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 “models & modeling perspectives” (MMP) about the nature of understandings and abilities that are needed for success in “real life” 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 textbook’s (or teacher’s) cleaned-up version of the meaning of the relevant concepts or abilities; and second, applying what was taught in “realistic” situations; or
• making practice mathematical – first, putting students in simulations of real life sensemaking situations where they “express > test > revise” 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.

Examples of the latter approach will be presented and analysed.

All welcome. No reservation required, but an email to This e-mail address is being protected from spam bots, you need JavaScript enabled to view it would be appreciated.

This seminar will be webcast live at www.lkl.ac.uk/cms/live