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Insight Into Student Conceptions Of Proof, Steven Daniel Lauzon
Insight Into Student Conceptions Of Proof, Steven Daniel Lauzon
Theses and Dissertations
The emphasis of undergraduate mathematics content is centered around abstract reasoning and proof, whereas students' pre-college mathematical experiences typically give them limited exposure to these concepts. Not surprisingly, many students struggle to make the transition to undergraduate mathematics in their first course on mathematical proof, known as a bridge course. In the process of this study, eight students of varied backgrounds were interviewed before during and after their bridge course at BYU. By combining the proof scheme frameworks of Harel and Sowder (1998) and Ko and Knuth (2009), I analyzed and categorized students’ initial proof schemes, observed their development throughout …
Growth In Students' Conceptions Of Mathematical Induction, John David Gruver
Growth In Students' Conceptions Of Mathematical Induction, John David Gruver
Theses and Dissertations
While proof and reasoning lie at the core of mathematical practice, how students learn to reason formally and build convincing proofs continues to invite reflection and discussion. To add to this discussion I investigated how three students grew in their conceptions of mathematical induction. While each of the students in the study had different experiences and grew in different ways, the grounded axes (triggering events, personal questions about mathematics, and personal questions about a particular solution) highlighted patterns in the narratives and from these patterns a theoretical perspective emerged. Reflection, both on mathematics in general and …
What Are Some Of The Common Traits In The Thought Processes Of Undergraduate Students Capable Of Creating Proof?, Karen Malina Duff
What Are Some Of The Common Traits In The Thought Processes Of Undergraduate Students Capable Of Creating Proof?, Karen Malina Duff
Theses and Dissertations
Mathematical proof is an important topic in mathematics education research. Many researchers have addressed various aspects of proof. One aspect that has not been addressed is what common traits are shared by those who are successful at creating proof. This research investigates the common traits in the thought processes of undergraduate students who are considered successful by their professors at creating mathematical proof. A successful proof is defined as a proof that successfully accomplishes at least one of DeVilliers (2003) six roles of proof and demonstrates adequate mathematical content, knowledge, deduction and logical reasoning abilities. This will typically be present …
One Problem, Two Contexts, Danielle L. Gigger
One Problem, Two Contexts, Danielle L. Gigger
Theses and Dissertations
In this study, a group of students were presented with two mathematically isomorphic problems but in radically different contexts. Analysis of their thinking and reasoning as they worked to solve and explain each problem demonstrates that the thinking and reasoning that emerged in each problem responded to clear purposes that the problems elicited in these students. The first problem was posed in a context that relied on experience and intuition rather than a formal mathematical description. The second problem was posed in a formal, set-theoretic context. While the analysis offered here reveals similarities in the students' final reasoning in the …