abstract: This research investigated preservice teacher collaboration in the context of an undergraduate teacher preparation program. Small groups of preservice students were examined over five collaborative work sessions as they collaboratively designed and delivered instructional projects for their fellow classmates. This study contributes to understanding factors that influence the quality of preservice collaboration to help teacher educators better prepare preservice students for current collaborations with their peers and future collaboration in professional settings. A parallel mixed methods design, with an embedded two case study, was employed to analyze and interpret two research strands, quantitative, and qualitative. Quantitative results served as complementary to corroborate the qualitative findings. The quantitative results and qualitative findings indicate that past collaborative experiences and beliefs about future professional collaboration impacted students’ current collaborative efforts. Students with a flexible orientation toward collaboration and/or expanded beliefs about professional collaboration were more likely to heedfully interrelate than students with fixed orientations or simple beliefs about collaboration. Preservice students’ perceptions of the quality of their own heedful interrelating remained stable across the phases of the collaborative task. However, analysis of the HICES noted significant differences in groups’ perception of the quality of their collaborative interactions. Finally, analysis of the two-case study indicated that high quality heedful interrelating among group members created the more effective collaborative instructional project. A model of how preservice beliefs and orientations may influence their heedful interrelating during collaboration, and impact their efforts in designing and creating effective collaborative instruction was presented. The dissertation research contributed to a more thorough understanding of factors that influence preservice collaboration as they prepare for professional collaboration, when the outcomes of collaboration are critical not only for themselves, but also for their own students. Implications for educational practice and further research point towards the continued need to better understand the processes of preservice collaboration, and factors that impact their interaction as they learn to collaborate for improving instruction, and how teacher preparation programs can support and best address their needs as they prepare for their critical careers. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2016

The nature and function of Task Complexity, in the context of senior secondary mathematics, has been identified through: a search of the research literature; interviews with experts that focused on the nature of task complexity; expert use of the Williams/Clarke Framework of Complexity (1997) as a tool to categorise the complexity of a task, and observation and analysis of the responses of senior secondary mathematics students as they worked in collaborative groups to solve an unfamiliar challenging problem. Although frequently used in the literature to describe tasks, ‘complexity’ has often lacked definition. Expert opinion about the nature of mathematical complexity was ascertained by seeking the opinions of experts in the areas of mathematics, mathematics education, and gifted education. Expert opinion about task complexity was stimulated by questions about the relative complexity of two tasks. The experts then categorised the complexities within each of these tasks using the Williams/Clarke Framework of Complexity. This framework identifies the dimensions of task complexity and was found by experts to be both useful and adequate for this purpose. A theoretical framework was developed to assess student ability to solve challenging problems. This theoretical framework was used to design a test to assess student ability to solve challenging problems. The information this test provided about the problem solving ability of the students in this study informed my analysis of student response to complexity.