Re-working Math

I saw this on pinterest and it just struck a chord with me.  I all too often think about this in regards to my math instruction.  I find that I am spend far too much time feeding the answers to the students and not letting them think it out.  There just isn't time.

But really, if I am constantly feeding the students the answers, they will never be able to do anything without me.  This learned helplessness will happen where the students just wait until someone comes along to tell them exactly what to do, never letting them think for themselves.  I really have to force myself to schedule time devoted to mathematical thinking.  It is just too easy to let it go but I KNOW that when I teach my students to think, the way their brain works in my class changes for the better.

What I am finding particularly successful this year in getting them to think more deeply in math is asking my students to solve one problem in two different ways.  You see, every year I teach a math concept (any math concept).  My students then come back and tell me how their mom was teaching it a different way and that a near brawl occurred because "how can we do it differently than my teacher told me?????!!!!????"  So in order to stop this misconception that I am always right and that the way I teach it is the ONLY way, we have been doing these "Two Ways" problems.

The idea is very simple.  I give the students one problem to solve.  We take a bit of time and dissect the language of the problem to really find out what is being asked.  Then, once I am sure the students understand, the get a few minutes to begin solving it on their own.  I then let them work in pairs.  The goal is not to just find ONE way to solve it but TWO.

And let me tell you...this is HARD HARD HARD.  The students want to be done at solution number one.  What's more, they want to just find a number solution and forget about explaining themselves.  The first few times I do this, I get very simplistic, basic answers.  But now, after about a month of doing these once a week, my students are beginning to produce answers that really are justified, full of academic vocabulary, and show an understanding of the math we are learning. 

While they are working, I am walking around asking them guiding questions:
What are you doing?
Can you explain this to me?
What can you tell me about your thinking process?
For those who need a bit more guidance, I try to help them get to the answer without giving it away.  Soon, they realize that this is about the math process...not the right answer.

As I am walking around, I am looking for student solutions that are different from each other and show varying strategies.  I then put these up on the ELMO during our debrief.  I have the students in the class look at the solutions and dissect them.

What did the solver do?
Why do you think this person did this?
What was done correctly?
How did this differ than the other solution you were shown?









I jot a few of the solution strategies down, and we have a class list of how to solve problems.  As the weeks go by, this list gets larger and larger...and the kids have more and more strategies to pull from.

The hardest part of this whole thing, for me, is coming up with the problems.  So I sat down, and wrote one for each of the Common Core standards.  That way, I have something for everything I am teaching.  And I have made it available for you.  I have 3rd, 4th and 5th grade done now, but  6th {hopefully} soon.   You can get the 5th grade one here.  

You can get the 4th grade one here! 

And 3rd Grade is available here!

Now it is your turn.   How do you get your students to become math *thinkers* in addition to math *doers*?