Marketers know that a product’s brand is everything. If a product is not selling to its potential, one solution is often to tweak the brand, or “rebrand” the product. Kentucky Fried Chicken changed their branding to KFC to de-emphasize ‘fried chicken” and appear to be a more healthy option. If it works in business, shouldn’t it work in education?
In math classrooms across the world, students are told on a regular basis to “show their work”. I wish I had a nickel for every time those words came out of my mouth during my educational career. It is certainly done with good intentions—it is critical that students are able to communicate mathematically. Both communication and reasoning and proof are process standards that should be incorporated into our math instruction.
And analyzing the “work” a student has shown provides the teacher with valuable feedback.
My problem is not with the process, it’s with the words, so I have been experimenting with rebranding “show your work”.
As I see it, there are two major problems with asking students to show their work. First, the words hold a very negative connotation in the minds of students. It’s something they have to do. Furthermore, the words are often delivered in a way that is not conducive to cooperation. “John, if I’ve told you once I’ve told you a million times, you’ve GOT to show your work.” “Valerie, I’m not taking this paper until you show your work!”
Second, many students don’t show their work because they don’t know what the heck it means! My favorite is the student who circles the multiple-choice answer they think is correct and then x’s out the other choices. If you ask, they are “showing their work”.
For my suggestions, I will address the second problem first. Students have to be specifically taught what it means to show mathematical thinking (see how I’m rebranding it?). This happens through a great deal of modeling and coaching, and it starts by communicating your expectations at the beginning of the year. Students need to understand why it’s so important for them to communicate their process. Then you need to teach students how to document their thinking. You have to be consistent with your expectations throughout the year because it needs to become a habit for students. Something they just do without thinking about it. Keep in mind, however, that if you’re going to convince students that you are committed to this process, the assignments you give them must be consistent with your message. Which of the two assignments below sends the message that the process is as important as the solution?
Now, to overcome the negative connotation of the words “show your work”, we have to stop using them. Think about it, when you are solving a problem do you think to yourself, “Hmmm, I’ve got to show my work.” I don’t think so. What I DO do, is make notes to myself as I interact with the problem. Those are now my go-to words when working with the students—I document my mathematical thinking by making notes as I interact with the problem.
Using this approach, students are more open to the process and, through coaching, they learn how to take notes on their own and determine important information. It’s a thinking process, not a rote procedure.
I’d love to hear your comments about this!
You can grab the Mathematically Speaking problem using this link.