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.

Interesting idea! At the start of the post I was skeptical, but reading the feedback given by the students at the end has swayed me to think about doing a similar thing.

ReplyDeleteOf course you wouldn't have to do this during a test - you could do it with a worksheet in clas, homework et. I think I'll start by trying it in class with a set in which some of the students rarely show their working out and see how it goes.

Thanks

I think I will try this with my students, too!

ReplyDeleteI am particularly focused on how they can explain their thinking and this strategy is brilliant - so simple and (apparently) so effective. Thank you for sharing it!

@surreallyno

This is great. Really great. I think it would work well at all levels. I hope someone with a high school classroom tries this and reports back! I also wonder what would happens if you gave a single question and told them the wrong answer (letting them know that it is wrong) and asked them to explain how a person could come up with that solution. Might be too much.

ReplyDeleteThank you for sharing!

I like the idea of having a worked out problem that has an error and incorrect answer. Then I have the students analyze the problem to find, explain, and correct the error. I think this method allows me to assess students understanding of a concept much more deeply. However, I've only this method during classroom and not on summative assessments, yet.

ReplyDeleteI want to try this!

ReplyDeleteI've used this strategy in my elementary school classes when the students are too antsy to share the right answer instead of talking about their process. In that case, I'll just say, "Okay the answer is _____, now tell me how you got it." It deflates the eager beaver students, but quickly turns the direction of the conversation.

ReplyDeleteThe lesson I learn from your example is that it is probably best done purposefully and not too much at once. We don't want to rob the students of the "a-ha" moment of finding a correct answer for themselves. An entire test where answers are already provided takes a lot of motivation out of doing the work. Having 1-2 problems on a test or assignment with answers already provided is probably a better balance.

This is nice! I wonder if students did this routinely, would the idea of proofs and proving later on be less mysterious? In geometry, we sometimes prove things that are "visually obvious." Experience with needing to give a reason for *why* it works not just *that* it works seems like it would be helpful.

ReplyDeleteBTW, here's a posting on proof at the Mathematics Teaching Community: https://mathematicsteachingcommunity.math.uga.edu/index.php/180/proving-versus-proofing

I teach high school algebra 2 and calculus and I use a version of this approach frequently. I don't provide the answers, but I show them how to use the CAS functionality of the calculator to solve, factor, integrate, etc. and then ask them to show the steps. Most students report that they feel much less nervous about tests and the work they show is higher quality. Of course the grading is BRUTAL because you have to examine every single step...

ReplyDeleteExcellent. I think I might try this for one of my quizzes. I'll let you know how it goes.

ReplyDelete