The ability to succeed in Science, Technology, Engineering, and Mathematics (STEM) careers is contingent on a student's ability to engage in mathematical problem solving. As a result, there has been increased focus on students' ability to think critically by providing them more with problem solving experiences in the classroom. Much research has been conducted on mathematical problem solving, beginning with Polya's (1945) seminal work. Subsequent work has extensively studied factors that influence students' success in problem solving. However, there is a need to accumulate this research so that it can be successfully connected to practice. One way to accomplish this is to develop an overarching problem solving theory. Schoenfeld (2011) developed such a theory and attributes an individual's goals (personal aims to achieve), resources (knowledge available), and orientations (beliefs, values) as influential factors in the decisions made during any goal-oriented activity. This theory was tested and a model created for mathematics teaching but not formally for students' mathematical problem solving. This study fills this gap by testing and validating Schoenfeld's theory for problem solving as a way to document and assess students' problem solving process. The six students that participated in this study were incoming and returning freshmen at an HBCU participating in a summer bridge program. This multi-case study investigated the problem solving process of these students. A conceptual framework was created based on Schoenfeld's (2008) problem solving theory, along with Carlson and Bloom's (2005) framework for problem-solving process and Debellis and Goldin (2006) framework for affect. Within this conceptual framework, the decisions students made during problem solving were attributed to their goals, knowledge, affect, and external contextual factors. To test this theory, empirical evidence was collected to: (1) provide detailed, rich descriptions about how and why students make decisions during problem solving and (2) validate the scope of the proposed problem-solving theory. Data collection included the use of individual task-based interviews followed by video-stimulated response interviews. The transcripts were transcribed and analyzed and coded for these factors. Cross-case finding for each factor was reported. Empirical evidence validated the proposed problem solving theory. That is, students' goals, knowledge, and affect were factors that influenced the choices students made. Although external contextual factors did impact students' motivation, it was not prevalent for all students. Furthermore, the data indicate that affect is the driving force that moves the student through the problem-solving phases. If students do not believe that it takes exploration and patience to solve problems, if negative emotions are felt, their ability to access knowledge needed to connect mathematical ideas were hindered. However, if they hold favorable beliefs about mathematics and problem solving, then a negative emotion will be used as motivation to continue the problem-solving process. These findings confirm that affect is the factor that may be the most influential predictor for students' decision to persevere. Therefore, the problem solving theory includes all factors (i.e., goals, knowledge, and affect) that influence the decisions students make during the problem solving process. These findings confirm how the factors are intertwined and connected to influence student's ability to persevere. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]