DIGITAL LIBRARY
LEARNING FRACTIONS IN PRIMARY SCHOOL SHOULD FOCUS ON REASONING OR ARITHMETIC?
1 Universidad Peruana de Ciencias Aplicadas (PERU)
2 University of Oxford (UNITED KINGDOM)
About this paper:
Appears in: ICERI2021 Proceedings
Publication year: 2021
Pages: 1444-1451
ISBN: 978-84-09-34549-6
ISSN: 2340-1095
doi: 10.21125/iceri.2021.0403
Conference name: 14th annual International Conference of Education, Research and Innovation
Dates: 8-9 November, 2021
Location: Online Conference
Abstract:
The aims of this study were to investigate the impact of quantitative reasoning and arithmetic on children’s fractions learning by means of an intervention study, and to test whether non-verbal ability moderates the intervention effect.

Quantitative reasoning is the ability to use relations between quantities to come to new conclusions; for example, knowing that if a cake is shared fairly among three children and two cakes are shared fairly among six children, the children receive equivalent amounts of cake (Hallett, Nunes, & Bryant, 2010; Hecht, Close, & Santisi, 2003). Arithmetic is the ability to understand relations between numbers defined by arithmetic operations (Guedj, 1997). These abilities are conceptually and empirically distinct and each one plays an important role in learning mathematics.

In this study, participants were randomly assigned to one of three groups: an intervention that promoted quantitative reasoning about quantities smaller than a unit; an intervention that consisted of teaching fraction arithmetic; a business-as-usual comparison group. The analyses tested:
(1) whether each of the intervention groups performed better than the comparison group in the outcome measure Chelsea Mathematics Diagnostic Test: Fractions (also used at pre-test); and
(2) whether non-verbal ability moderated the intervention impact.

Children in Grade 4 (103) from four schools in England participated. They were pre-tested before random allocation to a group. Each of the intervention groups participated in 8 weekly half-hour sessions with a researcher in small groups outside the classroom. The aim of this brief intervention was to support classroom instruction through additional teaching rather than to replace it. An immediate post-test, given the week after the intervention, and a delayed post-test, given six weeks after the intervention finished were carried out.

Analyses of covariance, controlling for pre-test performance and non-verbal ability, showed a significant impact of the quantitative reasoning intervention: Cohen’s d effect size=0.44 at the immediate post-test and d=0.45 at the delayed post-test. The arithmetic intervention had a significant impact only at the delayed post-test (d=0.28). Non-verbal ability was a significant moderator of delayed post-test performance.

It is concluded that a focus on quantitative reasoning teaching supports children’s fractions learning. This additional learning remained stable after several weeks. Non-verbal reasoning moderates learning in the long term. The implications are that including lessons to promote quantitative reasoning is an effective way of improving fractions learning and that children whose measured non-verbal ability is lower might benefit from a more extended quantitative reasoning intervention.
Keywords:
Primary education, mathematics education, fractions learning, quantitative reasoning, arithmetic.