More than the sum of its parts: Exploring the development of ratio magnitude versus simple magnitude perception

Abstract

We encounter various forms of quantity in our daily lives. These not only include symbolic labels like numbers of coins or sizes of clothes, but also include naturally occurring continuous quantities like sizes of fruit or sweetness of drinks. Indeed, a wealth of research in psychophysics has demonstrated that we humans perceptually extract many different forms of quantity information from the environment (e.g.,

From non-symbolic to symbolic proportions and back: a Cuisenaire rod proportional reasoning intervention enhances continuous proportional reasoning skills

“…However, contrary to this hypothesis, children who completed the 24 sessions of the intervention showed a decline in their ability to compare discrete quantities, specifically in contexts where whole-number information interfered with the proportional one. These results beg the question if proportions are processed in a modality-independent manner (Matthews et al, 2016;Park et al, 2020), why do gains in continuous proportional reasoning not transfer to discrete quantities? We offer two potential explanations: One related to our intervention's instructional structure and the other to the developmental trajectory of discrete proportional reasoning.…”

“…A small set of studies have investigated how non-symbolic proportional comparison skills relate across formats (Mock et al, 2018;Park et al, 2020). Recently, Park et al (2020) examined non-symbolic proportional comparison skills in preschoolers, second graders, fifth graders, and adults across continuous (circles, lines, and blob areas) and discrete (collections of circles) nonsymbolic formats. The authors also evaluated absolute magnitude comparison skills across these four formats.…”

From Non-symbolic to Symbolic Proportions and Back: A Cuisenaire Rod Proportional Reasoning Intervention Enhances Continuous Proportional Reasoning Skills

“…However, contrary to this hypothesis, children who completed the 24 sessions of the intervention showed a decline in their ability to compare discrete quantities, specifically in contexts where whole-number information interfered with the proportional one. These results beg the question if proportions are processed in a modalityindependent manner (Matthews et al, 2016;Park et al, 2020), why do gains in continuous proportional reasoning not transfer to discrete quantities? We offer two potential explanations: one related to our intervention's instructional structure and the other to the developmental trajectory of discrete proportional reasoning.…”

“…A small set of studies have investigated how non-symbolic proportional comparison skills relate across formats (Mock et al, 2018;Park et al, 2020). Recently, Park et al (2020) examined nonsymbolic proportional comparison skills in preschoolers, second graders, fifth graders, and adults across continuous (circles, lines, and blob areas) and discrete (collections of circles) nonsymbolic formats. The authors also evaluated absolute magnitude comparison skills across these four formats.…”

Revisiting and refining relations between nonsymbolic ratio processing and symbolic math achievement

“…Third, we added ratio and simple magnitude comparisons for circle stimuli (see Matthews & Chesney, 2015;Meng et al, 2019) as a new format of nonsymbolic comparison tasks along with the line and dot formats from the original study. We added circles for three reasons: 1) Unlike dot arrays, they have no obvious whole number analogs; 2) unlike lines, they are not easily partitioned such that count based strategies are plausible; and 3) despite their use in other RPS studies (e.g., Park, Viegut, & Matthews, 2020;Matthews & Chesney, 2015;Meng et al, 2019), their relations to symbolic mathematics performance have yet to be investigated.…”