Date of Award

4-5-2024

Document Type

Dissertation

Degree Name

Doctor of Education (EdD)

Department

School of Education

First Advisor

Nicole Enzinger, Ph.D.

Second Advisor

Cristy Alcaraz-Juarez, Ed.D.

Third Advisor

Dana Olanoff, Ph.D.

Abstract

Experiences involving the multiplication of fractions are common in daily life. For example, when preparing a meal, you may ask yourself questions such as, if 3⁄4 of a cup of flour is needed to make a dessert for 4 people, how much flour will I need to make 1⁄2 of the dessert for 2 people? (Lortie-Forgues et al., 2015). As you determine how much flour is needed, you may think conceptually by visualizing a cup-size measuring cup filled only 3/4 full. Since you need only half of it, you may think of dividing the 3/4 cup in half. The cup would now be partitioned into eighths, with three eighths needed for your recipe. Conceptual understanding of fractions is needed for solving mathematical problems that occur in our daily lives; yet, students often only use procedural knowledge of fractions operations and lack understanding in their vital underlying concepts, limiting their ability to reason about fraction concepts (Mack, 2001; Parrish & Dominick, 2016; Star, 2007; Van de Walle, et al., 2023; Yeh et al., 2017). Conceptual understanding refers to an integrated and functional grasp of mathematical ideas that goes beyond knowledge of isolated facts and methods, to understand why a mathematical idea is important and in which contexts to use it (Berger, 2017; National Research Center, 2001). One of the most persistent difficulties with fractions is that students do not have the experiences with fractions they need to make sense of them as quantities (Empson & Levi, 2011; Tsankova & Pjancik, 2009).

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