Chapter 9: Mathematicians Use Intuition

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 questions to encourage students to connect to their intuitions while solving problems

Andrew Stadel‘s fantastic resource: Estimation 180

Andrew Stadel‘s blog: http://mr-stadel.blogspot.com/

Kristin Gray‘s blog: https://mathmindsblog.wordpress.com/

Joe Schwartz‘s blogposts about Estimation 180:

• Our First Real 3-Act about mileage
• That’s Gold, Jerry! Gold!!
• Building Number Sense
• Boogers and Bloody Noses

Andrew Gael‘s blog: https://thelearningkaleidoscope.wordpress.com/