Students with confidence will boldly move toward the edge of their understanding, willing to take risks in order to keep moving forward.
The Visual Cliff is a theory that was originally developed to see when humans developed depth perception. They placed a baby on a plexiglass surface about a foot above the floor. A high-contrast fabric is pressed up against the plexiglass for part of the floor, and then visually drops so that it appears there is a cliff despite the plexiglass continuing safely. At about 10 months, babies will not crawl across the plexiglass to their parents because they see the visual cliff. Recent research shows that babies as young as 3 months see the cliff by measuring heart rate and breathing, but when they are about 10 months, they realize they don’t have the physical skills to make it across the perceived cliff.
Our students have their own visual cliffs: They perceive that they do not have the skills in math to make it across, and therefore hesitate in their belief in themselves. I vividly remember the moment one of my former students suddenly saw the cliff. She went from being a confident math student who was willing to share her ideas to saying, “I’m not very good at math.” It was the moment that multiplication flashcards and time tests began in third grade. She saw speed was what made you a good math student, and suddenly doubted the solid floor of mathematical understanding that she had been walking on for the last two years! As teachers, our actions can create cliffs, or it can help students realize that if they keep walking, they will easily get to the other side.
In her book Mathematical Mindsets, Jo Boaler outlines the importance of a growth mindset specifically in mathematics and how we can build this in students. One of these mindsets is the importance of making mistakes! Studies have proven that the more successful the person, the more mistakes they’ve made. Our brain grows more from learning from mistakes than it does from always being correct.
We have to be strategic and intentional in teaching students this mindset that will help them avoid a mathematical visual cliff. There are many ways that we can do this through virtual learning. Here are 5 ways:
A Mistakes Make Our Brain Grow Journal
Whether collectively as a class or individually as students, start a Google doc to share how they’ve learned from their mistakes. One idea is to have an image of a small brain in the center of your google doc. As your students learn from their mistakes, record their new learning and increase the size of the brain. This can continue until the brain fills the page and you can add a new brain to another page. Check out our FREEBIE!: Brain Growing Animated Slides
Eureka Moments: Celebrating Mistakes
Create a presentation, or subscribe to our email list to receive a free one, of things that were invented by mistakes. Share all of the many inventions we have because people were willing to experiment, adjust, learn, and make mistakes! These are all attributes of mathematicians.
Hidden Mistakes
Mistake training is something that is used in therapy to help with perfectionism and anxiety. We have to train ourselves that it is okay to make mistakes. Give the students an assignment and challenge them to make mistakes on a specific task. Have them make a silly mistake and one that is hard to find. Share one student’s “Mistake Task” and see if the class can find them and discuss what they could learn from them if they were real mistakes. A free “Hidden Mistakes” activity to use with students for K-2, 3-5 and 6-8 will be sent when you subscribe to our email.
Physical Response
When students make a mistake, have a class signal. This allows even the students who are muted on Zoom to show you that they made a mistake. Think of the power of thumbs up that you “got it.” I have never given so many thumbs up in my life as I have since we started Zooming school! If we have our students give us a “mind blown” signal when they make a mistake, it communicates two things: 1. That making a mistake helps your brain grow. 2. That, “got it” is just as important as, “I made a mistake, and I’m learning.”
Don’t Grade Everything
Feedback is a much more effective tool than receiving a grade when a student is learning. Consider giving students feedback when they are still learning a concept, whether through email, in small groups or even whole class if you see a common error. The percent grade seems final to students. If students understand that you are going to value their work and thinking while they are practicing, they will be more willing to make mistakes. It also can eliminate parents doing work for the kids. If parents know the assignment isn’t “graded,” they are less likely to interfere with the students while they work.
Visual cliffs are just that — they are what we see. The babies in the experiment were hesitant to cross the visual cliff, but if their mother was on the other side encouraging them, they would crawl across. Let’s make instructional moves that allow students to know that even if they perceive a cliff, they can keep persevering and they will safely make it to the other side.
