Dissertation/Thesis Abstract

Considerations of numbers used in tasks for promoting multiplicative reasoning in students with learning difficulties in mathematics
by Risley, Rachael Ann, Ph.D., University of Colorado at Denver, 2016, 179; 10112620
Abstract (Summary)

This study explored the impact of numbers used in instructional tasks on the construction and generalization of multiplicative reasoning by fourth grade students designated as having learning difficulties or disabilities in mathematics (SLDs). In particular, this study addressed the following research questions: (1) In what ways do SLDs’ conception of number as a composite unit afford or constrain transition to multiplicative reasoning? (2) Which specific numbers, used in instructional and/or assessment tasks, may support or interfere with SLDs’ progression from additive reasoning to multiplicative Double Counting (mDC)? Results suggested that in early participatory stages, using numbers with multiples familiar to the students, such as 2 and 5, promoted multiplicative solution paths (e.g., counting by fives while simultaneously keeping track of how many fives they have counted). This use of familiar numbers allowed for students’ reflection on their multiplicative thinking. Introduction of more difficult numbers—any number for which the child was yet to master multiples—tended to limit the multiplicative thinking and move students back to more known (additive) solution paths. In later participatory stages, the introduction of more difficult numbers promoted the progression within mDC.

Indexing (document details)
Advisor: Tzur, Ron
Commitee: Davis, Alan, Johnson, Heather, Sands, Deanna
School: University of Colorado at Denver
Department: Educational Studies and Research
School Location: United States -- Colorado
Source: DAI-A 77/10(E), Dissertation Abstracts International
Subjects: Mathematics education, Elementary education
Keywords: Elementary mathematics, Learning difficulties, Multiplicative reasoning
Publication Number: 10112620
ISBN: 978-1-339-75773-5
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