Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities

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

Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art

The teaching and learning of mathematical modelling is an important research field all over the world. In this paper we present a survey of the state-of-the-art on empirical studies in this field. We analyse the development of studies focusing on cognitive aspects of the promotion of modelling, i.e. the promotion of modelling abilities resp. skills, or in newer terminology, modelling competencies. Furthermore, we provide a literature search on the role of empirical research in important mathematics education journals and point out that this topic is only seldom treated in these journals. In addition, Proceedings of the conference series on the teaching and learning of mathematical modelling and applications were analysed in order to identify the role of empirical research in this important series and the kind of topics which are examined. The literature research points out the dominance of case study approaches and cognitively oriented studies compared to studies which used quantitative research methods or focused on affect-related issues. Finally, the papers in this special issue are described and developments and future prospects are identified