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Teachers' Learning of Fraction Division With Area Models [electronic resource]

Utah State University. Education and Human Services.

[S.l.] : Utah State University. 2023 Ann Arbor : ProQuest Dissertations & Theses , 2023

1 online resource(288 p.)

Source: Dissertations Abstracts International, Volume: 85-02, Section: A.
Advisor: Moyer-Packenham, Patricia S.

Thesis (Ph.D.)--Utah State University, 2023.

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional development (PD) program. The data were used to generate case-based descriptions and to conduct a cross-case synthesis.Ma's Knowledge Package for Understanding the Meaning of Division by Fractions and Vergnaud's Multiplicative Conceptual Field provided the conceptual framework for the PD tasks. The Knowledge in Pieces (KiP) epistemological framework provided a lens for the analysis of the participants' engagement in the tasks.Results from the analysis of interview data contributed to the literature by identifying participants' underlying conceptual resources. Some of these conceptual resources were idiosyncratic, such as conceptualizing partitive division with fractions as a type of density. Other conceptual resources and their functions were common, such as knowing that the quotient is based on scaling the divisor to a value of one yet being unable to identify it in some contexts.Additionally, distinct psychological structures emerged that might be common among learners when engaging in partitive division with fractional divisors. The participants in this study exhibited multiple models of partitive division that generalized into two distinct structures of partitive division with fractional divisors. These models generalized into part-whole models and unit-rate models. Part-whole models attended to a single referent. The referent was seen as a quantity, part of which was known; or a process, part of which was completed. Unit-rate models attended to separate referents for the dividend and divisor. This finding extends the research literature as the structures and their variants seen in the present study do not appear to have received much attention.Results of this study can be leveraged in curriculum design for teacher education on the subject of division with fractions. Results suggest that the KiP epistemological framework is a productive analytical framework for future research on learners' connections between partitive division and other mathematics topics to which it is foundational, such as rate, intensive quantity, proportion, derivatives, probability, and statistics.

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