Date of Award

May 2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Teaching and Leadership

Advisor(s)

Joanna O. Masingila

Keywords

Anghileri's (2006) Levels of Supports, Conceptualization of Angle Concept, Real-world Context, Retrospective Analysis, Sixth-grade Students

Subject Categories

Education

Abstract

A strong foundation in students’ understanding of the multifaceted nature of the angle concept is of paramount significance in understanding trigonometry and other advanced mathematics courses involving angles. Research has shown that sixth-grade students struggle understanding the multifaceted nature of the angle concept (Keiser, 2004). Building on existing work on students’ understanding of angle and angle measure and instructional supports, this study asks: How do sixth-grade students conceptualize angle and angle measure before, during, and after learning through a geometry unit of instruction set in a miniature golf context? What instructional supports contribute to sixth-grade students’ conceptualization of angle and angle measure in such a context? I conducted a retrospective analysis of existing data generated using design-based research methodology and guided by Realistic Mathematics Education (RME) theory. Using Cobb and Yackel’s (1996) Emergent Perspective as an interpretive framework, I analyzed transcripts of video and audio recordings from nine days of lessons in a collaborative teaching experiment (CTE), focusing on two pairs of students in sixth-grade mathematics classes. I also analyzed transcripts of pre-interviews before instruction, midway interviews during instruction, and post-interviews after instruction with each student in the two pairs. To answer research question one, I developed codes from data guided by the existing literature. For research question two, I used Anghileri’s (2006) levels of supports framework. Overall, the findings revealed that sixth-grade students conceptualized an angle as a static geometric figure defined by two rays meeting at a common point, and conceptualized angle measure through their body turns. In addition, Anghileri’s three levels of supports, such as the use of structured tasks, teacher’s use of probing questions, generation of conceptual discourse were evident in contributing to students’ conceptualization of angle and angle measure during the miniature golf geometry unit of instruction. The findings of this study have implications for the school mathematics curriculum, and how to teach and to prepare teachers to teach angle and angle measure. This study emphasizes the need to redefine the angle concept in the curriculum documents, the need to increase activities involving body turns and the use of Anghileri’s (2006) levels of supports in the teaching and learning of angle and angle measure in a real-world context. Further research is needed to identify instructional supports, in particular activities that can support students’ conceptualization of slopes and turns as angles in a real-world context.

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Open Access

Available for download on Sunday, August 15, 2021

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