Nurturing mathematical creativity and curiosity in Foundation Mathematics students

Rachel Passmore, University of Auckland, New Zealand, r.passmore@auckland.ac.nz

Encourages students to see elegance in solutions. Gives challenge problems a but beyond the level of the course for fun. Solutions go on intranet and discuss which they like and dislike. That’s a different kind of creativity than what is in this talk.

Len Lye, New Zealand sculptor with kinetic pieces or the millionaire with a sculptor park, Gibbs Farm (only open 2-3 days a year).

Definitions about creativity in mathematics

• Discovery of something new to you even if it’s known to others (Sriraman, 2004)
• Differentiate between professional and student creativity (Sriraman, 2004)
• Unusual ability to generate novel and useful solutions to problems (Chamberlin and Moon, 2005)
• Non-algorithmic decision making

Activities and strategies to creativity in mathematics

• Multiple solutions spaces (Marion Small, open questions) e.g. what 2 fractions when multiplied together give a product a little less than one fraction and a lot more than the other? (Notice there is no one correct answer.) Try to get students to shift from thinking there is only one right answer and being good means getting it fast.
• Choose values for a, b, c. (Could limit them to be 1 – 20, say). Write a story that could be solved by the expression a/b = c/x.
• Rich tasks. Hook students in at the start of a topic risps.co.uk. E.g. The answer is 1, what’s the question? Graph of straight line and parabola with bounded area of 1.
• Fermi questions, use estimation, focus on process e.g. how many water balloons would it take to fill this room?
• Dan Meyer’s Three Act Maths Tasks
• Rachel’s students didn’t know how to pose a mathematical question about a scenario. Now she gives them a couple of questions they have to answer and they add more that go on the board and they choose some of these to answer.
• com. Get students to create logos, e.g. Macdonald’s arches, or to make a design inspired by traditional cultural designs.