Studio Day

A few weeks ago, during our Studio day in my mathematics class, I had the pleasure of meeting with two students from Maywood Hills Elementary, a second grader and a fifth grader, to talk about their mathematical thinking.   This was a very eye opening experience for me because it proved to be a lot more challenging than I originally thought it would be.  I seemed to understand the fifth grader’s thinking pretty well because he was in the Recall stage on the CGI trajectory.  He used algorithms to solve the problems from the interview task card and I was familiar with this method so we seemed to speak “the same language”.  Occasionally, I’d have to ask for clarification, but for the most part, I understood the method he was using to solve the problems.

Working, with the second grader, however, proved to be much more challenging.  I really had to listen to his strategy because I wasn’t familiar with the way in which he was solving the problems I gave him.  He, for example, when adding two, 2-digit numbers, started from the left side of the problem, with the tens, rather than the right side, with the ones.   He then represented the tens by writing lines (10-sticks) and circles to represent the ones.   After this was done, he’d count the 10-sticks and/or circles (ones) to see if he could form groups of ten.  If he did have any groups of ten, for example, ten 10-sticks, he’d draw a circle around them and write a 1-stick to the left of the tens column to represent 100. 

I later found out, toward the end of my session, that my second grade student had used base 10 blocks to learn addition.  Once I found this out many of the things he had told me started to make a lot more sense.  He, for example, had drawn a square under his circled grouping of ten 10-sticks.  I now realize this represented a 100-square from the base ten blocks.  

 I so enjoyed working with this student and once  I understood his method I was actually able to help him find a mistake he had made.  This exercise truly showed me the challenges I’ll be facing in my future classroom, to figure out the thinking of my students.