One issue we were struggling with in home school was overcoming the fear of getting answers wrong in mathematics. Even at five years old, kiddo’s exposure to counting heavy math activities had provoked some anxiety. He could count to 30, he could identify numbers and do simple calculations while playing games, or around the house, but in a math learning context, he would get anxious and stop engaging.
At this point in homeschooling, I was using Natural Math activities from the book Moebius Noodles by Yelena McManaman and Maria Droujkova. There were fun activities such as symmetry and mirroring, creating functions, having fun making and playing with grids, and much more. The activities were fun, math time wasn’t prone to anxiety and conflict anymore, and we were progressing. We were still at the kindergarten level so I wasn’t overly concerned that we weren’t doing math fact work or determining calculations. However, I wanted to move beyond the form and function and start helping kiddo develop number sense.
Trouble was, whenever I tried to bring in math he had been doing in preschool, he got anxious. He felt pressure to get the right answer and it stopped being fun. We had conquered the “fun” aspect of math activities, but we needed to look more explicitly at numbers and their relationships to each other. We could go through the process of solving math facts, but now we needed to talk about the facts in a non-threatening way. In short, how can we banish the anxiety kiddo feels on always needing to provide the correct answer? I looked to web discussion forums for inspiration.
Cunningham’s law describes an online phenomenon about asking for help. In essence if you want to get help online, you don’t ask the question you want answered, instead, you make an obviously false statement and wait for refutations. If you ask: “How do I do…” you won’t get much engagement. People don’t seem to want to answer direct questions, especially if they have appeared on the forum before. However, if you confidently post a wrong answer, you will get many people pointing out that you are wrong, and providing examples to show you just how wrong you are. Soon you will get the answer to your “How do you do X”, you just had to ask it in a way that people would react to and feel compelled to engage with. The xkcd comic series has a cartoon describing this obligation.
Don’t Ask a Question. State an Incorrect Answer Instead.
When I was starting out as a public speaker at software development conferences, I had a lot of anxiety. Part of it was because it was new and public speaking is hard, but part of it is because the audiences in software development can be ruthless if you get something wrong. Heckling and heated arguments can occur when you get it right, let alone if you mess something up or if you have an incorrect interpretation. At the time, software consultant Brian Marick was very kind to me and offered encouragement and advice. One tip he had was to start off with a mistake in a talk, and get it out of the way. That way you could just focus on your content and not worry about making a mistake. You’d already made the mistake, and it wasn’t so bad after all, so now focus that nervous energy in a positive way.
I found this helpful, and with experience I learned to improvise and incorporate my mistakes into the talk. If I got a fact wrong and I was corrected, I thanked the person for taking the time to help me, and corrected my materials as best I could. Mistakes weren’t so bad, and in fact, they added a richness to my corporate training. Sometimes, this was due to me getting an important detail wrong. At the time I traveled so much I would forget what city I was in, or what company I was currently at.
I also used to use incorrect answers to warm up a shy group. If I had a group that was reluctant to engage with the activities in the training, I had a secret weapon. I’d deliberately pose and then answer a question with the wrong answer, and usually someone in the audience would blurt out that it was wrong. Or at least you could see them move from surprise to chuckles, once they figured out I was doing it on purpose. People would warm up and start adding in ideas about a better solution. It also helped with groups who didn’t know each other. If they were a bit reluctant or shy to collaborate, I would break the ice by suggesting incorrect solutions, then transition to correct examples.
There seems to be an innate need for many people to correct something that is wrong. If it worked with adult learners why not try this with kids?
In the book Moebius Noodles, they discussed teaching subitizing. This is something adults have developed through working through math over a number of years, but many of us weren’t explicitly taught. I liked the idea, but I had never heard of trying to teach it before. I started reading and watching videos about how to teach my kiddo how to subitize. Trouble was, if I held up fingers or a dice or pointed to a small group of toys and asked “How many?”, the old math anxiety would flare up. The fun would stop, and kiddo would be disappointed. I felt that we could easily work from 0-6, especially since we used dice in games and he was familiar with that number range. However, instead of doing it right, I was going to do it wrong and see what happened.
I started with body mirroring activities. We stood facing each other, and I bent one arm at the elbow and held my palm facing up. Kiddo mirrored me, watching intently. Next, I adjusted my hand so I was holding up three fingers. Kiddo mirrored me, watching quietly and intently. Then I blurted out: “I am holding up FIVE fingers!” He stared at me in shock. He didn’t say anything, so I said it again. “I am holding up FIVE fingers!” He gave me a puzzled look, so I repeated myself. “I am holding up FIVE fingers!” He responded this time: “No Daddy, you’re wrong.”
I repeated myself: “I am holding up FIVE fingers!” “No Dad, that isn’t right.” I asked him what was wrong with what I was saying. “It’s wrong, you are not holding up five fingers.” He looked concerned and wasn’t sure how to proceed. This time, I started using silly voices, making faces and hamming it up. “I am holding up FIVE fingers!” Once he realized I was being silly, he started to laugh, but kept telling me it was wrong. Finally, I asked him why it was wrong. “You’re holding up three fingers.” “Pardon?” “You’re holding up three fingers.” “Pardon?” “You’re holding up THREE fingers.” He was starting to giggle now. “What? How many?” “DAD! YOU ARE BEING SILLY. YOU’RE HOLDING UP THREE FINGERS!”
Aha! Finally! Math without fear!
I then asked him to do it. He started hamming it up and holding up random numbers of fingers and deliberately stating the wrong amount. He would ham it up until I guessed and corrected him, and then we would switch. After about 5 minutes, we were doing a basic subitizing exercise that was incorporated into our mirroring activity.
This was a huge breakthrough. We hadn’t had an experience like this in weeks/months. Now we could build on this.
Wrong Answers Only
In our daily work, I started to incorporate subitizing, simple arithmetic and counting. We would use manipulatives like mathlink cubes, Lego bricks, rocks, basically anything we could use to visualize. However, we had a rule. wrong answers only! I wanted to try to get the anxiety out, and model how math should feel. It should be challenging, but it should also be fun. It should be about discovery and exploration, and the mental math and memorization will come with doing, not by being judged on your accuracy.
I deliberately chose math problems that were below his current level, and then had him come up with the wrong answers only. I could tell that he really wanted to provide the right answer, but I would delay that and remind him that we were going for wrong answers only. In fact, the reward here was for the silliest answer. After a while, he would be practically vibrating to try to correct it, and then and only then would I ask him for the correct answer.
Here were some variations:
- Try to make me laugh, or make yourself laugh with your answers.
- Make them sillier and sillier.
- If they want precision, then I have a rule that there needs to be 3 silly answers first, before doing the correct one.
- If they are tired of doing wrong answers and want to do right answers, follow their energy and switch it up.
My goal here is reframing the learning. Instead of a winner takes all, high stakes math fact question, we explore and see what happens. Instead of getting a question wrong and fixing the answer, we embrace mistakes, and to try to banish fear. Part of this approach is to get kiddo used to the format of solving problems. Part of it is to overcome anxiety and panic when posed with a math question and being expected to get the right answer, every single time. If you can get the wrong answer and the wrong answer is the correct answer, then you have the capabilities to get the correct answer when you need to provide the right answer.
Switch the Context, Gently
I wanted to tap into the knowledge he had, and to get him to demonstrate it to us, but without any anxiety or fear. I worked hard to be matter of fact and not point something out and wreck the energy of the activity.
Once we were having fun answering with only incorrect or silly answers, it was obvious that he had the capabilities to answer correctly. Once he was tiring of silliness, or if he was starting to answer with the correct answer, I would silently shift. I might verbalize this if it felt confusing, or I might just go with his energy and watch him answer correctly. I didn’t praise him for the wrong answer, or the right answer, I reacted the same way no matter what he did. I was rewarding the approach and the effort, not the answer itself.
After a while, we could do subitizing without fear. I would hold up fingers, he would answer correctly. Then I would get him to do it with me. We would take turns with fingers, dice, toys, cereal pieces, or anything else that was a small number to count. To add some variation, I started holding up 1 finger on my right hand, and 2 on my left, slowly easing in to some basic arithmetic.
If he started to freeze up or show signs of anxiety, I would ask for “wrong answers only”. If he was really starting to get wound up, we would move and work out his emotions together, and return to mathy stuff later on, or the next day. After a while, he would ask to not do silly or wrong answers, and preferred to work at providing correct answers. To keep the positive energy going, I didn’t tell him if his answers were correct until he asked me because he was curious. I was careful not to reward him for being correct only, but to reward his efforts and the process we were doing. If he got one wrong, I built up his self esteem and let him know it was ok.
Finally, we were moving out of math anxiety, and were developing a solid base we could work from. Subitizing, counting activities and simple arithmetic could be completed without anxiety, fear or conflict. This was a major step forward.
3 thoughts on “Adventures in Homeschool: Embracing Math Mistakes”
What a beautiful technique, described in detail for people to learn! You developed this our of the corporate training, serious stuff – yet it also reminded me of theories behind improv work, and training for clowning or stand-up.
Thank you for the kind words and insight Dr. Maria. Come to think of it, I did a lot of improvisation and comedy when I was in school. That likely provided the foundation to improvise while speaking and teaching.