Poladian L (2013) Does authenticity help in engaging life sciences students in mathematical models? IJMEST, 44, 865-876)
The latest special issue of the International Journal of Mathematical Education in Science and Technology (IJMEST) has a collection of papers focussing on Quantitative Skills in Science. This particular paper caught my eye as I had been thinking about this issue of authenticity in teaching maths for biologists. What exactly constitutes authenticity? Is it in the content of the course, i.e. using biological examples to embed the mathematics or is it in the teacher, i.e. someone who uses maths within biological research? Or perhaps it is both?
Poladian tracks the move in traditional mathematics service courses towards situating the maths within realistic and relevant scenarios. But what Poladian points out, and what I think is missing from a lot of maths for biologists courses and textbooks, is the idea of teaching through mathematical modelling, showing that the processes of modelling are of greatest importance and using modelling as the central theme of the course. These processes include developing tools which can interpret and solve a real-life problem and making connections between concepts and procedures. An interesting example of this is described: using the same model in two different situations (spread of an epidemic and population growth in an ecological niche) and two different models for one biological scenario. This allows students to see the mathematics that underpins the biology.
The paper describes ways in which ideas relating to authenticity and realism were developed and implemented in a first year compulsory maths service course for life sciences students at the University of Sydney. It was a follow-on module from an Applications of Calculus course and focussed on models based on differential or difference equations for students intending to major in biology, psychology or medical sciences. Authentic contexts included examples from ecology, pharmacology and epidemiology and did not include many of the usual physics-based examples such as springs, pulleys and motion. Interestingly the mathematics was shown in both context and in context free forms. Student survey responses showed that many students were positive about the choice of contexts and this helped some, though not all, students to see the relevance.
In addition to this choice of authentic contexts there was clearly a contribution at a more emotional level. The enthusiasm of the lecturer and his ability to make connections with current research and items in the newspapers were also important. This suggests that, in order to teach mathematics for biology students, a mathematician needs to show enthusiasm for the biology and the potential for mathematics to enhance biological research.