Aspects of Engaging Problem Contexts From Students' PerspectivesTamara Kay Gandolph StarkDepartment of Mathematics Education, BYUMaster of ArtsToo many students have negative feelings towards mathematics which is causing them to disengage in their classrooms. This has led to student under-achievement. This study attempts to better understand how teachers can help students to reengage with mathematics by using more engaging contexts to develop mathematical content. The study began with the characteristics realistic, worthwhile, enjoyable or motivating as a framework for posing engaging problem contexts, which were synthesized from the current research literature. As students discussed what made contexts engaging, my understanding of what engaging problem contexts looked like expanded. The characteristics realistic and worthwhile were combined. Students felt contexts were more realistic and worthwhile when the contexts were authentic, purposeful and related to their everyday lives or a potential career situation. Furthermore, students felt context was enjoyable when it was interactive or included a good story. Finally, students discussed their frustration with repetition within problem contexts. Even if certain types of problems were engaging at first, if they saw them over and over again, they became unengaged. Students wanted to see a variety of new ideas and different kinds of contexts. This study better informs teachers and curriculum writers on what to include/exclude to make contexts more engaging for students.

The tasks with which students engage in their mathematics courses determine, for a large part, what students learn. Therefore, it is essential that teachers are able to design tasks that are worthwhile for developing mathematical understanding. Since practicing teachers seldom incorporate worthwhile mathematical tasks in their lessons, we would expect that they did not become proficient at designing worthwhile tasks while in their teacher education programs. This thesis describes a study that investigated what preservice secondary teachers attend to as they attempt to design worthwhile mathematical tasks. Three participants were selected from a course at a large private university where preservice teachers are taught and practice the skill of task design. This "Task Design" course was observed, and the three participants were interviewed to determine what they attend to while designing tasks. There were seven main characteristics that the main participants in the study attended to the most often and thought were the most important: sound and significant mathematics, reasoning, appropriateness, clarity, communication, engagement, and openness. How the participants attended to these characteristics is described. Some implications for teacher education, such as requiring preservice teachers to explain how their tasks embody certain characteristics, are given based on the results.