Date of Award

6-2024

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Mariana Levin, Ph.D.

Second Advisor

Tabitha Mingus, Ph.D.

Third Advisor

Laura R. Van Zoest, Ph.D.

Fourth Advisor

Hillary Swanson, Ph.D.

Keywords

Cognitive disequilibrium, concept projection, conceptual accommodation, knowledge development, mathematical linguistic features

Abstract

This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning Analysis (MLA) of the reasoning of 14 students from an Algebra II course. It reveals the critical role of cognitive disequilibrium as an essential cognitive state for conceptual development and the process of reorganizing knowledge systems. The study uncovers the fluctuations in students’ reasoning patterns and the significant impact on students’ reasoning patterns of task-specific features, such as linguistic cues embedded in contextual tasks. The findings of the study underscore the importance of incorporating cognitive challenges and context-rich tasks into educational practices and advocate for instructional designs that promote metacognitive awareness and reflective thinking. This research contributes to our understanding of cognitive dynamics in learning mathematics and suggests implications for curriculum development, instructional design, and future educational research. Key insights and their far-reaching implications for enhancing mathematics learning are discussed.

Access Setting

Dissertation-Open Access

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