Habit and Mindsets are Difficult to Change

In March, after attending a workshop by Gary Stager at ASB Unplugged I posted The Future of Math Education and two recent articles on math education have me thinking about this topic again. The New York Time article, Why do Americans Stink at Math, by Elizabeth Green and Jessica Lahey’s article, Teaching Math to People Who Think They Hate it from The Atlantic should be the sources for a professional learning community (PLC) study. The purpose of this post is not to fully analyze these two articles. The purpose is to share a few of the main ideas in hopes that they will stimulate thinking and a dialogue.

The main idea behind Green’s article is that:

“The new math of the ’60s, the new, new math of the ’80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.”

And even though these curricular initiatives were designed to transform math education, little has actually changed. Green presents one major reason for this inertia.

“Consequently, the most powerful influence on teachers is the one most beyond our control. The sociologist Dan Lortie calls the phenomenon the apprenticeship of observation. Teachers learn to teach primarily by recalling their memories of having been taught, an average of 13,000 hours of instruction over a typical childhood. The apprenticeship of observation exacerbates what the education scholar Suzanne Wilson calls education reform’s double bind. The very people who embody the problem — teachers — are also the ones charged with solving it.”

The “apprenticeship of observation phenomenon” is something that all educators face when it comes to changing practices in their subject matter. We’ve seen over the years that educators have a difficult time changing their mindsets. To add to the problem, parents have a view of how education should be based on their experiences. When educators actually do change practices, parents can be critical because the changes don’t match their vision (frustrated parent’s rant on Common Core math practices).

Lahey profiles the work of Steve Strogatz from Cornell University. Strogatz is teaching an introductory math course for non-math majors. “The curriculum he teaches is called Discovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts (DAoM); it was developed at Westfield State University byJulian Fleron and three colleagues and funded by a grant by the National Science Foundation.” The learning focuses on using “student-led investigations into problems, experiments, and prompts.” The curriculum looks promising and they are already sharing the results through student quotes, videos, other data.

I’d love to dive deeper into these ideas even though I’m one of those individuals who thinks he hates math.

The Future of Math Education

Lately I have been asking the question, “What is  math education going to look like in the future?” As of right now, I don’t have a clear picture and I’m fairly optimistic that significant changes will not take place in the near future. While I frequently hear from teachers (not all) that math requires students to practice learning the steps to solving problems that will lead them to being able to apply their learning afterwards. It seems to me that they are saying that the traditional lecture, in class practice, and homework practice is the way that it has to be.

“If we taught dancing like we teach math we’d never let people dance until they drew out all steps on paper.” Seymour Papert (From Gary Stager’s TEDxASB talk)

On the other hand I’m hearing from others that math education has to change. Forget the flipped classroom and Khan Academy, they’re talking about substantial changes. What are they?

Dan Meyer’s 2010 TED Talk, “Math class needs a makeover”, certainly got people thinking about this topic back in 2010.

Since then I’ve been on a quest to search for the future of mathematics. I had a small epiphany at the recent ASB Unplugged Conference when I attended Gary Stager’s workshop, Electrifying Children’s Mathematics. Now I’ve seen Gary speak many times but this was the first time that I participated in one of his hands on workshops. By actually being able to work through the exercises in a constructivist way I was able to make just a little bit of sense out of the possibilities in the math classroom.

Gary started the presentation by showing us that,

“The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. ” (Stager and Cannings, 1998)

We then watched a video of math instruction in an elementary class where the teacher uses Piaget’s theory to help students construct knowledge on concepts. The videos are the work of Constance Kami, Professor of Early Childhood at The University of Alabama at Birmingham. My take-aways from this video are that…

  • students don’t need to know all of the ways to solve a problem. Whatever works for them is sufficient.
  • the refrains from telling the student whether or not their answer is right or wrong. teacher should let the students talk through their methods and to let them work through the problems together. The less teacher involvement, the better.
  • doing endless numbers of problems that you already understand does not do you any good.

We then moved into the hands on portion of the workshop and in a very short amount of time I realized the value of playing with tools and ideas to learn mathematical concepts.

We played with Turtle Art. We were given a simple exercise to get started and then were left to play on our own. The connections to mathematical thinking were easy to make and the results were definitely visual.

We used MicroWorlds to try to figure out a problem that we later learned was unsolvable. Something that is referred to as the 3N + 1 Conjecture, Collatz Conjecture, Ulam Conjecture, and many others. It was amazing how much math we were having to use to struggle through this problem. It was a good learning experience and it’s probably better that we didn’t know that it was unsolvable.

But, my favorite activity had to do with determining values for iTunes radio users’ actions. The work had us tackle computational thinking. Gary was very clear about his views on teaching computational thinking skills.

Computational thinking is useful when modeling a system or complex problem is possible, but the programming is too difficult.

The activity involved assigning values to the following actions.

Photo from from Sam Costello
We also considered when the person just let the song play.

This was a room full of math teachers and I’m pretty sure that none of them had the programming skills to code the algorithms behind these choices. We did struggle with equating a value while thinking about the users’ thinking and how the numbers would be used behind the scenes. Many of our students have no idea of what is taking place behind the scenes when users click on a button. While very few actually have to know how to do the programming, there is definite value to understanding the computational thinking.

So, after the workshop I asked a couple of math teachers if they felt that they learned skills and/or knowledge that they could take back to their classrooms and, the general consensus was, “most definitely”. These were primarily teachers in international schools.

So, what are your thoughts on the future of mathematics?