How Do You Teach Math?

Today I am at a Statewide Math Academy in my home state.  Our keynote this morning was by Phil Daro and one thing he said has really resonated with me and I’d like to pose this question to all of you:

Do you teach math to help your students get an answer or do you teach math to help your kids understand mathematics?

Phil showed this example of a common way that textbooks have us teach ‘addition of fractions with unlike denominators’:

This method of solving the problem teaches kids to get an answer (the answer is in green), but does nothing to develop their understanding of the mathematics.  It really struck a cord with me because with the emphasis switching to ‘multiple strategies’ to solve problems, the way I’ve seen it implemented in classrooms is teachers now just teaching lots of different ways to get the answer.  Instead we need to be teaching understanding and letting the students decide how they want to attack the problems.

I firmly believe this is one of the reasons why there is such a backlash to the Common Core, because teachers are now teaching lots of ways to get to the same answer.  If the goal is to get an answer, just teach one way!  But if the goal is to teach understanding of mathematics, LET THE KIDS use strategies they develop as their understanding of math develops.  Please don’t directly teach students strategies and methods as just a new way to get to an old answer, that’s what gives Common Core a bad name.