ERIC Number: EJ1462130
Record Type: Journal
Publication Date: 2025-Mar
Pages: 20
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0013-1954
EISSN: EISSN-1573-0816
Available Date: 2024-02-23
Numerical Magnitude Understanding of Natural and Rational Numbers in Secondary-School Students: A Number Line Estimation Study
Kelsey J. MacKay1; Filip Germeys2; Wim Van Dooren1; Lieven Verschaffel1; Koen Luwel1,3
Educational Studies in Mathematics, v118 n3 p429-448 2025
Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type (natural vs. rational) and structure of the notation system (place-value-based vs. non-place-value-based). To do so, a 2 (number type) × 2 (structure of the notation system) within-subjects design was created in which 61 secondary-school students estimated the position of four notations on a number line: natural numbers (e.g., 214 on a 0-1000 number line), decimals (e.g., 0.214 on a 0-1 number line), fractions (e.g., 3/14 on a 0-1 number line), and separated fractions (3 on a 0-14 number line). In addition to response times and error rates, eye tracking captured students' on-line solution process. Students had slower response times and higher error rates for fractions than the other notations. Eye tracking revealed that participants encoded fractions longer than the other notations. Also, the structure of the notation system influenced participants' eye movement behavior in the endpoint of the number line more than number type. Overall, our findings suggest that when a notation contains "both" sources of difficulty (i.e., rational and non-place-value-based, like fractions), this contributes to a worse understanding of its numerical magnitude than when it contains only "one" (i.e., natural but non-place-value-based, like separated fractions, or place-value-based but rational, like decimals) or "neither" (i.e., natural and place-value-based, like natural numbers) of these sources of difficulty.
Descriptors: Number Concepts, Numeracy, Secondary School Mathematics, Secondary School Students, Arithmetic, Fractions, Reaction Time, Eye Movements, Error Patterns, Cognitive Processes, Difficulty Level
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Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Data File: URL: https://osf.io/guk9x/?view_only=4f96a2db26ac4aca8e03e50c283391ad
Author Affiliations: 1KU Leuven, Centre for Instructional Psychology and Technology, Leuven, Belgium; 2KU Leuven (Brussels Campus), Department of Work and Organization Studies, Brussels, Belgium; 3KU Leuven (Brussels Campus), Research Centre for Mathematics, Education, Econometrics and Statistics, Brussels, Belgium