PKAL Faculty for the 21st Century
F21 Class of 2005 Statement
How colleagues in different disciplines come together to reshape the undergraduate STEM learning experience
After decades of increased specialization and discipline-focused research some science researchers are exploring more interdisciplinary directions. While mathematics and physics and some areas of biology and chemistry have long had close connections, more and more science work combines any of these areas as well as other disciplines. One of the major challenges with this shift in research is communication. For example, to a biologist a hypothesis is a theory to be tested through experimentation, but to a mathematician it is a fact to be assumed before beginning to work on a question. As a mathematician I see value for both STEM education, in general, and mathematics education, in particular, in interdisciplinary work with my colleagues.
From my science colleagues, I have discovered they prefer using Leibnitz notation whereas calculus books have nearly uniformly moved away from using this representation. This is a small matter that is easy for me to adjust in my classroom to facilitate learning across the sciences. Utilizing this representation introduces students to a notation that is more mathematically difficult for them, thus enhancing their mathematical skills, while better preparing them for their science courses.
Further collegial conversations lead me to rethink the problems and projects I assign in my calculus courses. Recently, mathematicians have been putting more problems from other STEM disciplines into texts and utilizing them in courses, but these are problems written by mathematicians for mathematicians. Often the units are missing, or are not particularly relevant and the numerical values are generally unrealistic. I have been equally guilty of this practice in efforts to make “interesting” questions for my students. We are not experts in each of the fields and it is very time consuming to create good calculus application problems without expertise in other STEM areas. However, through collaboration with my physics and chemistry colleagues I have been able to not only incorporate problems in my classes that are framed in the correct scientific context, but have been utilizing the same problems that my colleagues use in their courses. I am currently working with biologists and economists to incorporate similar problems in my course next year. This work would not be possible without the help of my colleagues from other disciplines.
I also plan to take this linking of the courses to another level. The aim is to address issues we see in our STEM undergraduates who struggle with seeing the connections between disciplines. My colleagues and I will actively help the students synthesize the connections by overtly using the exact same problem from both a biological and a mathematical perspective (for example) in their two courses. These new problems have also opened up new ways for me to illustrate the beauty and power of mathematics to my students, thus not only enhancing my course in an interdisciplinary, but also disciplinary way.
I plan to extend this work and to find other such opportunities as I believe that by consciously utilizing the same problems in calculus, introductory biology, physics, chemistry and economics we dramatically enhance the undergraduate STEM learning experience. We start the students with a synthesizing experience, we enhance each of the disciplines in their own rights, and we illustrate the need for disciplines to work interactively while introducing some of the difficulties that currently exist in terms of vocabulary. This experience at the undergraduate level will help students to better appreciate their colleagues in other disciplines in a way that has only recently begun to happen in STEM fields.