“In the beginnings of arithmetic and algebra, the main purpose is not to get the pupil making calculations. The main purpose is to get him into the habit of thinking, and to show him that he can think the problems out for himself.
“Pupils ask ‘Am I allowed to do this?’ as if we were playing a game with certain rules.
“A pupil is allowed to write anything that is true, and not allowed to write anything untrue!
“These are the only rules of mathematics.”
—W. W. Sawyer, Vision in Elementary Mathematics
[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]
Inspired by Sawyer’s Two Rules
I love this quote so much, I turned it into a printable math activity guide. I hope it helps inspire your students to deeper mathematical thinking.
Here’s the product description…
Join the Math Rebellion: Creative Problem-Solving Tips for Adventurous Students
Take your stand against boring, routine homework.
Fight for truth, justice, and the unexpected answer.
Join the Math Rebellion will show you how to turn any math worksheet into a celebration of intellectual freedom and creative problem-solving.
Help your students practice thinking for themselves as they follow the Two Rules of the Math Rebellion: “A pupil is allowed to write anything that is true, and not allowed to write anything untrue! These are the only rules of mathematics.”
Denise Gaskins' Let's Play Math 