Friday, February 8, 2013

I Used to Think, Now I Think

This month I did the routine called, "I used to think, now I think."  In third and fourth grades, we have been focused on perimeter and area.

I already knew that students have a hard time with perimeter and area.  Mainly, they seem to mix up these two terms.  We spent time exploring perimeter and area in many different ways in my classroom.  We used geoboards on the iPads to build rectangles with a given perimeter and area, we measured them on "hallway polygons" taped down in the hall, we measured the area of Sao Paolo, Brazil to experiment with irregular figures, and we used base-ten blocks to explore the many ways to make a figure with an area of 5 square centimeters.

This routine extended my thinking because it gave me a window into what misconceptions students still had.  It also gave students a way to express in words what math thinking was going on in their minds. Here is a sample of what kids shared:
  • I used to think perimeter was by multiplication.  Now I think perimeter is by addition and base times height = area.
  • I used to think perimeter and area were hard becaus I did not know what was the inside and what was the outside. Now I know that perimeter is the outside of a shape or polygon and area is the inside of a shape or polygon.
  • I used to think area and perimeter were the same thing and would add both together.  Now I think perimeter is the outside of the area.  Area is the squares inside the perimeter.
The fourth graders reflected on Edmodo, which was  great option because I was able to give them some feedback.  A sample of one student's post and our conversation on Edmodo is below.
A challenge or puzzle I have is, would this have been a better activity had I given them the "I used to think" before I taught perimeter and area?  In the past, students in third and fourth grade have been hard pressed to tell me all they know about a topic when they had limited schema.  However, my third graders had a difficult time thinking back to a time when they knew less about this topic than they know now.  Many of them said, "I have always known about perimeter and area."  It helped for them to think of another student, a second grader, coming into our room and thinking about how little they may know about this subject and then to comment on how little they used to know.  The book says to stick with doing both at once at the end of a subject because students can't possibly identify misconceptions and ingrained assumptions until they have been confronted.  This type of reflection can only happen after new learning has occurred.   The book also suggests that students will do better as this is established as a regular routine.  I regularly have students reflect on their learning, but I think that the process has become bogged down, so this was a good way to switch it up on them so they had to reflect in a different way.  I am going to keep this reflection routine in my back pocket and try it again with both classes and see if there is improvement in the depth of their responses.


  1. Jeff, your post was very timely for me to read. I am working on modifying many of these routines for ECE and am faced with the same challenge you stated. When you think of schema for a 4 year old, It's going to be even harder for them to reflect on a time when they didn't know something. I am planning to use this routine as I begin a unit on Farms. My plan is to modify it by allowing my students to write about (draw a pix) of what they think they know about farms as an instroduction to the unit and pre-assessment. My plan is to then do the "I used to think, I now think..." routine at the end of the unit AFTER giving the children a chance to review the pictures they drew at the beginning of the unit. It may be cheating a bit, but your post made me think I'm not so off target by giving them the scaffolding to "learn" how to reflect. Thanks!

  2. What a neat hands-on activity for the kids! My second graders struggle with thinking about what they used to think after they've learned something. Like your third graders, often insist they've always known something. Or they make something up like "I used to think schema was an animal," which I know isn't true! I've adapted this routine by having them write down (or I chart) what they think something is *before* I teach a lesson or at the beginning of a unit. Then, we go back an talk about their previous thoughts at the end. I think/hope it makes them realize how much they're learning. Thank for sharing this, Jeff!

  3. I agree with all of you--especially wondering if I was "cheating" by having them record their ideas before we studied a concept. I have reframed it in my mind as Leslie did, as scaffolding. I did it once without, as an end of study reflection. It did not go well. I switched the next unit of study to writing it down before and they had much more success in reviewing it and being able to state what had changed in their thinking. Thank you all for sharing!

  4. I like how you are always using technology in your lessons. I would think, too, that the "I used to think" would be good before a unit and the "Now I think" at the end. I haven't tried this lesson yet, but will try as the book suggests. I would also like to try the Edmoto to give students feedback. You give me many good ideas, sensei.

  5. Jeff, I saw the tape on the floor in the 3/4 pod and thought that was a great way for students to experience area and perimeter. It is taught in 2nd grade, but evidently the knowledge didn't stick. I think you've done it in a way that will be more meaningful and lasting for the students.
    Also, I never thought I would say this but blogging and making comments is a great way for the teachers to share thoughts and ideas. Thanks for making me work outside of my comfort zone.