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.
My students seem to equate “show your work” with the standard algorithm. So when they can do it in their head with an intelligent strategy they’re reluctant to write down their process. Documenting thinking, as you suggest, encourages them to put their ideas on paper, emphasizing the process over the result. I’ll have to work get past my old habits, it’ll be worth it.
Interesting! The problem is that all the note taking and interacting with the problem is what leads them to the calculation they should do. When they skip the Understand part of the process, they often end up choosing the wrong calculation.
At the beginning of the year, I tell the kids they don’t have to “show their work”. Which then make the kids cheer. I then tell them that they need to “share their thinking”. And we discuss what that means. Whether it be showing work/algorithm/calculations, the formula you used, what you put into the calculator, a written explanation of how you arrived at your answer, a definition, etc. The look on their face is usually a sigh of relief when you have now given them permission to be able show their thinking in a different way.
I’ve been teaching my students to use a KWI chart, what do you KNOW, WHAT questions do you need to answer, IDEAS for solving. At first they treated it as a project in itself, but now that they see it as a tool, they are having more success. Plus, when students get stuck on a problem I can say “What do you know?” and that gets their gears turning.
That sounds like a great structure, Robin. Easy to internalize!
I don’t say show your work anymore I know say show your thinking. It has a different effect and I don’t know why.
Very different, MIchelle, I think because “show your work” is not kid friendly.
Me too– show your work sounds like work! Kids don’t respond to it. I don’t disagree!
I tell my students they have to prove it. This way I’m acknowledging that they may be able to do the problem in their head, but I still get to see their thinking. Prove it!
Yes, proof is an important process standard!
I think this learning progression from Jill Gough (https://twitter.com/jgough) on what it means to show your work is super helpful for students: https://jplgough.wordpress.com/2015/01/30/ll2lu-show-your-work-grade-4/
Yes, I agree. It definitely helps to clearly define for students what their work should look like! That’s half the battle. 🙂
I think it helpful to ask students to prove how they know or defend their answer. I think this happens first with words-talking through the problem. Most children need to be prompted with questioning. “How did you know to do this part? Why did you decide _____?” My main goal was to lead them toward higher levels of mathematical thinking, which would enable them to develop an informal proof of their conclusions. I was trying to lead them away from saying they just knew the answer or thought it in their heads. Of course, basic facts do not fall in this category. Higher level questions lead to higher level thinking.
Nice insight, Danielle. Questioning is an art form. I’m always surprised by what I learn listening to students’ explanations! Great formative assessment.
Thanks for sharing your work. I know quite a few of my students really don’t know what it means to “show your work” either. I’ll give rebranding a try!
Glad to hear it, Kelly!
I’ve replaced “show your work” with “show me your thinking”. It has greatly improved their attitude and ability to document how they solved a problem. It allows for flexibility in how they show it. It doesn’t always mean a standard algorithm. It can involve more than numbers.
Yes, I’ve used that as well, Amanda.
I find it helpful to refer to what they show as their “thinking” as well. I also stress the importance of understanding the problem before attempting to solve. Students label what is known and unknown, and this helps them formulate an equation to represent the situation/can be used to solve. As my second graders are doing so much mentally, the transition from using base ten tools, to open number lines, to showing their mental thinking using equations is important. I agree that lots of opportunities for practice in this are crucial. Equally as important are the opportunities to share thinking as a whole group so that students can see the diversity of thinking shown to arrive at the same solution. We do much exploration and discussion in small guided groups, yet the time spent talking about our thinking as a whole group allows students to see other potential strategies. Thanks so much for this wonderful post!
Great point about whole groups sharing, Sarah! I agree that’s it’s very powerful for students to hear strategies other students have tried.
I will definitely try the “rebranding” approach. Thanks, Donna.
I think you’ll be amazed at the results, Pamela!
I value thinking so I ask to show your thinking – in steps. Making their thinking visible for me to see and to share with other students. This helps students learn from each other – collaborative learning.
I tell mine to show me what is in their head because I want to think the way they are! I also started this activity another teacher uses called compare/repair where the kids get a problem or two per day and they work it by themselves, then they go to back of room and get in a group of 3 and compare answers and help repair if necessary. This has helped with showing work!
I love the compare/repair idea!!
Compare/Repair! I’m going to try this today! Compare/Repair seems a fine example of rebranding language to make the task more agreeable. For sometime I’ve been presenting their efforts as “Write your steps so others can follow your thinking.”
I tell my students to “show me what you did to solve this problem”. I explain that we use addition. subtraction, multiplication, and division to “compute”. I further explain that we can “compute” by using pencil and paper, mental math, or a calculator.
Then I explain that if they use mental math, that I need to see “what is going on in their head”. They need to document this by writing it down. I model this, by using math talk to explain my thinking.
Thank you for the nudge.
I have also eliminated the term ‘homework’.
I exclusively use ‘practice’ instead. The location is irrelevant. In fact, its prob’ly better if you practice in my presence first, so we can avoid creating/compounding bad habits.
Also, I make a distinction between ‘passing’ (ABC) and ‘receiving credit’ (D).
I will definitely now remove the phrase ‘Show Your Work’ from my vocabulary!
I am all about sharing so I ask my students to “share their strategies” or I might ask them to “Teach me your way of solving the problem” I don’t like to remind students that this is work.
Wow! I will be using that phrase THIS week: “Teach me your ways of solving the problem.”
I really enjoyed reading this post! I have been asking students to “show their thinking” using pictures, words, or numbers, etc… I’ll try to include the “go-to” words you’ve shared here. Thanks!
I am a French Immersion Grade 1 teacher for First Nation kids. First, I would like to thank you for your blog and all your products on TPT. Both changed the way I see and teach math.
Math talk is a challenge for me because of the second language. I teach them little sentences (like the ones you ask to write in the math journal). Would you know by any chance any book talking about that challenge? Math talk in a second (even third in my case) language.
Also, if by any chance you would be interested in translating your products in French, I can help. John Van de Walle’s book was translated In French and your product are the perfect complement to this book.
Thank you again!
Love Van de Walle, and I’m so glad you find my blog and resources useful! Unfortunately, I don’t know of any books specifically for second language math talk.
I started using your re-branding words when I read your wonderful article the last time you posted it. Some of my students are so opposed to making any extra effort(lazy) they would rather guess and get it wrong, than show their thinking/process /whatever I call it or ask them to prove that it’s the correct answer. I’ve tried everything. This is the second year I’ve taught them math. Suggestions are greatly appreciated.
Thank you for your thoughts and a new perspective! I teach English language learners and words are everything! Even though I feel like we’ve expressed what it means I can’t wait to try your wording tomorrow!!
I tell my kids they need to show their process. I also explain it to them this way: If you write down your process and you make a mistake, I can help you fix the problem so you don’t make the same mistake again. If you do it in your head and make a mistake, I can’t flip your head open and dig around in your brain to see how you solved it to help you not make the same mistake again. For the most part, they get this and understand the importance of showing their thinking
I’m in the habit of saying “show me how you solved that” or “can you explain how you got that?” or “show me your math thinking.” It sounds better, but probably amounts to much the same thing with my young first graders. What perks my interest, and brings up many questions, is teaching them more effectively how to do that. I fear that I show them my way of showing a solution rather than guide them to clearly document their thinking. I would like to improve. I already have my PD reading stack for the summer, but I could add one more book. Suggestion?
This really gets into the Process Standards, or what Common Core calls the Mathematical Practices. I highly recommend Christine Moynihan’s book, Common Core Sense: Tapping the Power of the Mathematical Practices. Her books are so user friendly and packed with great ideas!
I’ve found that asking ESL Students to ‘show me the steps you took to get this answer’ has been a phrase they grasp quickly. As they talk I jot down notes, or red flags, so we can return to address misconceptions later. This allows me to put together small groups with similar needs. When students have an opportunity to listen to each other in small groups they’re more likely to take some risks and alter their thinking.
Great suggestions! Thanks for sharing!
I also found my middle school students resistant to showing work, so I ask them to
‘justify their answer.’ In proving their answer to me, it shows their thought processes. It has worked for me pretty well over the past few years.
It’s amazing what a small change in our words can do!
I always say “Show me your thinking.” There are lots of get tech options now too for students to record their thinking on video or audio to explain the process they used. Great for accountability, motivation and assessment.
Donna, Thank you. I love it!
I love this idea! Simply changing your language can make a big difference
I totally agree the phrase “show your work” needs rebranding. We personally use a variety of some of the phrases offered in the comment section. My comment is an observation of the two types of assignments referred to in the article. While the one on the right is the one to choose for the topic of the article, the one on the left is best for practice to become accurate in computation. I believe both have a purpose.
We call it our “proof” or “evidence of our thinking” and relate it to a detective having to provide proof. I also demonstrate exactly how to provide their evidence during my mini lesson. 🙂
Love that! ♥