What's the problem we're trying to solving in math education?

The way we ask a question tends to frame our solution. This was one of the most long-lasting lessons that I learned at the d.school's week-long Teaching and Learning Studio. The activity we did early in the week to introduce this idea is one that I still do with teachers. I'll do my best to recreate that experience here.

First, I need you to break into one of two groups. Each group will do a different task. Let's assign your task based on your birthdate. If the day of your birth is odd, then do the first task. If it is even, then do the second one. (e.g. I was born on the 29th, so I'd be in group one.)

To begin, click on the appropriate link provided below. It will open up a copy of a Jamboard with the task's question. You can do your work on the Jamboard (it is yours to keep) or on a separate piece of paper.

Task One (odd birthdates)

Task Two (even birthdates)

Don't read any farther until you've completed your task or you'll ruin the surprise.

Once you've completed your task, click on the other task question and consider how that question might result in different solutions and why.

The first group often comes up with a variety of creative vases. Some have multiple openings at the top. Some hold the flowers sideways. However, because of the way the question is framed, they are all obviously vases.

Very few vases show up in the second group. Instead, flowers grow on the wall or hang from the ceiling. One participant had the flowers floating in a clear container with a fan at the bottom. Sure, it might not actually be feasible, but it is a much more creative way to start seeking solutions.

IBM does a version of this activity in their

Enterprise Design Thinking Course

I ask educators to do these tasks to highlight that most of our efforts to innovate in math classrooms amount to the first task. No matter what we do, we just end up with another vase. This is one reason why Kathy and I wrote Designing Math Adventures - because we want learners to experience something more than another math lesson.

So, what's the question you'll ask to frame your next school year? I'd like to collect them in the comments. Thanks for contributing to our creative problem-solving.

Can innovation be a bad thing?

And there's lots of ideas about innovation, theories of innovation, rules of innovation, like you should open up your innovation more. You should think about all these different types of innovation, you should practice disruptive innovation. There's all these theories out there about how you boost innovation. And when I went into do my initial interviews at LEGO, they hadn't read all those books. In fact some hadn't been written then, but they had done all those things that consultants and academics say you should do, and it almost put them out of business. And I thought that was really interesting. You know, how can we be so wrong?

This quote comes from an interview with David Robertson on his book Brick by Brick. I have been trying to share ideas from the interview with anyone interested in education reform. Given that innovation is such a buzzword in education these days, I think Robertson's book might serve as a cautionary tale for those trying to reform education.

So why did innovation nearly destroy this popular toy? Robertson explains:

what had happened is that when they'd innovated, they just came out with a whole lot of toys that weren't very LEGO-ey. They weren't very popular. ... 

I got the sense that the toy-designers in the 90s were allowed to be as creative as they wanted. As a result, LEGO put out a slew of new toys but the new toys did not fit together the way the old LEGOs did; this limited the creativity of the users. So the kids disengaged.

I sometimes wonder if we are in danger of doing the same thing in education. We see teachers being very creative in designing their lessons. For example, using technology to innovate the way they deliver content. However, by focusing on innovation in teaching are we sacrificing students' ability to be innovative? When I shared this question with a colleague, he said, "I know that those times when I thought I created the perfect, creative lesson - those were the times when students seemed least likely to be engaged."

There are several other ideas I took from the interview that might apply to education but it feels like I dropped a pretty big bomb in that last paragraph. Perhaps this is a good place to stop and see if some of you might want to add your two cents. I look forward to reading your thoughts.