If math is a 30cc 2-stroke garden leaf blower then where are all the leaves?

Leaf blowers are annoying, right? They make noise and wake people up on Sundays and even Thursdays. They emit harmful carbon dioxide, are heavy to carry and are hard work for the user. And you have to wear ear defenders which look kinda dorky.

Leaves are what make a leaf blower worthwhile. Only when you see the ease with which a leaf blower can gracefully and efficiently corral leaves does it start to make sense as a piece of garden machinery. Better still, ask someone to try to gather leaves with a simple table fork. After a few hours of this, see how readily they will accept the need for a leaf blower.

This whole metaphor – for it is a metaphor for something and we’ll see what that is in a minute – hit me the other day whilst I was watching a cool and zeitgeisty TV show. I immediately realized how profound it was. Clearly, we need to completely revolutionize the way that we teach maths and the leaf blower gives us a clue.

Ask any teacher what the biggest problem in education is right now and they’ll say that it’s motivating students. You see, kids get bored in math class. This is clearly not because they expect to be constantly entertained and lack self-discipline. It is because they can’t connect the math they are learning with their everyday experiences. Everyone says so. And this is where my metaphor comes in.

You see, math is like the leaf blower. The leaves are like authentic problems that the math can solve. Do you see it yet? I am saying that we have to present kids with authentic problems to solve, let them struggle a little – this is like the part where I suggested picking up leaves with a table fork – and then they will see the need for the math. This works because math only has any value inasmuch as it can be used to solve commonplace, everyday problems (that are slightly contrived).

The leaves

Let’s put this into practice by posing a problem. You work for your county painting fences (of course, here you should substitute the name of your actual local county). You need to paint a fence that’s 30 feet long by 6 feet high. You have to give it three coats of paint. It takes 30 minutes to paint a six-foot length of the fence and the paint takes 20 minutes to dry.

You can spark their curiosity – I call this ‘roping the mark’ – by showing a video like this:

By now, the students will be drawn in to the conflict inherent in the grand narrative that you have set-up. And so it’s time for the next stage.

The table fork

Ask your students for the solution to the problem. At first, most are likely to suggest painting the whole fence once, waiting 20 minutes, painting the fence again and so on. If you add these times together then you get an answer. However, some students are likely to realize that some of the fence paint will be dry before you reach the end of the fence and so, provided you have an infinite supply of labor like most counties do, you don’t have to wait that long.

The sensible approach here is to start partitioning the fence into lengths. However, these lengths will be essentially arbitrary. A student might work out what length of fence is painted after 20 minutes and this should then develop into a discussion about the thickness of the paintbrush and how long one stroke takes.

The leaf blower

By this point, your students will be ready to hear a ten-minute mini-lecture where you give them an algorithm for working out the fence-paint problem whilst introducing them briefly to differential calculus. This is like what they do in Japan.

The payoff

Instead of having your students learn abstract maths for which they cannot immediately spot a commonplace use, they will now have all of their maths taught to them in an exciting and engaging way. From henceforth, your students will be motivated.

All you have to do is keep looking for leaves which, in my experience, usually get stuck in garden beds or the entrances to drains.

Actionizing Thinkiness

Now, there is nobody who would deny that knowledge is important. Nobody. We all recognize that it has a central role. However, it is clear that, with an abundance of knowledge now available to students at their fingertips via the internet, we must shift teaching practices from a model of knowledge transmission to one of developing certain dispositions that transcend subject areas and other boundaries, just like what a balloon full of hot air does. We know that didactic teaching that sees students as submissive receptacles for knowledge passed-down from on high by a coercive authority figure is pretty much useless for developing students who can think at all.

It was W B Yeats who famously said something about buckets. Or perhaps that was Einstein. Or maybe that was the one about the fish and the bicycle or the fish and the tree. It doesn’t matter. A truth is a truth even if the quote is not.

But nobody is against explicit teaching in its appropriate place. Let me make that clear.

Actionizing Thinkiness I

If we don’t teach children how to think then they won’t be able to process thoughts. We must also teach them how to analyse the process of their own thinking. This also requires thinking. Then again, they must develop an evaluatory capacity for monitoring the analysis of their own thinking. This requires yet more thought. Thought about in this way, it is absolutely clear that thinking should be at the heart of the curriculum and, if we wish to develop a future capacity for thinking so that students develop in to actively thinking, thoughtful, sentient citizens who think lots then the process of actionizing thinkiness should be at the very heart of our pedagogy.

Actionizing Thinkiness II

For instance, we know that if we actionize thinkiness then the flow-on benefits are meaningful and substantial, as demonstrated by this diagram:

Actionizing Thinkiness III

So, how can teachers go about actionizing thinkiness? At the Extraordinary Learning Foundation™, we have developed a few templates and things like that. One of them enables students to develop their decision-making thinking. Faced with a decision to think about, students fill in three columns, preferably with a pencil in case they need to erase something (we also have computerised versions):

Actionizing Thinkiness IV

This powerful thinking tool can be used for making any kind of decision, from whether to have scrambled eggs for breakfast to whether to invade Iraq. Moreover, meta-thinking can be invoked by asking students to think about each others’ thinking processes which are now visible!

Knowledge is important. It is crucial. But in the future, our students will have computers and the internet to know stuff for them. We need to focus on enabling them to think. Building lessons around the imperative to actionize thinkiness will ensure that they think lots.