Problem-based learning (PBL) is an instructional approach that formed in medical school and holds students responsible for their learning as they solve a hypothetical real-world problem. Research on this instructional approach in K-12 settings is emerging, with most of the existing literature utilizing high school students and science. Few studies have focused on PBL's possible impact on positive student outcomes in elementary students, particularly engagement and self-efficacy in math. The current study asked questions aimed at understanding this potential relationship at both the large and small scale. The questions that guided the current examined differences in engagement and self-efficacy between students who experienced a PBL math unit and those who experienced traditional, teacher directed instruction. Factor analyses yielded a new model of engagement with three dimensions: Persistence, Value, and Focus; Working with Others, and Enjoyment and Interest. Further analyses revealed that there were differences between Parallax and control students in the Working with Others factor but not the other two factors or self-efficacy. The classroom with the highest engaged and efficacious students had a teacher who allowed them to have the autonomy necessary to become deeply invested in the material and established an environment where students felt comfortable and confident enough to ask questions and show their work. The teacher with the lowest reports of engagement and self-efficacy was more controlling in how she wanted students to complete their work and created an atmosphere where students relied on her for permission and help to move forward with the new tasks presented. While quantitative findings did not indicate that students who experienced PBL reported higher levels of any of the engagement domains or self-efficacy, results contribute to the emerging research and understanding of if PBL can impact student outcomes in elementary settings. Qualitative results illustrated the possible differences of implementation of the same PBL unit in two separate classrooms and the resulting impact on student engagement and self-efficacy. Implications offer suggestions for instructional practices that might help researchers further understand and evaluate engagement and self-efficacy in math in elementary classroom PBL contexts. [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://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]