As a new teacher, I upheld the longstanding requirement among math teachers that students must always show their work. And like many teachers, I deducted points when students refused to comply. But the more pushback I got from them--"you shouldn't make us work the problems out if we already know the answers"--the more I questioned the wisdom of this rigid requirement. And eventually my message for students changed from you must show your work to you may show your work. Here's why.
A common reason teachers give students to show their work is that "I can't help you if I can't see what you did." But seeing students' work isn't the only way to know what they did. In fact, you can often learn more about students' thinking when they explain--out loud and/or in writing--what they did than when they just show what they did. (See Standard 3 of the CCSS Standards for Mathematical Practice: Construct viable arguments and critique the reasoning of others. Also check out Marilyn Burns and her team conducting Math Reasoning Inventory interviews with students.)
A problem with requiring students to always show their work is that it risks emphasizing mathematical procedures and computation to the exclusion of mathematical thinking. The more programmed students are to show their work, the less likely they are to develop mental math and intuitive problem solving skills. I'm reminded of a robot--I mean, student--who was about to work out 2 x ½ on his paper until I interrupted him by saying, "put your pencil down, and look at me." I then asked him what two halves add up to, and he looked back at the problem and laughed at himself as he wrote 1 on his paper.
Another example was when students were asked to determine if the product of .49 and 3.25 was greater than .1 and less than 1. My hope was that at least some students would reason in their heads that the product had to be greater than 1 (i.e., they might have thought something like, "since half of 3 is greater than 1, then .49 x 3.25 must be greater than 1"). But once again students weren't concerned about the values of the factors. They just saw two numbers that needed to be multiplied, and that's what every student did. No points lost for not showing their work, but no thinking or learning either. And lots of time lost when this happens over and over.
Shouldn't we be more concerned when students do show their work in cases like these than when they don't? There's a difference between doing math and knowing math, and requiring students to always show their work reinforces doing math more than knowing it.
Why the emphasis on "requiring" in the previous sentence? Because I'm not saying students shouldn't show their work, but that we shouldn't force them to show their work, much less penalize them when they choose not to. Giving children choices like this is a key to empowering them. If they can solve problems in their heads, great. And if they can't solve problems in their heads, but think they can, that's great too. Let them learn about themselves as learners, and make adjustments--with your feedback and help as necessary. Let's stop demanding that students show their work, and let them determine when to show their work.
(Note: See an earlier post of mine for a clever way to "make" students show their work when you really want to emphasize the problem-solving process.)
Image by Sjhuls, provided by Dreamstime license
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