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.
Of course that's the point with Common Core - to make it look like kids are doing more "rigorous" work when what they're really do is rote procedure that stifles creativity and thought.
We see the same thing happening with the seventeen day units from EngageNY that have kids reading one short story over and over and over and annotating it over and over and over...
It is impossible to listen to 20 or more students explaining there work. While all steps are not necessary, many should be shown. I want to know if the wrong answer was a silly arithmetic mistake or a computational one. If I see same wrong methods on multiple papers, I question how I taught a particular problem. While it is not necessary to show all work, work should be shown especially if it relates to new work taught. Sorry, but as a math teacher, I disagree with you. May is too arbitrary a word for most of the students I have taught. Also, work offers the student partial credit or maybe just losing a point for carelessness.
ReplyDeletePO, you raise excellent points and I will differ to you on this. The rote procedure angle is a little different in ELA than in math, so the comparison does not work well. I do hear from students that they're sick of the endless annotation and close reading procedures in ELA. But as you note, this does not necessarily have an analogue in math,
DeleteAnd I have no concept about what goes on in ELA.
DeleteOops - brain is dead. I meant I will "defer" to you, not "differ"! Ugh. Start to second semester has killed my brain cells...
DeleteIn the Middle School (Grade Six Special Ed in my case) I do stress showing work. In my mind this inculcates a habit of working problems through in steps. While most grade six and seven math can be done mentally, if a student never gets in the habit of writing down the problem and relies on mental steps they are at a disadvantage when "Math Gets Weird".
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