Math Mistakes Are Opportunities for Growth
When your student is making a recurring mistake, it is an opportunity to pause, and then ask together, “Okay, what parts of this are we not understanding? Is there a way we might approach this differently?” Instead of beating themselves up every time they get something wrong or make a mistake, your student will learn to see math mistakes as opportunities to evaluate, improve, and learn. This equips them with a skill that is useful for all of life.
When you help model working through mistakes, you are empowering students to become an advocate for themselves, and this is especially the case as they progress into the upper levels of mathematics where the level of abstraction can be especially challenging. This is true even for the student that tends to pick up new mathematical concepts quickly. I am an artist and art teacher. Often at the beginning stages of a project, I’ll say to myself, “okay, I’m just going to slop paint down, go with instinct to start out with, and see what I’ve got.” After I’ve done this, I can then look at it and say, “I need to be more intentional here,” and “Oh, this is where I’m having trouble,” or “I need to change this up.” In this process, what starts as a mistake when viewed in a certain light, quickly turns into an opportunity for improvement when viewed with a growth mindset.
As an instructor, it is important that I model this process of turning math mistakes into opportunities for my art students. When starting a class I show examples of my own work to show that not everything goes as planned, and use this as an opportunity to incorporate what would be otherwise considered a mistake into my learning process.
Since implementing this mindset, I’m finding that not only are my own art skills improving, my students are also improving at a much higher rate than they were before. They’re also coming back to my classes at a much higher rate too, because the class has become a safe place for them to make mistakes part of the process. Not only is it a safe place for mistakes, it is also a place that actually celebrates those mistakes as learning opportunities. My fellow artist and I grow comfortable saying things like, “something doesn’t seem right here,” and “oh, I see, I see where I’m having trouble.”
My process for art skill development can be translated and used in math as well. If your student is not understanding something or having trouble with a new concept, we can help them to see that it’s not a reflection of their intelligence, potential or their skill. Instead, we can help them understand that the struggle to acquire knowledge is an intrinsic part of the learning process.
Eventually, all of us have to learn to deal with mistake-making, and the frustration of not getting it right away. Learning to view mistakes as opportunities is a good skill for all learners.
Math Mistakes and Math Anxiety
Earlier I mentioned that my art students come back again and again because I have made my class a place where they feel safe to ask questions and make mistakes. Some students who have had bad experiences with mathematics, can experience math anxiety and even panic when faced with the prospect of making mistakes or revealing they do not yet understand something. It is not uncommon for some students to have immediate panic when they see drill sheets, workbooks filled with word problems, lengthy tests, etc.. I encourage parents and teachers whose students experience math anxiety to consider these possible solutions.
• First, make sure you’re only drilling or testing on material that you’re confident the student knows well. Drilling is a great way to practice known skills but not a particularly effective (or inspiring) way to learn new skills. If you see your student shut down or meltdown at the site of a drill sheet, begin with a few problems and work up. Our worksheet generator allows for as few as 4 problems per sheet. Additionally, avoid timing the drills until the student requests to be timed.
• Limit the time you spend on a concept that your student has not yet mastered. For example, the attention span for an 8-year-old when trying to understand something is typically around 10 minutes. Use their age number plus two as a guide to determine what is average for your student’s age. If you want the math session to be longer you can either switch out to reviewing math the student has already mastered or work with games or activities using known skills. Another option might be 2 short sessions with a 2 hour break in between.
• When introducing a new concept, coach your student toward a more positive mindset by saying something like, “Okay, this is our first day on this, let’s see if we can catch a piece of it today”. Again, limit time spent per session on the new concept to their age plus 2.
• Collaborate with your student to set the pace for each day. If your math plan for the day involves a worksheet, ask “how many problems do you think you would be comfortable solving today?” or “Let’s start out with finishing the odd numbered problems first”. This way you can evaluate any areas which might need additional assistance. Bring them into this process, and help them regain a sense of their own learning.
• Lastly, I encourage you to give your student the permission to skip the questions that they don’t know how to solve. You can then say something like, “Oh good, you skipped that one. We know we don’t know that one.” This gives you an indication of what concepts to spend more time on with your student while sparing them the anxiety of being penalized for knowledge that they have not mastered yet.
The goal is to lessen stress, embrace mistakes, and provide your anxious student with many small victories. Through these kinds of processes, you and your student will begin to realize how to find learning success with limited anxiety. Knowing how to advocate for their own learning process is a skill that will assist them in becoming lifelong learners, and enable them to reach their full individual potential.
Math Mistakes and Test-Based Assessment
In the Math-U-See approach, we’ve included test pages to help students get used to the idea of test-taking and help determine whether your student has achieved mastery. We do not recommend taking the test until the student has demonstrated mastery in the practice and review sheets of a given lesson. If your student needs extra time to achieve mastery, extra online practice is found for elementary students on our worksheet generator and on the Extra Practice Pages for upper level students.
The “wait for mastery approach” to testing teaches your student to develop an understanding of what they need to be prepared for a test. This approach sets your student up for success in testing so when they see the word test at the top of the page, they feel confident in their ability to tackle it.
When there are errors on the test, try to keep them in the same perspective you would with daily work. When working through mistakes you can ask: Were multiple problems missed that use the same concept? If so, this might be an indication that they need to revisit a concept for some additional practice. Did the student work hastily? Were there distractions? These might indicate that your student was tired or not feeling well that day which might have made it hard to focus.
By asking these questions and having a conversation about the errors, you can again reinforce that mistakes are an opportunity for growth. Together you’ll learn and make decisions regarding next steps for continued success in both daily work and test prep. Please keep in mind, our Customer Success Team is here for you to support you and your student’s plans for building math confidence.
At the beginning of this blog post, I talked about the importance of instructors modeling mistakes and the learning process. The more that you and your student can embrace the perspective that mistakes are opportunities to grow, the more positive the learning process will become for both of you. And like myself and my art students, I’m confident that your student will grow to feel like math is something they can do, and maybe even enjoy!