Date of Award

5-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Nicole Panorkou

Committee Member

Joseph DiNapoli

Committee Member

Eileen Fernandez

Abstract

Mathematical problem solving is a topic that has seen an increased focus in recent years, highlighted by its inclusion as the first Standard for Mathematical Practice in the Common Core State Standards for Mathematics (CCSSM). However, elementary preservice teachers (PSTs) often struggle when solving problems that are nonroutine and require higher cognitive demand. Many have little experience solving this type of problem and show an increased level of anxiety around problem solving, which impacts the way they engage their students with problem solving. To support PSTs to become better problem solvers, it is important to provide opportunities for PSTs to engage in problem solving themselves. This dissertation explores the struggles that PSTs encounter while solving mathematics problems and the type of scaffolds that can support them to recover from impasses. A design experiment was conducted with ten PSTs working in pairs to solve six problems. When the PSTs hit an impasse, a scaffold was offered to see if it would help them to overcome the impasse and make their struggle productive. While the design experiment began with some scaffolds for each problem as conjectures based on prior research, these were open for modification as the experiment unfolded. Prior research with middle school students (Warshauer, 2015) has established a framework of types of student struggle. The findings of the current study showed that PSTs experienced similar struggles, and the study also expanded the framework to include three new struggles experienced by PSTs, namely struggle in developing a plan, struggle with not recognizing an unreasonable answer, and struggle with working with unproductive information. In terms of the use of scaffolds that can help those PSTs to overcome their struggles, this study found that some scaffolds, such as drawing a picture or trying a problem with smaller numbers, were particularly successful and were adopted and adapted by the PSTs in subsequent problem solving sessions. The study also found that some struggles, such as misconceptions and errors, had high rates of scaffold success, where others, such as the use of unproductive information, were challenging to scaffold successfully. In addition, the findings showed that sometimes a second scaffold was needed for the PSTs to complete the problems as some struggles became evident after the first scaffold was given. This study provides suggestions on how mathematics teacher educators can help their PSTs to become better problem solvers. Through the identification of both areas of struggle and effective scaffolds, teacher educators can design lessons in problem solving that encourage PSTs to both adopt and adapt specific scaffolds as new strategies for problem solving. The new struggles identified in this study provide teacher educators with areas to focus on and to address during instruction on problem solving. Beyond teacher education, this expanded framework can help any mathematics teacher to recognize their students’ struggles and support them with scaffolds that would help them make progress and become better problem solvers.

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