Capstone Project: Mathematics Across Disciplines

Author

Intisar Q. Hibschweiler

Professor of Mathematics and Chair, Department of Mathematics and Computer Science

Daemen College

Citation

Hibschweiler, I. Q. (2014). Capstone Project: Mathematics Across Disciplines. Daemen College.

Description

This senior thesis assignment is intended for mathematics majors.  It requires students to integrate coursework, knowledge, and skills to demonstrate a broad mastery of a specific topic within the mathematic discipline and apply the topic to an entirely different discipline.

Background and Context

This is a senior thesis assignment. This assignment is intended for senior mathematics majors, a capstone product that requires research in mathematics based on several resources.  This assignment will enable the students to integrate coursework, knowledge, and skills to demonstrate a broad mastery of the theories and background in a specific topic within the mathematics discipline and apply the topic to an entirely different discipline. Assignment instructions can be modified so that it can be used and integrated in any course that requires any form of a research paper and/or broad integrative knowledge at any level.

DQP Proficiencies the Assignment Intends to Assess (at the Bachelor Level)

  1. Construct a paper that draws on current research, scholarship, and techniques in a Mathematical topic. (Specialized Knowledge)
  2. Apply the theories from your selected mathematical topic to at least one other field of study such as Physics, Biology, Accounting, Chemistry, Engineering, Computer Science, and others. Develop an approach that draws on both the mathematical theories and theories from other fields of study.  (Broad, Integrative Knowledge)
  3. Locate, evaluate, incorporate, and properly cite multiple information resources in different media. Use MathSciNet format, www.ams.org. (Intellectual Skills: Use of Information Resources)
  4. Translate a verbal problem into mathematical algorithms, generate quantitative analysis of the problem, and present the resulting calculation to solve the problem stated. (Intellectual Skills:  Quantitative Fluency)
  5. Construct and organize a well-supported argument or explication in writing and use at least one other visual representation (graphs, mathematical software), so that material can be understood by your class peers and other students with a limited mathematical background.  (Intellectual Skills: Communication Fluency)

Reflections

The program plan for the students enrolled in this course requires successful completion of courses from other disciplines related to the field of mathematics prior to enrollment in this course. The students are required to complete 6 credits in computer science, 6 credits in calculus-based physics, and through completion of general education requirements and and a minor, the students can complete a sequence of courses in one discipline such as economics, accounting, biology, chemistry, business and others.

Students taking this course are also required to successfully complete a one credit prerequisite course, namely MTH 459, Introduction to Mathematical Research. Students enrolled in MTH 459 are required to submit a polished research proposal and an annotated bibliography. In addition, in all mathematics major courses the students are required to complete projects and homework that require demonstrating skills in mathematical writing, quantitative skills, information literacy, and the use a variety of technological tools (e.g., algebraic and visualization software, statistical packages, a high-level programming language)  to solve real-world mathematical problems.

Often the students do not understand the assignment expectations and why the feedback on their first draft indicated very poor performance in certain proficiencies.  The feedback required a great deal of suggestions for improvement.  Incorporating research and writing in the discipline early on in the major required courses is essential for successful completion of this type of assignment. The students often find such assignments very challenging and often a cause for a great deal of frustration. This is because the students in this course encounter a shift from a course focusing mainly on content to a course that focuses on connecting both content and skills. The course is limited to 5 students per semester because it requires a great deal of time from the faculty member.

The value of this course to the students has been documented through alumni surveys, review and analysis of the course-required self reflection and portfolio, students’ evaluation of the course, and assessment of students’ work.  The students report that the research paper was a key growth and cornerstone among the learning experiences at the undergraduate level. The students also report on how the assignment in this course helped master skills that were not addressed in other courses.


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