Counting on proportions? An examination of the interplay between proportional reasoning and whole-number information
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Abreu Mendoza, Roberto Alfonso.
Counting on proportions? An examination of the interplay between proportional reasoning and whole-number information. Retrieved from
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TitleCounting on proportions? An examination of the interplay between proportional reasoning and whole-number information
Date Created2023
Other Date2023-05 (degree)
Extent213 pages : illustrations
DescriptionAdults, elementary school children, and even preschoolers can readily compare nonsymbolic, non-countable, continuous proportions. This exceptional nonsymbolic ability is in stark contrast with students' difficulty in understanding symbolic proportions, particularly fractions. Although students are introduced to fractions in the third grade, middle schoolers, and even college students struggle understanding fractions. An exciting, promising approach to ameliorate students' struggles with fractions is to leverage nonsymbolic proportional reasoning to improve their understanding of fraction magnitudes. In a recent review, we found that nonsymbolic proportional interventions can lead to small-to-large effect size improvements in fraction knowledge. Nonetheless, not all nonsymbolic formats engage proportional reasoning similarly. In contrast tocontinuous proportions, older children and adults have trouble comparing countable, discretized proportions, particularly when there is misleading counting information (also referred to as whole-number information) contradicting the proportional magnitude. When working with these proportions, students tend to employ erroneous whole-number strategies instead of engaging with proportional magnitudes. If we aim to improve students' understanding of fractions through nonsymbolic instruction, we need to determine the cognitive skills that lead to skillful nonsymbolic proportional reasoning and provide a comprehensive explanation for the relationship between nonsymbolic and symbolic proportional skills. In Chapter 2, I first aimed to determine the cognitive mechanisms contributing to successful nonsymbolic discretized proportional reasoning among second graders. In particular, I examined the role of inhibitory control, the executive function that allows overcoming automatic responses, as this type of nonsymbolic proportions requires disregarding misleading counting information. Behavioral correlation studies indicate a moderate relation between nonsymbolic and symbolic proportional magnitude understanding; however, no work has contrasted the different contributions of continuous and discretized formats. To inquire about these distinct contributions, I used online behavioral tasks (Chapter 3) and functional imaging methodologies (Chapter 4). Specifically, Chapter 3 examines the relations between middle schoolers' nonsymbolic and symbolic proportional reasoning using correlational and cluster analyses. Finally, Chapter 4 uses a multivoxel pattern approach, representational similarity analysis, to determine whether adults' brain patterns while comparing fractions resemble those of continuous or discretized comparison skills. Together, the work of my dissertation provides a detailed explanation of the relation between nonsymbolic and symbolic proportional skills, which, in turn, could offer insights for educational interventions aiming to enhance fraction understanding.
NotePsy.D.
NoteIncludes bibliographical references
Genretheses
LanguageEnglish
CollectionGraduate School - Newark Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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