The University of Montana
Department of Mathematical Sciences

Technical report #17/2008

Models-modeling perspectives and the philosophy of pragmatism

Richard Lesh
Indiana University

Bharath Sriraman
The University of Montana


Abstract

Long ago, the American pragmatist John Dewey emphasized the fact that making science practical involves significantly different educational goals than making practice scientific. Recent studies based on models & modeling perspectives of learning and problem solving (Lesh & Doerr, 2003; Lesh & Sriraman, 2005) demonstrate that the knowledge and abilities that students develop tends to be significantly different depending on whether learning activities focus on: (a) realizing mathematics - by first teaching what is to be learned and then applying these concepts or abilities in realistic situations, or (b) mathematizing reality – that is by first putting students in sense-making situations where the conceptual systems that they develop on their own are later de-contextualized and formalized. Throughout this paper, the examples and observations suggest that, regardless whether we focus on conceptual development or skill development, a large share of what it means to “understand” is likely to be neglected unless adequate attention is given to learning activities where students are encouraged to mathematize reality – by expressing>testing>revising your own ways of thinking as opposed to being guided along artificially narrow paths toward idealized versions of the teacher’s or textbook’s ways of thinking.

Keywords: conceptual systems; model eliciting activities; models and modeling; Pragmatism

AMS Subject Classification: 97

Download Technical Report: fdf (605 KB)

Pre-print of paper accepted in ZDM- The International Journal on Mathematics Education, vol.41, no.1, xx-xx