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Building Fraction Magnitude Knowledge with Number Lines: Partitioning versus Analogy
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Alexandria A. Viegut; Percival G. Matthews – Developmental Psychology, 2023
Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…
Descriptors: Fractions, Mathematics Skills, Number Concepts, Skill Development
Developmental Trajectories of Numerical Magnitude Representations of Fractions and Decimals
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Wang, Yunqi; Siegler, Robert S. – Developmental Psychology, 2023
We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…
Descriptors: Elementary School Students, Secondary School Students, Grade 4, Grade 5
Malleability of Whole-Number and Fraction Biases in Decimal Comparison
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Ren, Kexin; Gunderson, Elizabeth A. – Developmental Psychology, 2019
Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…
Descriptors: Number Concepts, Fractions, Bias, Arithmetic
Individual Differences in the Development of Children's Arithmetic Fluency from Grades 2 to 3
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Xu, Chang; LeFevre, Jo-Anne; Skwarchuk, Sheri-Lynn; Di Lonardo Burr, Sabrina; Lafay, Anne; Wylie, Judith; Osana, Helena P.; Douglas, Heather; Maloney, Erin A.; Simms, Victoria – Developmental Psychology, 2021
In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…
Descriptors: Foreign Countries, Arithmetic, Mathematics Skills, Age Differences
Training Young Children on Sequential Relations among Numbers and Spatial Decomposition: Differential Transfer to Number Line and Mental Transformation Tasks
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Xu, Chang; LeFevre, Jo-Anne – Developmental Psychology, 2016
Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of…
Descriptors: Young Children, Preschool Children, Numbers, Mathematics
Nonsymbolic, Approximate Arithmetic in Children: Abstract Addition Prior to Instruction
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Barth, Hilary; Beckmann, Lacey; Spelke, Elizabeth S. – Developmental Psychology, 2008
Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this…
Descriptors: Kindergarten, Arithmetic, Reading Instruction, Young Children