Graduation Term

2022

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics

Committee Chair

Jeffrey E. Barrett

Committee Member

Jennifer Tobias

Abstract

Students should learn some definitions of geometric shapes in school mathematics (Hals, 2020). The motivation for this study is the existing problem in preservice and in-service elementary teachers' understanding of definitions and properties of polygons (Cunningham & Roberts, 2010; Marchis, 2012) that can affect the quality of their teaching (Shulman, 1986). This study examined various types of tasks to improve 26 Pre-service Elementary Teachers' (PSTs) understanding of definitions for familiar and unfamiliar polygons. Thanheiser et al. 's (2016) task design cycle and van Hiele's theory were used to pose and modify tasks to prompt PSTs to define and categorize polygons. The findings from the first design cycle revealed a need for tasks that required inventing and applying new definitions for unfamiliar objects. Patterns of PSTs reasoning on these later tasks indicated the extent of struggles PSTs experience, such as lack of coherence in their use of hierarchical diagrams and tending to provide fragmented collections of binary relations among categorical types of shapes without directing the entire hierarchy to a cohesive account through extensions of properties. These findings could help design appropriate tasks to improve PSTs' understanding of definitions of two-dimensional shapes. KEYWORDS: definitions; pre-service elementary teacher; quadrilaterals; hierarchy classification diagram; two-dimensional shapes; van Hiele model; task design cycle; classroom-based teaching experiment; hexagon; pentagon

Access Type

Dissertation-Open Access

DOI

https://doi.org/10.30707/ETD2022.20221020070310165639.1000000

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