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.

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?

First off Blair, thanks for thinking about math(s) and sharing your thoughts here. Lots of people are writing and thinking about the future of math education and this is really alarming for me. We are still talking about it like it is something that

maybeneeds to change, sometime, in the future, but not now or not even tomorrow. Alarming. Why are we still talking about the change and not demanding it? We know that the majority of our students will be more successful if we approach math education in completely different ways, yet take a look at math classrooms – they look exactly same as they did when you were at school. Teacher talks and gives examples. Student takes notes. Test includes replica questions (but now you need to do them quickly!) Ugh.My biggest worry with math education is that it produces far too many adults who hate math. They openly talk about their failures in the subject and the nightmare and pain it caused them in high school. This needs to change. Parents need to stop telling their kids that some kids are good at maths and some aren’t. This is false. Parents need to stop giving their kids an out and telling them that there is some kind of genetic marker that makes a kid a good maths student. False.

I think your three take-aways from the video are spot on. Give kids time and support to solve problems and find success, as with success they might be more likely to find some enjoyment. Don’t give them all the answers and don’t make it so black and white – it can be frustrating. Open the questions up, make them deeper and create opportunities for mathematical diaglogue. Don’t ever give textbook questions for mandatory homework.

As for “all kids need computational thinking”, I haven’t pinpointed my feelings just yet….

Hi Blair

I’ve been following closely the progress of my two boys (Grade 1 and 3) through their Maths education and I’m disappointed that they find what is presented to them to be very dull and algorithmic. Maths should be fun and creative and beautiful. Right from Grade 1 it all seems to be about money and measurement and application to the real world. I would like to see an emphasis on beautiful mathematics, and kids being allowed to progress at their own rate with creativity rewarded. I also hate “mad minutes”. If you were trying to teach basketball skills to a 7 year old would you put them under pressure to see how many shots they could make in a minute?

David, it’s great to hear from you. I wish that I could experience “fun and creative and beautiful” maths. I just don’t know what that is like. Yeah, the “mad minutes”approach doesn’t seem to be the answer.

It’s interesting that you and Ange were the ones to respond to this post. Two Aussies who love maths, students and learning. Ange spearheaded a move to integrated maths at Graded. Not an easy task since Graded is an American school that is steeped in tradition.

I hope that our paths cross again in the near future. We need to get back to KL for a visit. Thanks for the comment.