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*?


  1. I love this idea! When I worked as a trainer for a large company, I was amazed at the number of recently graduated adults who could only focus on the "right" answer. Problem solving skills are so important for the real world. Yes, the right answer is important, but you have to be able to think about the process before you can even hope to get the "right" answer!

  2. This is great Stephanie. I hear you. I am always trying to give enough think time and explanation time to my kids. It is getting easier for them to share their thinking now.
    I use the idea that we all take different routes to get downtown, but we still arrive. Math works like that too. If you can explain your thinking, we can help direct you if you get lost or we can try your route instead.
    I am looking forward to seeing your Grade 3 package when it comes out. The concepts will be slightly different, but they will be in alignment mostly with our curriculum as well.

    Charlene/Diamond Mom

    1. I totally say the same thing Charlene! I always use the freeways though. You can take the 5 or the 405, but you are going to end up in San Diego one way or another! ;)

  3. What a great idea! My kids have been surprising me with alternative (but correct!) ways of doing long division thanks to all the time they spent using manipulatives this year. I think when we get to bar modeling I'll try challenging them to show me "two ways."

  4. Great idea! I will be looking forward to the third grade version!

  5. This is fantastic, Stephanie. Our program asks kids to do this, but helping them understand why to bother with it is the tricky part, since they just want to be done. I can't wait to check this out.

  6. Beautifully explained, Stephanie. It is so very important to get our students to be thinkers and not doers. I'm so glad that I stumbled across your blog a year ago. It has made me a thinker and not a doer, too :)

  7. You're so right! We are using Math Journals for the first time in 4th grade this year and it has been amazing! The kids first had to get used to not knowing the answer right off the bat. Our motto is Try Something, Even if it's Wrong! Even incorrect answers give us useful information. Then once the kids chose a strategy to try, changed the strategy if necessary and solved the multi-step problem, they have to explain their thinking. Talk about challenging! Math Journal problems have come from many sources but it has absolutely changed my math instruction and changed the way my students think.

  8. You're so right - we often train our students to be dependent on us.

    You asked how I turn my mathematicians into thinkers. I actually wrote a post on the procedures I use:

    I just subscribed to your blog and am looking forward to reading more of your stuff!

  9. Great post Stephanie. I have been teaching math through problem solving the last three years. This year I had parents that questioned whether their students were learning the math skills they needed because it wasn't drill and skill instruction. When students have to apply the skills through problem solving, I have found that they actually maintain their skills better and my kids have fun solving the problems. We focus on showing our thinking in three ways: pictorial, procedural, and words. The students are eligible for higher than a 3 if they can show an additional way to explain why their answer makes sense. We are currently doing a great project called the Math Curse that I think your kids would love. After reading the Math Curse by Jon Scieszka, the students write a sequel to the story using an introduction, 10 story problems, and a conclusion. The introduction has to explain how they got the curse, the ten problems have to be written from the five common core strands with two from each strand, and the conclusion has to explain how they got rid of the curse. After the kids write their stories, we publish them using Smart Notebook so the students can make the stories interactive. We will begin posting about our project when we return from can find us at

  10. LOVE everything about this post. I'm not sure which is harder though--teaching the kids to be thinkers or getting teachers to shift their own thinking/beliefs to start teaching kids how to be thinkers?? (Got that?? hahaha) I totally agree with you and have been preaching that myself for quite some time!! In fact, one main reason I moved to 1st grade this year from 4th grade math (after teaching it for 5 years) was to work on foundational skills and thinking in students. The 4th graders came in worn, damaged, and incorrectly trained. They learned that math was about memorization, formulas, and--my favorite (not)--the right answer. They were afraid to try and afraid to be wrong. So, of course, you can imagine their frustration when I expected them to think. They soon realized that having the right answer was not the end, but just the beginning. OMG, I can go on and on about this!!! I am happy to say that these little firsties I have have been such a breath of fresh air for me and they are REALLY rockin' the mathematician shoes! It has been a good move and I know that these kiddos will be more prepared for upper level math when it comes time for them to move on. Thanks for sharing your feelings!!

    Tales of Frogs and Cupcakes

  11. This idea is exactly what the program called CGI is all about. It is amazing!

  12. Here is a website that explains more about CGI and it has good resources.

  13. I was wondering if you ever made the 6th grade ones? This is an amazing idea by the way!!!


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