video
Models & Modeling Perspectives on Scientific Inquiry and Mathematical Problem Solving
1 March 2007
(90 minutes)
Richard Lesh, Rudy Distinguished Professor of Learning Sciences, Indiana University
Science educators speak about teaching scientific inquiry. Mathematics educators speak about teaching problem solving (or problem solving strategies, metacognitive processes, or habits of mind). Professor Lesh focuses on the fact, that in virtually every field where researchers have investigated differences between experts and novices, experts not only do things differently than novices, but they also see (or interpret) things differently. In particular, he will introduce research done over many years on gmodels & modeling perspectivesh (MMP) about the nature of understandings and abilities that are needed for success in greal lifeh situations where some type of mathematical thinking is needed for success. He will comment on the relationships with scientific inquiry and problem solving and the important ways that MMP is significantly different from both. He will also describe some important ways that the knowledge and the abilities that students develop tend to be significantly different depending on whether learning activities focus on:
- making mathematics practical | first, guiding students along (necessarily narrow) conceptual trajectories toward a textbookfs (or teacherfs) cleaned-up version of the meaning of the relevant concepts or abilities; and second, applying what was taught in grealistich situations; or
- making practice mathematical | first, putting students in simulations of real life sensemaking situations where they gexpress > test > reviseh their own relevant ways of thinking. Second, analyzing, decontextualising, systematising, and formalising student-generated conceptual tools to endow them with more elegance, power, sharability, and reusability.
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