Theses and Dissertations

ORCID

0009-0001-7837-6353

Advisor

Robichaux-Davis, Rebecca

Committee Member

Anthony, Kenneth

Committee Member

Franz, Dana

Committee Member

Gallo, Katarzyna

Date of Degree

8-12-2026

Original embargo terms

Immediate Worldwide Access

Document Type

Dissertation - Open Access

Major

Curriculum and Instruction (Elementary Education)

Degree Name

Doctor of Philosophy (Ph.D.)

College

College of Education

Department

Department of Teacher Education and Leadership

Abstract

Mathematics teachers’ knowledge of rational numbers is very important due to the prominence of fraction concepts across the K-12 curriculum. Preservice teachers (PSTs) typically only have a procedural understanding of fractions and lack conceptual understanding (Newton, 2008). PSTs struggle to construct pedagogical representations that correctly show the size of parts and wholes (Lee & Lee, 2019). The purpose of this study was to investigate PSTs’ ability to compare fractions by examining their selection and creation of appropriate and accurate fraction representations in context, including the use of area, length, and set representations. The purpose was also to determine the extent to which their ability to select appropriate representations correlated with their ability to create accurate representations. The theoretical framework includes the five modes of representation as determined by Lesh et al. (1987), the three types of representations that are used to represent fractions, and content knowledge and pedagogical content knowledge as defined by Shulman (1986) and expanded upon by Ball et al. (2008). This quasi-experimental study assessed PSTs at the start and end of a senior level elementary mathematics methods course. The PSTs completed a pre and posttest using the FRACT (Fraction Representation and Comparison Test) to determine if they could accurately compare fractions using appropriate and accurate representations for a given context. The treatment group received focused instruction on fraction comparisons and was engaged in different activities than the control group. The data collected from the participants was analyzed using repeated measures Analysis of Variance (ANOVA) tests and by comparing mean scores to identify statistically significant correlations that existed among the variables. Results indicate that the teaching methods used for the treatment group were effective in increasing PSTs’ abilities to draw appropriate and accurate representations for fraction comparison in area, length, and set contexts. Implications of this study for teacher educators include increasing use of teaching methods like manipulative sorting, practice with drawing representations that align to area, length, and set contexts, and creating same size wholes and equal partitioning of fraction representations. This study further contributes to literature regarding the use of contextual scenarios to understand rational numbers.

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