From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions

Journal of Experimental Child Psychology
Melissa DeWolfKeith J Holyoak

Abstract

To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These f...Continue Reading

References

Apr 2, 2004·Child Development·Robert S Siegler, Julie L Booth
Aug 23, 2008·Child Development·Julie L Booth, Robert S Siegler
May 17, 2011·Cognitive Psychology·Robert S SieglerMichael Schneider
Sep 21, 2011·The Quarterly Journal of Experimental Psychology : QJEP·Teresa Iuculano, Brian Butterworth
Jun 16, 2012·Psychological Science·Robert S SieglerMeichu Chen
Jun 12, 2013·Journal of Experimental Psychology. Human Perception and Performance·Melissa DeWolfKeith J Holyoak
Nov 11, 2014·Journal of Experimental Psychology. General·Melissa DeWolfKeith J Holyoak
Nov 18, 2014·Journal of Experimental Psychology. Applied·Monica RappKeith J Holyoak

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Citations

Jul 31, 2016·NeuroImage·Melissa DeWolfMartin M Monti
Aug 16, 2016·Journal of Experimental Child Psychology·Melissa DeWolfKeith J Holyoak
Feb 28, 2017·British Journal of Psychology·Michelle Hurst, Sara Cordes
Jan 18, 2017·Cognitive Science·Melissa DeWolfKeith J Holyoak
Oct 12, 2018·The British Journal of Educational Psychology·Terry Tin-Yau Wong
Apr 27, 2019·Frontiers in Psychology·Elizabeth Y ToomarianEdward M Hubbard
Feb 23, 2020·Cognition·John V Binzak, Edward M Hubbard
May 1, 2021·Child Development·Christina Areizaga BarbieriJulie L Booth
Nov 9, 2020·Journal of Experimental Child Psychology·Kexin Ren, Elizabeth A Gunderson
Aug 28, 2021·Journal of Experimental Child Psychology·David W BraithwaiteMichelle A Hurst

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