ERIC Number: ED663416
Record Type: Non-Journal
Publication Date: 2024
Pages: 254
Abstractor: As Provided
ISBN: 979-8-3840-8761-8
ISSN: N/A
EISSN: N/A
Structural Reasoning of Children in the Context of Single Digit and Multi Digit Multiplication
Reyhan Safak
ProQuest LLC, Ph.D. Dissertation, The Ohio State University
Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive processes and obstacles involved in supporting the development of structural thinking involved in single-digit and multi digit multiplication. Design research was used to examine how elementary school children may describe and use their knowledge of structure in the process of moving from single digit to multi digit multiplication with a focus on how the distributive property may be utilized as they make that shift. Data analysis consists of two phases. In Phase 1, instances of structural reasoning were identified within each teaching experiment for each case. In Phase 2, cognitive obstacles the students experienced were explained according to how they those impediments manifested and, in turn, impacted the students' capacity to leverage their structural reasoning skills within this study. Data analysis revealed that while Ali was utilizing his memorized multiplication facts in single digit multiplication, Sevtap preferred a tactile strategy, counting by her fingers to facilitate the computational process. For multi digit multiplication, Ali utilized formal algorithm and intuitive use of distributive property. On the contrary, Sevtap exhibited a significant efficiency in her utilization of a distinct visual aid--the cookie model. Her proficiency in leveraging this model underscores her capacity to translate abstract mathematical concepts into tangible and comprehensible representations. This contrast in their approach sheds light on the diverse cognitive pathways each student employs in utilizing their structural reasoning abilities in multiplication problems. Cognitive obstacles students experienced during the teaching experiments were also very different from each other. While Ali perceived area model as array model in his first attempt, Sevtap's confusion between multiplication and addition are important to consider when strategizing and structuring future lessons aimed at imparting multiplication concepts. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]
Descriptors: Mathematics Instruction, Multiplication, Elementary School Students, Thinking Skills, Cognitive Processes, Barriers, Student Attitudes, Tactual Perception, Intuition, Efficiency, Models, Visual Aids, Mathematical Concepts, Teaching Methods, Lesson Plans, Concept Formation
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A