Math is a Learning Subject: More Small Steps for Differentiation

My favorite thing about math is that is a messy thinking subject. It is a learning subject. It should be messy and full of questions. We need to teach kids that it can be glorious when it suddenly is no longer messy and the patterns and the discoveries are right in front of our faces!

We have to model this for students, and more importantly we need to give them opportunities to make math a learning subject. So often we want to give all the answers, and tell them all the patterns, and show them how magical it is, that they lose their passion for discovering math at an early age. They begin thinking that math is a performance subject…teacher asks the question, student gives the answer…25 times in a row…on a worksheet.

Instead we need to give students meaningful explorations that can often run in the background of the school day.  These can often be very simple, and they really allow for differentiation. Some students will take these explorations much further than others.

Here is a third grade example:


The keys to making this work are:

  1. Give enough time for the exploration. This one will be 2 weeks.
  2. DO NOT, and I really mean this, DO NOT give them the answers. (This is very difficult, I know.)
  3. Tell them to work with each other! Isn’t that how we learn best? The second we want to know something we email, text or call someone. Let them teach each other.
  4. Make them research it, prove it and let them feel some confusion. This teaches perseverance and also that math is truly a learning subject. Bring in iPads, computers or have them look it up at home. (Hint: Use school tube when searching! Great resource!)
  5. Be sure that they understand that the most important part is not the answer they give you, but rather the method they use to solve it and WHY IT WORKS. That is the number one most important thing that they can get out of this inquiry activity.

Will all of the students be able to do this? Possibly…their level of understanding will vary from student to student. But in the end, when you bring them all together let the students do the talking. They will get there, if not now…they will have some prior knowledge for 4th grade.


Making Learning Targets More Meaningful

Last year there was a push in my school district to examine how we set up and deliver learning targets. I converted all of my mini lessons from adult language to kid friendly “I can” statements, made sure they were at the top of every lesson I taught and read them carefully to students.  I assessed whether they met them or not at the end of lessons with my formative assessments, and I would spend time frantically trying to “catch up” students who didn’t meet them.

Something still didn’t feel right to me.  I felt like the students were not owning their learning. So over the summer I did some research about how to make learning targets more meaningful to students.  I stumbled upon Marzano’s Levels of Understanding. I had this bright idea that maybe students could rate themselves at the beginning of a lesson, and again at the end.  I wasn’t sure how that would work until yesterday.

First I had to post the levels of understanding on the wall where students could refer to them often. I  explained them with the pretend learning target of “I can make cupcakes”.

0: You have the recipe and the ingredients out, but you can’t even get started.


1:  You get the ingredients mixed (with an adult) in the bowl, but that’s all you can really do.


2:  You get it all mixed, pour it into the baking pan, but you can’t work the oven, it is too hard for you.



3:  You did it! You made an awesome cupcake! (I would totally eat that cupcake, wouldn’t you?)



4:  You not only make the cupcake, you add sprinkles and serve it with milk, because it’ll taste better.

I gave this a try during math yesterday.  I read the learning target: “I can write a number up to 1,000 in expanded form.” I asked them to rate themselves on their learning target in their math journal. As I peeked over their shoulders, I noticed a few 1’s and a lot of 2’s and 3’s.  I went through the mini lesson, had them practice several problems, and gave them an exit slip.

After they were finished filling in their exit slip I brought them to the carpet for closure.   I asked them to rate themselves again right on their exit slip.  Then, I explained that to get to recess, I was looking for people who achieved a 3 on the level of understanding chart. Suddenly I noticed some uncomfortable shifting and squirming with a bunch of the students at the carpet.  A couple of them raised their hands and asked if they could redo their slip.  I realized that holding them accountable this way was weeding out the students who finished their exit slip in a hurry (not caring if they got it right) to get to recess.  The number of students that I would have to follow up with the next day dropped from 8 to 2!

Holding them accountable with this scale let them know that THEY were the ones in charge of their learning, not me.  While I am not sure if I’ll be able to do this for every lesson, I’m sure going to try! The impact on their learning and their precision to the learning target was awesome.