Producing highly skilled elementary mathematics teachers capable of facilitating mathematics learning in ways aligned with The Principles and Standards for School Mathematics (NCTM, 2000) and the Common Core State Standards for Mathematics (CCSSM), is a common objective of teacher preparation programs (National Governors Association & Chief Council of State School Officers, 2010). After decades of effort, Brown (2003) argues, teachers continue to teach in the way they were taught; thus, they disregard mathematics standards. As Abell, Appleton, and Hanuscin (2010) note, students’ preexisting ideas relevant to the nature of learning and teaching stem from experiences in their schooling, life, and formal classes. Specifically, related to mathematics, these experiences often reflect the difficulty in learning mathematics, fear of mathematics, and consequently, a dislike for the subject (Abell et al., 2010; Wilson, 2014). These preconceived beliefs influence how preservice teachers (PSTs) perceive subject matter. Beliefs also impact the decisions they make about teaching and learning mathematics. In this exploratory descriptive case-study I investigated in what ways three PSTs describe their experiences as K-12 mathematics learners, how the PSTs perceive their abilities to teach mathematics prior to participating in an introductory elementary mathematics methods course, how the PSTs perceive their abilities to teach mathematics after participating in an introductory elementary mathematics methods course, and what catalysts, relative to their experiences, do the PSTs consider noteworthy in the development of their beliefs and concurrent pedagogy about teaching mathematics to elementary students. I utilized constant comparative methods (Strauss and Corbin, 1998; Denzin and Lincoln, 1994; Strauss, 1987; Miles and Huberman, 1984) to analyze the data and identify overarching themes related to the goals of the study.

This study examined the effects of differing amounts of structure within the problem based learning instructional model on elementary preservice teachers' science teaching efficacy beliefs, including personal science teaching efficacy and science teaching outcome expectancy, and content knowledge acquisition. This study involved sixty (60) undergraduate elementary preservice teachers enrolled in three sections of elementary science methods classes at a large Midwestern research university. This study used a quasi-experimental nonequivalent design to collect and analyze both quantitative and qualitative data. Participants completed instruments designed to assess science teaching efficacy beliefs, science background, and demographic data. Quantitative data from pre and posttests was obtained using the science teaching efficacy belief instrument-preservice (STEBI-B) developed by Enochs and Riggs (1990) and modified by Bleicher (2004). Data collection instruments also included a demographic questionnaire, an analytic rubric, and a structured interview; both created by the researcher. Quantitative data was analyzed by conducting ANCOVA, paired samples t-test, and independent samples t-test. Qualitative data was analyzed using coding and themes. Each of the treatment groups received the same problem scenario, one group experienced a more structured PBL setting, and one group experienced a limited structure PBL setting. Research personnel administered pre and posttests to determine the elementary preservice teachers' science teaching efficacy beliefs. The results show elementary preservice teachers'science teaching efficacy beliefs can be influence by the problem based learning instructional model. This study did not find that the amount of structure in the form of core ideas to consider and resources for further research increased science teaching efficacy beliefs in this sample. Results from the science content knowledge rubric indicated that structure can increase science content knowledge in this sample. Qualitative data from the tutor, fidelity raters, and interviews indicated the participants were excited about the problem and were interested in the science content knowledge related to the problem. They also indicated they were motivated to continue informal study in the problem area. Participants indicated, during the interview, their initial frustration with the lack of knowledge gained from the tutor; however, indicated this led to more learning on their part. This study will contribute to the overall knowledge of problem based learning and its structures, science teaching efficacy beliefs of elementary preservice teachers, and to current teaching and learning practices.