## Monday, October 26, 2015

### Productive Struggle

Here is part of the quiz I gave on Friday:

The first time you go to the gym, there is a fee you have to pay to sign up.  You also have to pay every time you use the gym.  If you use the gym 5 times, you will have paid $70. If you use the gym 10 times, you will have paid$110.
a) What is the cost per time you use the gym?
To give a little bit of context, we have been working with linear functions for the last five weeks or so.  I have completely overhauled the unit from last year in order to (hopefully) have students develop significant conceptual understanding and then leverage that as we work towards fluency. In order to reach this goal, part of what I am doing is giving students more tasks where there is not a set procedure for them to follow and supporting them through productive struggle.

With this quiz question, about 1/3 of the students aced it, and 2/3 had no idea. There was very little middle ground. The majority of students who were able to solve this problem are also the ones who have been persevering through problems all week-talking through them with their partners, asking questions, and sharing ideas with the class.

I was frustrated that despite spending significant time on this type of problem in class, 2/3 of the students were not able to answer this question. My solution was to do more of these problems with more scaffolding.

But then I went to talk to one of my co-workers and asked for his advice. He had two pieces of advice for when the class is so starkly split in understanding of a concept.
1) Raise the level of demand/difficulty, at least for part of the task. This evens the playing field and doesn't leave 1/3 of the students frustrated because they already get it.
2) Take a break and come back. Use the break time to come at the concept from a different angle or do something totally different. It should be different enough that it's not only the same kids feeling successful.

This was exactly the advice I needed to help me keep on this path of students as sense-makers, productive struggle, and building conceptual understanding.