This past week I attended the NCTM Regional Conference held in St Louis, MO. At the conference, one of the sessions I attended was by Rita Barger from the University of Missouri-Kansas City about commons myths about learning and succeeding in math. This series of 5 posts will share what I learned from the session.
What is it?
The “you have to be taught how” belief is the belief that you can’t do anything mathematical until someone shows you how. When I think about this belief, I wonder if it were true, how math would even exist to the extent it does today? Clearly, the mathematicians who have established the mathematics we teach our students, weren’t held back by this belief. That being said, I know that not every student that steps into my classroom will be a mathematician. Maybe none of them ever will, and that’s okay. I’m not in the business of generating math Phd’s, but rather, I hope my students can think critically and not be afraid to approach problems they might not yet understand. And, if students feel that they need to be taught how to do something before trying it, we have a big problem.
What causes it?
Me. You. Teachers everywhere. When we require students to do things a certain way, we lead our students to believe this, completely unintentionally. If a student tries to solve a problem, and arrives at the answer in a different way than we’re expecting, we might thank them for approaching the problem this way but encourage them to look at it from a different approach (our approach). I’m certain this is largely to make our assessment easier. It’s much easier to assess process when students are supposed to fit a specific template of process. Why would a student continually try to do things their own way? We’re just going to “fix” them later anyways. We like to encourage students into solving our way by asking them to “show their work”. Sometimes, teachers may refuse to give full grades if work is not shown.
Rita says that when we teach shortcuts, we can build on this belief. Often in math classes, we teach students an idea a certain way and then a few days later we make that idea obsolete by showing them a quicker, easier way to do the exact same thing (the concepts of polynomial long division and synthetic division come to mind). I struggle with this idea, because I know why it is valuable to show students the longer, harder way of doing things so they can appreciate and understand the shorter, easier methods we introduce later. But if we can do something quicker and easier, why wouldn’t we just teach that?
I think that the curriculum we are expected to deliver to our students also contributes to this belief. We have so many topics and concepts we are expected to get through, it doesn’t leave much time for students to inquire and discover math on their own. So, to make up time, we take some shortcuts, show some quick tricks. These quick tricks don’t teach our students how to think about math. If we are going to show them these tricks and shortcuts, there is no motivation to make connections on their own and find their own shortcuts.
What does it look like?
If students buy into this belief, they likely won’t even attempt to solve a problem until you tell them how to. They may simply skip problems they haven’t been taught how to solve, with the expectation that you will come back to teach them how to do it later. This belief becomes a big problem when students begin to miss class time or stop paying attention for any length of time.
What can we do about it?
Once again, Rita suggests brain teasers as a way to counter this belief. Since the teacher doesn’t just provide a solution, students will need to find a way to solve it themselves, hopefully allowing them to realize that they don’t need to be taught to how to solve a problem.
Another idea is to get your students to solve problems in more than one way. This will show them that there is no one “right” way to do arrive at a solution. And, if you have a student who finds a solution in a way you have not seen, or did not expect to see, make a big deal about it and acknowledge that extra thinking and creativity that was used to find it.
We need to find a better to get our students to “show their work”, because we want to into their minds and assess the process of their problem solving. Instead, maybe we could ask students to “show their thinking”. It might seem like a very little difference, but it could open the door to allow our students to be creative in explaining themselves. Some may draw pictures, use diagrams, or even write sentences to describe what they’re doing. I would be very interested to see how students would choose to do this. This is a very simple change that I hope to make immediately.
Five unhealthy beliefs in math that exist today are: