Chapter 9: Mathematicians Use Intuition

Study Guide for Chapter 9

Terry Tao’s post: There’s more to mathematics than rigour and proofs

Leone Burton’s article: Why is Intuition so Important to Mathematics but Missing from Mathematics Education? ($)

Evelyn Lamb‘s article introducing readers to Bill Thurston: The Mathematical Legacy of William Thurston

A lovely video of Thurston, showing how he used his imagination, manipulatives, and diagrams to visualize mathematics. “From Knots to Narnia.”

Deborah Ball’s must-read article about manipulatives: Magical Hopes: Manipulatives and the Reform of Math Education, courtesy of American Educator: The Professional Journal of the American Federation of Teachers, v16 n2 p14-18,46-47 Sum 1992.

Figure 9.6: The Estimation Cycle

Figure 9.7: Lesson components that encourage students to build mathematical intuition


John Stevens‘s Would You Rather? resource (home of the quarters problem and lots of other rich tasks)

Printable 2-page version of the questions to encourage students to use their intuitions, pages 224-226

Andrew Stadel‘s fantastic resource: Estimation 180


Andrew Stadel‘s blog:

Kristin Gray‘s blog:

Joe Schwartz‘s blogposts about Estimation 180:

Andrew Gael‘s blog: