Incorporating Mathematical Reasoning in Interdisciplinary Courses
Dr. John Jungck, Professor of Biological Sciences and Director of the Interdisciplinary Science Learning Laboratories at the University of Delaware, was the featured speaker at the New Normal professional development dinner meeting for high school math teachers on Thursday May 16. Though tenured as a biologist, Dr. Jungck lists additional titles of research mathematician and photographic artist, two subjects that have influenced his scientific inquiry during his career.
Professor Jungck used manipulatives as well as common, everyday items to highlight methodologies that show how mathematical reasoning can be integrated into university-level courses in disciplines other than mathematics, and as a result, contemporary issues in education (curricular innovation, collaborative learning and subject-area coaching to name a few) can be accessed through the use of the mathematics of geometry, statistics, modeling and networks.
Dr. Jungck demonstrated how conceptual development of geometry and topology can assist students’ analysis of how DNA changes its three dimensional shape in the “3-R” cellular processes of replication, recombination and repair.
Biology textbooks seldom include a discussion of the underlying mathematics, a characteristic Dr. Jungck considers unfortunate. For example, he questions what it really means, referring again to DNA, to “separate strands”, “alleviate coiling”, “untwist the double helix” and “remove positive supercoils”? How is the structure of DNA affected during these transformations? Is there an energy loss or gain during these processes?
Dr. Jungck showed the audience of math teachers that the use of simple toys made of inexpensive materials such as rubber bands, tygon tubing, ribbons and zippers, can be employed to generate a different, more complex and more dynamic image of the “3-R” processes of DNA. And, through the perspective of this image, a clearer understanding can be gained of the tangling and intertwining of DNA, as well as a deeper appreciation for the complex regulatory mechanisms that prevent cell death by hopeless DNA entanglement each time the DNA replicates, recombines or is repaired.
By combining exploration of physical models in the context of mathematical concepts, Dr.Jungck believes that teachers can engage students in becoming active participants in the interpretation of experimental laboratory results. Instead of just reading phrases such as “alleviating coiling” and “unzipping DNA” students can explore these processes through their own experimen- tation with toys, models, manipulatives and simulations.
Before the audience realized, Professor Jungck’s lecture had concluded, but the message he left us with was clear – that by introducing basic concepts from the mathematical fields such as topology and geometry, teachers can provide students with tools necessary for quantitative exploration of various physical models.