The End of the Beginning

The historical development of mathematical modeling as its own unique area of mathematics reflects its roots in operations research, the growth of technology in society and its emergence as an integral tool for mathematics exploration, and the modern trend of applying mathematics to other knowledge domains in increasingly sophisticated ways. Both process and product, it is difficult to imagine a well-defined definition that also completely depicts what modeling is and where it is used. In moving from the environment of the practitioner to the classroom, there are a variety of institutional and pedagogical responses that range from case study examinations of existing models, to a systematic review of the mathematical content associated with modeling, to providing students opportunities to develop and present their own mathematical models for given tasks. It seems natural to have such a phase of "exploration," probing the various facets of modeling for their potential as the substance of educational experience and source of knowledge production in the classroom.