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.
As an instructor, it is important to find ways to model this process of turning math mistakes into opportunities for your students. For example, I’m an art instructor, and at the beginning of a new class I show examples of my own work that did not go as planned. I use this as an opportunity to model that what would be otherwise considered a mistake is an important part of my learning process.
Since implementing this mindset, I’m finding that not only are my own art skills improving, my students are also building skills at a much higher rate. 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 as part of the process—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.”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 skill. Instead, we can help them understand that the struggle to acquire knowledge is an intrinsic part of the learning process. Learning to view mistakes as opportunities is a good skill for all learners.
Math Mistakes and Math Anxiety
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 can be a 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 melt down at the site of a drill sheet, begin with a few problems and work up. Our Worksheet Generator allows for as few as four 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 two short sessions with a two-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 two.
• 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 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, 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 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 that 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!
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