vol 3 (2) ◽  
pp. 468-495 ◽  
Author(s):  
Geetha B. Ramani ◽  
Susanne M. Jaeggi ◽  
Emily N. Daubert ◽  
Martin Buschkuehl
Keyword(s):  
Working Memory ◽  
Low Income ◽  
Conceptual Knowledge ◽  
Number Line ◽  
Kindergarten Children ◽  
Numerical Magnitude ◽  
Control Group ◽  
Domain Specific ◽  
Number Line Estimation ◽  
Numerical Knowledge

Ensuring that kindergarten children have a solid foundation in early numerical knowledge is of critical importance for later mathematical achievement. In this study, we targeted improving the numerical knowledge of kindergarteners (n = 81) from primarily low-income backgrounds using two approaches: one targeting their conceptual knowledge, specifically, their understanding of numerical magnitudes; and the other targeting their underlying cognitive system, specifically, their working memory. Both interventions involved playing game-like activities on tablet computers over the course of several sessions. As predicted, both interventions improved children’s numerical magnitude knowledge as compared to a no-contact control group, suggesting that both domain-specific and domain-general interventions facilitate mathematical learning. Individual differences in effort during the working memory game, but not the number knowledge training game predicted children’s improvements in number line estimation. The results demonstrate the potential of using a rapidly growing technology in early childhood classrooms to promote young children’s numerical knowledge.

The relationship between number line estimation and arithmetic competencies depends on age, operation and skill

2013 ◽  
Author(s):  
Julia Bahnmueller ◽  
Stefan Huber ◽  
Korbinian Moeller ◽  
Hans-Christoph Nuerk
Keyword(s):  
Number Line ◽  
Number Line Estimation ◽  
The Relationship
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