I’ve been trying to figure out the “best” way to write this blog post… finally I decided to just write it in whatever imperfect way it comes out because I think it’s one of the most powerful things that we can do as teachers and I want to spread the gospel far and wide!
But it’s not just the exit slip, it’s what you do with it. You’re getting some information about your students’ understanding, and then following up in a very strategic and targeted manner.
Here’s what I did recently with an exit slip on limits and continuity.
Intervention #1: Pulled small groups
I gave this exit slip at the end of a class period on Tuesday. On Tuesday afternoon, I quickly sorted exit slips into “yes” and “no” piles based on their answers to #1(a)-(c). Then I sorted the “no” pile into subcategories based on the mistake that was made. I ended up with these categories:
- On #1(a) – students who answered 2, which is the value of f(-2) not the limit as x approaches -2;
- On #1(b) – students who answered 3, which is the limit from the right not the limit from the left;
- On #1(c) – students who answered 2, which is the limit from the left and the value of f(3);
- On #1(c) – students who answered 1, which is the limit from the right.
I made new student teams based on like mistakes. On Wednesday, I projected a PowerPoint slide with their new teams; as they worked on some practice problems together, I visited each group to address the misconceptions in their exit slips and answer any remaining questions. (In the past I have pulled small groups to work with me at a side table, but this year I’ve decided to regroup teams temporarily and visit each team.)
Intervention #2: Targeted whole class intervention
When I looked at students’ responses to #1(d), I noticed that all students had said that the function was not continuous at x=1, but most did not reference the definition of continuity in their explanations. This told me that I needed some whole group instruction around the definition of continuity, specifically in how to justify their reasoning. So after I addressed each team’s individual needs on #1(a)-(c), I asked students to discuss the prompt below in their teams.
We had a discussion of the three conditions required for a function to be continuous at a point, and students were able to specifically identify the reasons for which each function was not continuous at x=0.
Intervention #3: Peer teaching
Finally, on problem #2, the mistakes were all algebraic/computational and had nothing to do with limits: students either forgot how to factor a difference of two cubes or made a mistake in dividing. In every team, there was at least one student who had correctly factored, simplified, and evaluated the limit, so those students supported their teammates in finding their mistakes and making corrections.
So how much time did this take?
Well… it has taken me longer to write this blog post! 🙂 It took me about 5 minutes to sort the exit slips into piles for intervention #1, maybe another 10 minutes to read the responses for #1(d) and create intervention #2, and about another 5 minutes to look at the work for #2 and make sure that each team had at least one student who had completed the problem correctly.
It took me about 25 minutes of class time to check in with every small group (and would probably have been less if I remembered my timer… oops!). And this is happening as the rest of the class is working on another task, so I’m not losing any time; I’m actually gaining time because I’m not reteaching to the whole class.
Is it worth it?
Absolutely! On their quiz last week, every student correctly identified a two-sided limit, a one-sided limit, and a limit that did not exist; nearly every student was able to correctly show that a function was continuous at a point using all three parts of the definition.
In all honesty, I think this is one of the simplest changes a teacher can make to improve student learning. And although this example is from my Calculus class, I have used this strategy in every class, at every level, with every student population. IT WORKS!
Shoutout to Cassandra Erkens of Solution Tree, who has been a consultant in my district for many years now, and who has helped me to refine my assessment and intervention strategies every year!