My experiment of teaching a course where preservice and inservice teachers share two hours of class time has been going well. (I introduced the concept here.) In fact, one of the preservice teachers said recently, "I wish all of my education classes had classroom teachers in them." I believe the following example explains why he feels that way.
That same preservice teacher was part of a small group (along with an inservice middle school math teacher and a community college instructor) who were analyzing middle school students' work on an algebra assessment. They were talking about how difficult it is to get students to share their thinking especially once they assume they have arrived at an answer. I concurred and explained that this was one of the reasons I focused on using metacognitive memoirs, saying, "I know the answer but I don't know what you're thinking." This gave the inservice middle school teacher an idea.
He wondered what would happen on the next test if he gave the answers and asked the students to focus on their thinking. A few days later, I (along with the preservice teacher and the community college instructor) received the following email:
Hi, I gave a test yesterday in my 8th grade math class and I gave them all of the correct answers at the beginning of the test to see if it would improve the work that they showed and how well they explained their thinking. They were shocked, but they actually caught onto the idea quickly, I didn't even have to tell them why I was giving them the answers, they came up with it themselves. While the test responses weren't perfect, students did a MUCH better job sharing their thinking than they ever have before. I am excited about how this turned out and I anticipate doing this more often in the future.
I asked the teacher if he would mind me sharing this experience and the test on my blog and he agreed. Not only that - he also provided how he implemented this new approach, a sample of students' work, and students feedback.
After handing out the test, the teacher began:
- Teacher: "Listen closely. This is a test. You know the rules as far as talking, etc."
- Teacher begins reading off answers.
- Students are following directions, no questioning until after the page flip.
- Student 1: “Why are you telling us all the answers?”
- Student 2: “I like this!”
- Student 3: “Don’t stop him.”
- Teacher keeps reading answers. There is no contesting of getting the answer and the kids keep filling in right answers for remainder of test.
- Student 4: “I don’t understand this...”
- Student 5: “Why did you just give us the answers?”
- Student 6: “Do we have to explain what we did for the answers you just gave us?”
- Teacher: “You’re not going to get any credit for having the right answers. You’re only going to get credit if you can explain how you get the right answers. So all of you are starting right now with all the answers and a 0%.”
- Student 4: “I like the other way better.”
- Teacher: “Let me just say one more time...You all have the right answers, so the explanations are where you can earn the points. With that in mind, go ahead.”
Here is what the test looked like after the teacher had read the answers.
And here are some examples of what students wrote:
After the test, the teacher asked for students' feedback on this approach to assessment. These represent some of their responses:
- "My head hurts because I actually had to think."
- "I realize now that I've never done a very good job explaining my answers."
- “This was like an English test!”
- “It took forever...like, I know what I want to say but I can’t explain it.”
- “Didn’t like volume of writing and repetition.” (Felt like there was too much writing and they were answering the same questions over and over.)
- “Didn’t see the point of giving out the answers because you have to do all that thinking to get the answer anyways.”
- “Liked it. I always spend time figuring out the problem so I don’t explain. This helped cut out the calculation step.”
- “Didn’t like because I don’t like explaining myself.”
- “Would have prefered to find answers instead of trying to explain because sometimes I can just get it (in my head).”
- “Liked having answers, otherwise I spend a lot of time trying to get the answer. This way I know the answer is right.”
I hope that I was able to adequately articulate this approach to assessing students' mathematical thinking. If you have questions or ideas, please leave them in the comments and I'll be sure to pass them along. We have 8 more weeks together in this course. I'm looking forward to whatever else they come up with in that time.