Today, we’ll be diving into a topic that sparks debate amongst students and parents alike: should students have to show their work when solving math problems? Some people are strong advocates for it, while others believe it can slow progress down. Let’s discuss the pros and cons of students showing their work, to help you decide what’s best for your student.
As you can see, there are reasonable arguments on both sides.
I used to be in the camp of requiring all work to be shown since that’s what was required of me. However, that changed when I started tutoring a student from Brazil named Gio. Gio could do an incredible amount of computations quickly in his head. I kept asking him to write his steps down because that’s what I was used to, but I quickly realized that all I was doing was frustrating him and slowing him down. So I asked him how he was able to do so much of it in his head. He told me that in his math classes in Brazil, mental math was the standard, and students used and practiced it often. It was really eye-opening. So at that moment, I shifted.
Here’s what I do in my house now. If my son is doing mental math well, and consistently getting problems correct, I do not require him to write down all of his work. I want to sharpen his mental math skills and free up his time to focus on the harder concepts we’re learning. Let’s be clear though, this is a privilege he has had to earn. If he begins to make too many errors, then he is required to show me the step-by-step process. This repetition should help slow him down and hopefully decrease his errors.
When I ask many parents why they think it’s important that their students show their work, I often simply hear “Because I had to!” My response to that answer is to go a little deeper. If you think showing work will help your student, then require it. But if they can demonstrate to you that the mental math techniques you’ve been teaching them are working, consider they can be successful without writing it all down.
As always, I believe we can always find the answers we’re seeking from others in the community, so please feel free to share what works best in your home or classroom.
Nicole the Math Lady
I had a similar approach to the Show Your Work dilemma: if you show your work, I can give partial credit. If you don’t, I can’t. Your choice. All four kids chose to not show their work, until they hit a tough concept and missed lots of problems. Suddenly, they wished they had partial credit – and willingly began showing their work.
My oldest is a senior in high school. Always homeschooled. Showing his work since Algebra I, using a logical line-by-line approach. The entire first year, he sulked about my required formatting, clearly showing all steps! This semester, he is taking Cal II at a local college. The tests are pencil and paper, no calculators allowed. At the top of every test is the statement: “If you don’t show your work, you don’t get credit.” My son is now so, so glad he has been showing his work all these years!!
I love the idea of having them choose which route they’d like to go. There’s a lot more buy-in and they have a reason to show their own work!
In the lower grades we required to show math. When he started Algebra 1 we beat up ourselves trying to get him to write down his answers as he doesn’t like to write and he could figure the answers in his head. We finally settled on only having to write down the steps when he got the problem wrong on the first try. We are now in Advanced Math he writes down more difficult problems and talk the problem through. I personally like the problems written down because it is much easier to find the errors, if there are any.
It’s funny…as they get older they don’t like to write down as much, but when they get to the harder math, it can make a bigger difference because of the logic.
Very timely! My son hates to show his work – but the result is often an incorrect answer and I have no way of figuring out where the mental misstep occurred! Also, sometimes he can “solve” a problem by looking at the multiple choice answer options and solving just enough of it to pick the right one. But even without the answer options, showing work has been an ongoing battle. I appreciate your input so much.
It’s an uphill battle, but it sounds like he’s got some problem-solving skills that will be useful in life!
I agree with you. If they know the work and get them all right then no but yes if they are getting them wrong so when I correct it I can see where the mistake is. Most of the time the mistake is a simple adding one number off
Yes…there are so many opportunities in math to get something wrong…that small mistakes can be annoying. But if they can do the work, I’ll take the win there!
100% agree!!! In fact, when my son verbalizes his work to me (when he has used mental math) it blows my mind how his brain gets to the answer in its own way. And I even end up learning something from him!
My daughter struggles a bit more, and showing her work provides benefit so I (and she) can see exactly where her struggle is.
Both ways are beneficial!
Thank you for bringing up this debate, I appreciate the validation of students not always having to show their work, I’m sure my son will, too!
I swear…these kids are definitely smarter than me. I was not trained to do mental math and hence, am not great at it. It’s amazing what can be done in the brain.
This was very helpful. Getting my kids to show their work is like pulling teeth at times. So my solution was to have them explain what they did verbally. If they can them I let them go on.
Yes…I hear ya…there are other hills to die on so if explaining their thought process gets the job done, then good.
Thank you for posting this! Very well thought out, and I appreciate it!
You’re most welcome.
I struggle with making my grandson do his work on paper. His mind does not always work the problems in the same way as the book teaches, and it makes it difficult for me to work with him step by step. Sometimes I think, let it go. His idea of working on paper is writing his answer on the paper. When he has some problems he cannot do that may require a table or diagram, he will tell me he can’t do things on paper, or doesn’t know how, and I say because you refuse to follow instructions and learn. I like your thought of making him earn the right to not work them out on paper. He is eleven, doing 8/7, and he just finished lesson 110. It is not too late to change things up. His mistakes are usually because he does not fully read what he is supposed to be doing. He hurries with his work. I think if he would work the problems on paper before hurrying to enter into the computer he might make less mistakes.
As you said, make him work for the right…and he only gets there by showing you he can. (But I think these kids brains are more developed than mine because they do seem to work pretty fast!)
I do have my son show his work and not because I had to, I’m 45 yrs old we didn’t have to show our full work in school math was math lol but with my 10yr old i do he is dyslexic and adhd his brain is really good at math and figuring out in his head but his brain also works fast and he make silly mistakes like writing 9 instead of 6 which he meant 6 so even though it’s time consuming not on all the problems I have him show work he then can see his mistakes and as well shows me he also has retained what he learned and knows how to still complete multi step problems . Showing work for him helps slow his brain and really see the problem I feel and some problems I will let him do on his head, he actually knows and is aware of what type he has to physical work out on paper and what he can do mentally 🙂
Yes…if it helps to slow that brain, I’m all for it!
My focus with math is helping my children learn how to communicate their solutions (not the answers) clearly to others. I care about the journey (how they found the answer), not the destination/answer. Just as we work through how to write a well thought out paragraph or essay, I want them to be able to communicate well in math.
As for what “show your work” entails, that will change depending on the level. When finding the least common multiple of 48 and 54, my child showed it was 2^4*3^3=16*27. My child then mentally concluded the answer was 432 (since 25*16=400 and 2*16=32). But my child didn’t “show that calculation.” That’s fine. The concept here (in PreAlgebra) is finding the LCM (using prime factorizations), not multi-digit multiplication. However, a student first learning how to multiply double digit numbers should show (or explain) this calculation.
As for expectations for the solution, as long as the methods used are valid, I love seeing the various ways my children solve the same problem. I will sometimes show a different way to solve the same problem, and sometimes we’ll discuss if there are any advantages to solving one particular way. Sometimes, there’s no advantage, but simply, “Hey, we solved this two very different ways, and got the same answer. That’s so cool!” I want my children to try different methods and realize most problems don’t have “one single right solution.”
As for accommodations, I agree “show your work” could mean “explain how you found your answer.” One gives a written solution, one an oral solution. Both of these focus on the solution, not the answer.
My goal is for them to communicate (whether it’s written or spoken) WHY their answer is valid (at a grade appropriate level).
I love the focus on solutions (instead of just right answers). This matters so much and in more than just math. Life lesson here!
The same goes for my 13yr old son. I saw him get frustrated and it was having a negative affect on his schooling when I required work to be shown for everything. So long he is doing well and is showing understanding I now accept mental math. However, if he is not getting it right and he needs help. I ask him to show me all the steps so I may see where the error occurred. More than half the time he finds the error on his own while writing out the steps.
Perfect…and that’s exactly what we want to happen.
I’ve homeschooled all of my kids and required them to show their work. It’s so helpful to see their thought process and easily correct mistakes that have been made. As they got older they did more mental math, but were still able to show their work when necessary.
Awesome. It’s a great skill to have in some many others areas that just math.
Thank you, this is a big debate in our house! My creative daughter struggled the most with writing the whole problem out. I appreciate I’m your encouragement to have them earn the privilege of not writing the whole problem out!
That’s right…we gotta make them work for it…(lol!)
This was so helpful! We have had many discussions about this! I love that you supported each idea. As a first year homeschool parent I am going to reevaluate how I handle this situation.
Wishing you well in finding the best solution for your kiddos!
I love your perspective on this. Thank you for this post.
My kiddo usually doesn’t like to show work and for a while that worked fine. However, now that she’s working multi step problems or larger equations we both see the benefits of showing work and I believe the most important benefit is being able to look back at the work when the answer is incorrect to see where the mistakes were made.
It does make it easy when they get to those multi-step problems. So many more opportunities to make a mistake.
Early on I had my daughter show her work so I could spot where her difficulties were. As she began to explain rather than just show her work, I could understand how she thought about problems. TBH it blew me away. She is much more fluid with math than I ever was. She’s a junior now and works almost completely independent. She now uses a whiteboard, checks her work and then transcribes into her notebook. And yes I periodically test-thankfully she’s honest & diligent.
Love the independence!
It depends on the child. My oldest did it in his head and always had the right answer but when asked to work out on paper he could not do it so I did not make him do it. Where my middle child has to work it out to understand it.
I wish I was better at doing math in my head. I personally still have to write most everything down. (I guess that has worked out for me ok though (lol!)
Thank you for this enlightening article. Our struggle at hime every day 😅
You’re welcome. Hopefully it will get a little easier.
I used to be very adamant about my kids showing their work. I love Math because of the methodical repetition that if you just follow these steps you will get it right every time. Of course, God gave me children whose brains work differently. I never thought you could be creative in math! It’s interesting how they come up with the answers to me sometimes, but it works for them (most of the time.) So as long as they are getting the correct answer I don’t worry about the work shown.
Isn’t it funny how we’re sometimes given children who’s brains almost work opposite to ours! (lol)
Wonderful discussion! I’ve been a stickler for showing work, so I can see where mistakes are being made. My eldest shows her work, but makes tiny mistakes, so it’s encouraging for both of us that she does indeed understand the concept. My middle child is dyslexic so he tells me the steps and I write them down for him. I may skip writing it down next time! I’ve also found anytime they can write on a dry erase board, they are much more willing to write anything!
That is so true about the whiteboard. I think it makes them feel like they are teaching which I think is cool.
I’ve never liked showing my work cause I always feel this strange pressure just to get it right
Is it working?
I do both sometimes but I think mental math is much easier
My mom and my violin teacher (she helps me w/ math) have worked REALLY hard to drill into my head that I must show my work. I did it for a lesson, it actually worked! I only needed help w/ 2 instead of 10!
Nicole’s #1 student,
Susannah F. Bremner
Great to hear!
Call a choice where students and parent talk it out fairly with a few rules to keep from more arguments breaking out
My mom and I have had this argument for my entire three years of homeschooling! From my student perspective as an 8th grader, showing work can be really really annoying depending on the concept/topic. But wow is it useful. I used to do math in my head, but even if I got the right answer it was by luck, not because I did the correct steps. I never used to understand all the steps to certain problems and learned that sometimes not showing work can be horrendous. I would get the steps mixed up or would skip some altogether. It’s especially annoying to mess up the process when it comes to algebra. So many topics just wouldn’t work by only using mental math. Nicole, your videos are an absolute life saver! I always used to struggle with understanding every single step of a problem to ensure success, but you make complex concepts easy to understand!! Math has always been my favorite subject, and your videos just make it better and easier. Thanks for all the help Nicole; I love your teaching style.
Thanks so much for your perspective as a student. I love it. Also, thank you for your kind words.