Graduation Term

2021

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics

Committee Chair

Amanda L Cullen

Committee Member

Cynthia W Langrall

Abstract

Measurement is an important concept in school mathematics (Clements, 2003). There are several studies and empirical evidence on students’ thinking about geometrical measurement of length, area, and volume (e.g., Barrett et al., 2017; Battista, 2007, 2012; Eames, 2014; Lehrer, Jenkins, & Osana, 1998; Miller, 2013; Outhred & Mitchelmore, 2000; Sarama & Clements, 2009); however, there is limited research on students’ thinking about surface area measurement. This study addresses a gap in the literature with empirical evidence of students’ thinking about surface area measurement. This study also aimed to examine students’ responses to tasks involving surface area measurement and categorize the strategies using the SOLO Taxonomy. Fifteen students in Grades 5–8 participated in paired interviews. The students were selected based on a participant selection survey that included two rectilinear area measurement problems. I interviewed the selected participants twice. Interview 1 included three tasks, and Interview 2 included one or two tasks, depending on the students’ previous answers. I utilized five key ideas of measurement when analyzing the students’ work on the surface area tasks: attribute, unit, structure, conservation, and additivity. Then I characterized the students’ strategies using the SOLO Taxonomy. The results of this study indicate that middle school students exhibited thinking about surface area that corresponds with four levels of the SOLO Taxonomy and represents increasing sophistication in their thinking: pre-structural, uni-structural, multi-structural, and relational. Pre-structural level strategies included counting items that were not linked to area or surface area, uni-structural level included operating on lengths in ways that would not produce area or surface area measures, multi-structural strategies included operating on lengths in ways that would produce area and surface area measures, and relational strategies included coordinating lengths and area measures to account for the composite area regions or surface area. KEYWORDS: Geometric Measurement; SOLO Taxonomy; Surface Area.

Access Type

Dissertation-Open Access

DOI

https://doi.org/10.30707/ETD2022.20220606094359163609.999994

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