Let me tell you a story from almost 22 years ago. I had been teaching science for a few years when I got hired in a small private school. A week before school started, I got my schedule (this was pre-checking on the internet when you got a printout during teacher week), and it said I was teaching Algebra IB. Since I am a science teacher and not a math teacher, I went to the principal to show her the mistake in my schedule. Her response surprised me. "If you can teach physics, you can teach Algebra I. To this day, I don't know if that is true, but it was a small school with a need, and I was game for most things. So I gave it ago.
I looked at the curriculum, and it was mostly things that had steps, graphing quadratic functions, factoring binomial expressions, exponential growth problems, FOIL, and the like. I decided the best way to go about this was to teach them to follow the steps in the same way one might follow a recipe, and since there were only 9 students in the class, it seemed like a good way to keep them engaged was to do the problems together as a class. "Thanks for doing step 1, Liz. Now, who wants to tell me what to do next."
Math teachers out there, I can feel you cringing. I know that you are thinking, "This is not how you teach math! They will never learn mathematical thinking that way!"
Rest assured that I know that.
Now.
I didn't know it then, but remember you are on my side in this story. I didn't know how to teach math and was just doing the best I could.
Anyway, during class, things seemed like they were going well.
Then, I gave them a test.
Things were NOT going well.
One student could do the first step of a problem before getting lost while others didn’t even know how to begin. I was confused by the differences in their approaches because it seemed like they should be getting stuck in similar places.
I had been relying on a classroom vibe as measure of how things were going and didn’t have enough math experience to recognize that the scaffolds I provided weren’t leading them to independence. I started analyzing my classroom practice and found the problem. When we solved problems together in class, we were solving them together as a group. What had seemed like the best way to engage every student was masking individual deficiencies in understanding. I had fallen into the pitfall of the using the classroom vibe.
Just because a group can solve a problem doesn't mean all of the individuals in the group can.
They could only solve problems together. It was like an assembly line. Liz knew how to do step one, which gave Eric just enough momentum to do step two. Drew could do step three.
So we all suffered from the Illusion of Competence until they had to do problems on their own without help.
This was my first real life lesson in the need for formative assessment. I realized that I needed to check in with them individually and frequently. I started giving a problem every day as an exit ticket that they had to solve on their own. I didn't expect them all to do it perfectly, but it let me know where they were. And we started having a 3 question, low stakes quiz every Friday over what we had done on Monday through Thursday.
Once I started doing those things, I had a better sense of where each student was with competence in each skill. Their test grades improved (to be fair they had nowhere to go but up), and we all learned more.
What I did then helped a lot, but I would handle it differently now to get more information during the teaching so I could adapt in real time.
For the next couple of weeks, I will write about how to collect good data in both formal and informal ways so you can be responsive to the students in front of you and avoid being surprised by upsetting tests scores.
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