id: 06474882
dt: j
an: 2015e.00536
au: DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J.
ti: From rational numbers to algebra: separable contributions of decimal
magnitude and relational understanding of fractions.
so: J. Exp. Child Psychol. 133, 72-84 (2015).
py: 2015
pu: Elsevier, Amsterdam
la: EN
cc: F43 H23 H33 C33
ut: mathematical reasoning; relational reasoning; fractions; magnitude
estimation; decimals; algebra understanding
ci:
li: doi:10.1016/j.jecp.2015.01.013
ab: Summary: 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 findings
suggest that at least two specific components of knowledge about
rational numbers ‒ relational understanding (best captured by
fractions) and grasp of unidimensional magnitude (best captured by
decimals) ‒ can be linked to early success with algebraic
expressions.
rv: