Instructor: Lisa Fontaine-Rainen
Ages: 8 - 14 years
Mathematics courses often teach students how to solve problems, use algorithms, and number crunch. Our Special Topics in Mathematical Explorations courses teach students how to pose problems, develop algorithms, explore ideas, prove (both formally and informally) their methods and ideas work, and propose next steps. Students can use the skills learned in these classes to stretch their regular math curriculum, challenge their assumptions about mathematics, and truly think like a mathematician.
Special Topics I will base our explorations on patterns such as in the Tower of Hanoi problem, explore advanced ideas in rates, ratios, and proportions, explore representing parts of wholes in different bases, and look at the relationship between mathematics and science. Students will use variables to represent problems – a basic knowledge of variables is useful, but not necessary.
Week 1: Introduction to mathematical thinking and the Tower of Hanoi
Week 2: Tower of Hanoi extension and explorations – discussion: is finding a pattern enough?
Week 3: Triangle Inequality Theorem – deriving it, using it, applying it to polygons with more sides, considering if it works in non-Euclidean geometries.
Week 4: More on patterns – Going from a table to an equation, reasoning about patterns
Week 5: More on patterns – Finding patterns in figures, sharing out of pattern explorations
Week 6: Explorations in ratios – what questions can expand our thinking on ratios? Dilutions and paint mixing.
Week 7 Introduction to rates, looking at rates with the eyes of a mathematician, dimensional analysis
Week 8: Trickier rate problems, problem posing and exploration
Week 9 Arithmetic in different bases – why and what questions can we pose?
Week 10: Representing parts of wholes in different bases
Week 11: Repeating radix numbers and different bases, and other radix explorations
Week 12: Looking for mathematical relationships in the world around us – Euler loads and elasticity
Week 13: Looking for mathematical relationships in the world around us – soil and student posed problems
Week 14: A flexible day to return to ideas we’ve explored previously and want to explore further, or extended problem solving
Week 15: Student presentations and further explorations