What This Document Is
This document presents a case study detailing the design and implementation of an upper-level undergraduate mathematics seminar focused on mathematical problem solving. Specifically, it explores one instructor’s approach to a capstone course required for mathematics majors, outlining the course structure, pedagogical choices, and observed outcomes. The seminar utilizes a research-based approach, centering around the field of graph theory to cultivate students’ abilities in mathematical investigation. It’s presented as a conference proceeding, offering insights into practical course development within a university setting.
Why This Document Matters
This resource is particularly valuable for mathematics educators – professors, instructors, and teaching assistants – interested in innovative approaches to teaching problem-solving skills and fostering undergraduate research. It’s also beneficial for curriculum developers looking to design or refine capstone experiences for mathematics majors. Students considering research opportunities in mathematics, or those curious about the practical application of theoretical concepts, may find the overview of a successful seminar model insightful. It’s most useful when planning course content, seeking inspiration for project-based learning, or evaluating the effectiveness of different pedagogical strategies.
Common Limitations or Challenges
This document focuses on a single instructor’s experience and a specific implementation of a problem-solving seminar. It does not offer a comprehensive guide to graph theory itself, nor does it provide a detailed curriculum for a general problem-solving course. The strategies described are tailored to the instructor’s research interests and may require adaptation for different mathematical areas or institutional contexts. It doesn’t include specific problem sets, solutions, or student work examples.
What This Document Provides
* A description of a capstone course designed to enhance mathematical problem-solving abilities.
* Insights into integrating research experiences into undergraduate mathematics education.
* A framework for using a specific mathematical field (graph theory) as a vehicle for developing research skills.
* Discussion of strategies for guiding students through the process of formulating and investigating their own research questions.
* An overview of observed outcomes, including publications and ongoing research projects resulting from the seminar.