How to Learn Math Part 3: Mistakes and Persistence

In session 3 of “How to Learn Math” we learned about the importance of making mistakes and the importance of developing persistence.

If you have heard the news about the “controversy” that the new Common Core State Standards will give students credit for saying 3 x 4 = 11, and you are worried, then this session is right up your alley! If you haven’t heard about this controversy, let me assure you it’s a completely manufactured controversy and total crap. My advice is to avoid reading anything about it. I especially implore you to avoid watching any news shows where they talk to “experts” for their reactions. Utter crap.

Anyway, back to another awesome session in this FREE online course. (I’m excited I’m getting such great information at no cost to me. I love it.)

The session started by talking about how when we make mistakes we are actually putting ourselves in a great position to learn. Here’s my first reflection:

It makes sense that greater learning happens when students make mistakes. This puts them in a state of disequilibrium, a great place to be in for learning.

The questions it leaves me with are how do the students realize they’ve made a mistake? Do they have to realize the mistake for themselves? Or is it as powerful if someone tells them they’ve made a mistake? Also, once the mistake is out in the open, what are they or someone else doing to help the student learn from the mistake? Basically what I’m getting at is what are the actions a teacher and/or student should do upon discovery of a mistake to take advantage of the student’s brain being at a prime spot for learning.

It also makes sense that people with growth mindsets would benefit greatest from this learning. A person with a fixed mindset would see a mistake as a reflection on their natural ability to learn math, which cannot change. A person with a growth mindset would see a mistake as a sign that this is an area where they can learn and grow from.

Next, Carol Dweck spoke about the importance of making mistakes and we were asked to jot down a list of key ideas we heard.

1. Everyone can get better at math when they work on it.

2. It is very important to show students the progress they have made.

3. Show students how to use the feedback they’re given to become better at problems like the one they are solving and at math in general.

4. When things are easy and you get everything right, you shouldn’t feel good. You probably weren’t learning or growing. Challenge should be the new comfort zone.

5. Mistakes are our friend. They are a natural part of learning. Often they give us clues about what we’ve done wrong, what we need to learn, and what we need to do next.

6. Teaching a growth mindset is very important for math achievement because it’s a subject where lots of students have a fixed mindset and have difficulty. When these students encounter problems that require effort, they think they’re dumb.

7. Students need to learn that they can grow their math brain through hard work, practice, and good mentoring.

Later we had to respond to a quote from the New York Times columnist Peter Sims. The part of his quote that stuck out to me was about being willing to be misunderstood, despite the conventional wisdom, possibly for long periods of time.

The idea that struck me most was the one about being okay with being misunderstood. I’ve had several experiences in my career where I have been known to go along to the beat of my own drum. I’m not doing it to be contrary, but because I feel strongly about doing things a certain way that I believe is best for my students. Just because other people disagree with me doesn’t mean that I should stop what I am doing.

When I taught 4th grade at my last school before taking a job as a curriculum developer, I did not fit in with my team because my teaching methods were so different from theirs. They thought I wasn’t a team player or that I was doing it to be put on a pedestal, when really I was just using the methods that research said would be good for my students. I tried sharing them with my team, but they didn’t want to hear it. At one point I even asked my principal if it would be better if I gave up what I was doing in order to follow my team to create a better team atmosphere, but she advised me not to. She said she would rather I keep doing what I was doing, which she thought was great for my kids, and hopefully eventually my team would see the value. It was difficult to do, and it didn’t endear me to my team, but I believed it was important to keep teaching the way that I was despite it not fitting with the “conventional wisdom” of my team.

We also responded to a quote from a mathematician, Laurent Schwartz. His quote speaks about how someone’s ability to answer questions quickly does not correlate to their intelligence in a subject. Rather, the important thing is being able to deeply understand things and their relation to one another.

The part about being called out as an imposter resonates with me. I felt that I was a fraud starting in algebra and up through my second semester of college calculus. I was able to follow along in lectures and to repeat the procedures I learned to earn As on my assignments, but I never really felt like I understood what I was doing. For example, in algebra, I knew that the equations we were working with were related to the way a graph looked, but because I couldn’t tell right away myself, and other people could, I thought I was secretly bad at math. This continued through the years. As we rushed through the curriculum, I could tell that I wasn’t fully developing an understanding of what we were doing and why. My ability to regurgitate steps helped me succeed, but that just made me feel worse about possibly being found out. Looking back, I think I had the capacity to do well AND understand what I was doing, but I probably needed more time to make sense of it for myself.

At the very end of the lesson we had to design a motivational poster related to what we learned in the session. I wasn’t feeling particularly artsy, so I only made up the slogan:

Mistakes are moments for learning.

Make a mistake today – Show your friends!

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