Wednesday, September 03, 2014

What Does a Number Look Like? Developing Mathematical Thinking

In days of old, mathematics at the early years was a lot of memorization.

Now we're really working to build mathematical thinkers: students who reason, debate, prove, question, and collaborate.

What do numbers look like:
  • when we tally?
  • as arrays?
  • compared to other numbers?
  • as expressions?
  • with an inequality?
  • in an equation?
  • when it is doubled, tripled, quadrupled. . . ?
  • divided in half, fourths, sixths. . .?
  • with one more or one less? 
  • in real time examples?
  • in expanded form?
  • word form?
We want to build flexible, facile mathematicians who can understand numbers in multiple ways, and see that understanding as one way to find solutions, see patterns, predict, analyze, order, and describe.

The more I learn math, the more I realize how this subject exercises the brain in ways that impact far beyond the subject itself. Agree?