Abstract
Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.
Highlights
Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement
The project that we report from this paper grew out of this struggle and explores the conjecture that mathematical modeling (MM) can be a vehicle for the integration of mathematics and biology (Brewer & Smith, 2011) and that engagement with Mathematical Modeling (MM) activities can contribute to more positive attitudes towards, and competence in, both biology and mathematics (Chiel, McManus, & Shaw, 2010)
We report from a project in which we develop biology-related MM activities and introduce them to year 1 biology students with the awareness of two potential caveats: that this engagement, often requiring the synthesis and application of mathematical knowledge gained elsewhere, might require a certain level of academic experience (Edelstein-Keshet, 2005); and, that an integrative approach to mathematics and biology education might have adverse effects, such as breadth at the expense of depth, or mathematics anxiety problems (Madlung, Bremer, Himelblau, & Tullis, 2011)
Summary
Research into the mathematical needs of non-mathematics specialists is by no means new (e.g., Kent & Noss, 2003). In its simplest form, this cycle involves taking a problem from an extra-mathematical domain (for instance, biology), translating it into mathematical terms, solving it through mathematical means, and translating the solution back into the terms of the extra-mathematical domain In this process, assumption building plays a central role. We conclude with a brief discussion of substantive implications (what do these analyses tell us about these students’ evolving experience of mathematics in the context of biology?), theoretical implications (what do these analyses indicate about the distinction, interplay, and tensions between ritualized and exploratory participation in discursive activity?), and practical implications (what do these analyses tell us about the potency of MM-focused pedagogy in biology courses?) of our analysis. In the light of above embedding of our analysis in the commognitive perspective, the research questions that this paper explores are as follows: What evidence of ritualized and exploratory engagement with assumption building can be traced in biology students’ engagement with MM activities? Before presenting our data analysis, we introduce the study’s context, aims, methods, and participants and outline the MM activities that were the backbone of our data collection
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