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Abstract Title: Street-fighting mathematics: Teaching mathematical courage
Abstract: Mathematics, the queen of the sciences, rules its domains with a strict, deductive hand---at least, that is what our students get taught explicitly.  Mathematics courses, for example, come packed with definitions, lemmas, and theorems.  At best, students learn to follow proofs made by others.  Seeing mathematics as a field where any mistake is fatal, students cannot imagine using mathematics to express or discover patterns in the world.  The explicit focus on rigor teaches rigor mortis.

After years lamenting this problem, I created "Street-fighting mathematics", an applied-mathematics course at MIT whose explicit lesson is courage.  It teaches six reasoning modes useful across science and engineering: dimensions, extreme cases, lumping, pictorial reasoning, successive approximation, and reasoning by analogy.  I will illustrate each reasoning mode with examples---and, as a pacifist, encourage you to use these tools, and others that you find, to produce bold mathematical street fighters.
Abstract Type: Targeted Poster
Targeted Session: Taking Responsibility for the Hidden Curriculum: Practices and Challenges in addressing the broader goals in physics education

Author/Organizer Information

Primary Contact: Sanjoy Mahajan
MIT and Olin College