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.

5 Tips to Reduce Teacher-Talk

Teachers talk too much, right? It’s a problem. It is a proven fact that low-SES students have a similar attention span to flightless birds. They are literally emus. Yet, we also know that teachers often can’t seem to help themselves. I went to visit Reginald (Reggie) Grover, Grade 3 teacher at the International Elementary School in UA. He’s been working with the Extraordinary Learning Foundation™ to address the problem of teacher-talk and he’s got some advice.

1. Ask a student to time the teacher-talk

Reggie picks one of his students, Max, to time all sessions of teacher talk. After 5 minutes, the student rings a bell. Well actually, it’s not a real bell. That would be a waste. Conscious that modern students are digital natives, Reggie gets Max to ring a virtual bell on Max’s cellphone. Sometimes, Max replaces the bell with the sound of breaking-wind. Reggie smiles, “There’s gotta be a metaphor in there somewhere!”

teacher talk

2. Use shared gestures

Teachers can set this up any way they like. The important thing is that Reggie and his students all know what the gestures mean. When Reggie points at something and smiles then that means, “Great job guys! You’re on the right track!” If he points at something with his foot or one of his knees then the students know that this means, “You’re not necessarily wrong guys but you might just want to take five and have a think about that.”

“It works really well,” confirms Reggie, “especially when the students are looking at you.”

3. Build resilience, grit and mindsets

Sometimes, the bell rings and Reggie’s time is up before he has said what he planned. “It still happens,” sighs Reggie, “I can’t always quite make it!”

This leaves part of a task or activity unexplained. “This is where kids need grit, resilience and a mindset. After that bell goes off and I am caught mid-sentence then I think that this is exactly the experience that my students will have to struggle with in real-life.”

Reggie festoons his classroom wall with posters to motivate the students in these situations. One simply reads, “Don’t give up!” over a picture of a beach at sunset. Another celebrates making mistakes.

“Some kids have just naturally got the right mindset and others haven’t,” he explains.


4. Use relevant, authentic contexts

“I used to do things like read a class book and then ask the students to write about it,” says Reggie, “I remember doing Charlotte’s Web. The trouble is, it required a lot of explaining; characters, narrative arcs. And my students aren’t spiders. How could a story about spiders be relevant to them? How could it be authentic?”

This illustrates that asking students to complete tasks that they don’t already know how to do usually involves a lot of teacher talk.

“Now, I ask them to write to a prompt like ‘my perfect lunch’. They’re still writing but it’s much more relevant to them. They’ve written similar pieces many times before and so they hardly need my help at all. I don’t have to say or do anything. And that’s the ultimate goal for any teacher.”

5. Prepare your resources

Teacher talk can be reduced by having printed resources containing explanations, instructions and examples. Reggie suggests combining these ‘prompt sheets’ with any activities or questions you want the students to complete.

“In math, you can make up a sheet with instructions and examples on it with maybe some questions at the end. You can even get ahead of yourself and put a few of these together into something like a booklet. Publishers often produce these ready-made.”

Over to you

So are you ready to reduce teacher-talk in your classroom? Try Reggie’s tips and let us know how you get on!


Speaking for Meaning

Consider a child who speaks the following phrase:

“Is not underhand over the post garden implications.”

In one sense, there is nothing ‘incorrect’ about it. All of the sounds, or ‘phonemes’ to use the jargon, are in the right order and everything has been pronounced accurately. But, of course, the phrase has no meaning and the child is therefore conveying no meaning whilst speaking it.

Speaking is clearly more than simply the rote regurgitation of ‘correct’ sounds.

At West Bay University, most of our education research involves finding out what pre-service teachers’ attitudes are to various aspects of education. We are not alone; this exercise dominates research across the field and with very good reason. We wish to discover whether pre-service teachers approach their vocation with constructive or destructive informal pedagogies; whether they believe in authentic, contextualised, real forms of learning or whether their own childhood experiences have locked them into paradigms of rote memorisation.

Our research into attitudes towards the teaching of speaking shows that many pre-service teachers haven’t even considered it! This shows the emphasis that society has previously placed on this crucial area – none! Here at the Extraordinary Learning Foundation™, our mission is to change all that.

Moving on from our first phrase – where meaning was clearly absent – I wish to now present a more complex and nuanced example. Imagine if a child in Grade 2 were to declare the following.

“Democracy is a good way to protect people’s freedom.”

What would you think now? You might be inclined to suppose that this child was ‘smart’. Yet, the work of the German psychologist Edmund Rotz shows us clearly that a child at this stage of development could not possibly associate appropriate meaning to such a phrase. In actuality, what we are witnessing is rote verbalisation without meaning. The child has no idea what she is saying.

For speaking to have meaning, it must be situated in real, authentic, appropriate contexts; contexts that are familiar to the child. Speaking about democracy and freedom at this stage of development is too abstract. Children’s speaking should be focused on what is relevant and meaningful; that which carries meaning for the child in his or her everyday experience. Childspeak must be situated in, around and inside of real, rich, authentic contexts that are motivating to the child. It is only then that we will experience real speaking for meaning. Here at the Extraordinary Learning Foundation, we have summarised this idea with the following diagram – the fruitcake model of speaking:

The fruitcake model of speaking

I am speaking to Haneck von Beer about his approach to speaking for meaning with his Grade 4 class. Haneck works at the Grunig Institute and it is the lunch recess. All of Haneck’s class have eaten their lunch and are out exploring their ideas in the imaginarium resources area.

“There’s this kid, George,” Explains Haneck, “All he ever wanted to talk about was planets and space and yet he has no direct experience of these concepts.”

This is, indeed, a common problem.

Haneck continues, “And so I asked him whether he had any pets.”

I smile, I can see where this is going and how the principles of the fruitcake model will apply.

“George says that he has a cat,” Continues Haneck.

I nod.

“So I ask him to talk about his cat. For the first time, I heard George speak in a real, authentic, appropriately situated, meaningful way.” Haneck smiles.

If only all educators had such skills! “What did George say?” I ask, totally subsumed in this moment of genuine authenticity.

“He said, ‘I have a cat and it is brown’.”

Learning Limbs

There is a spider that lives in the Swiss alps, the elastichspinne, that makes its web in pretty windy places. Some elastichspinne’s have been recorded as making more than a hundred webs, each of which is blown away by the wind before they even catch a single fly. Whilst spiders are not themselves great learners, this spider illustrates one of the key features that all great learners have; grit or the ability to stick at something. Here at the Extraordinary Learning Foundation™, we see grit as one of the four learning limbs that we must ensure that our young learners sprout.

The Four Learning Limbs

The Four Learning Limbs

The head represents curiosity because the eyes are always looking and the ears are always listening. The legs represent grit because they are the stable base that supports learning. The arms represent adaptability because arms are capable of being put to many different uses. The torso represent creativity because that it what is left.

Many of the schools that work with us here at the Extraordinary Learning Foundation™ use this model in every lesson in order to raise children’s meta-cognitive consciousness so that they can deploy these learning limbs deliberately and consciously. There has been much research into this area and such meta-cognitive strategies have been shown to be highly effective.

I’m sitting at the back of Dana Rece’s Grade 9 class at the Central International School in Utaga. Dana is resplendant and glowing in a purple shawl. The buzz of excitement in the room is adiabatic. The children sit at their study pods, discussing the science investigation that they have just been working on.

“OK class,” Dana Rece states, making a gesture that signals that it’s time to listen-up. “Discuss which learning limbs you have been using today with your study buddies.”

Dana Rece waits for a few moments in order to give her students plenty of time to Talk-it-out™.

“OK,” Dana gestures again, “Katia; what did your group think?”

Katia, a vital girl with glowing red hair and intense eyes answers, “We think we were using some grit. It got pretty tough going when all the paper towels kept splitting.”

“Uh-huh,” Acknowledges Dana Rece, “And what limb is that?”

“Yeah, that’s the legs,” replies Katia.

“And why the legs?” Dana continues to probe.

Katia is quick with her response, “Because they are the stable base that supports learning.”

“Good.” Affirms Dana Rece, “Anyone else come up with any other Learning Limbs™?”

A compact young man with a broad smile indicates that he wishes to speak.

“Go on, John,” Katia encourages.

“Well,” Says John, “I think we used some creativity in designing the inquiry process together – when we sketched it out on the big sheet.”

“Excellent,” Dana Rece nods her head, “And what limb is that?”

“That’s the torso,” Says John, before he continues, “And it is the torso because that’s what’s left.”

A broad smile breaks across Dana Rece’s face. “Great work today class! Good job!”

Mind tools for the whole child: Think-it-out™

As Clayton Dyer’s class rush out to recess and the pleasant hum of happy, laughing children recedes, I take the opportunity to grab a few words with this expert, long-standing collaborator of the Extraordinary Learning Foundation™.

In his tailored beige cardigan, Dyer strikes me as the epitome of the Zeitgeist.

“We teach children, Tait; that’s the key.” Dyer smooths his elegantly trimmed beard as he speaks, “We don’t teach content. We don’t teach subjects. We teach children.”

It’s a profound statement and one that summarises my own thirty-year journey of discovery about the phrenology of learning. It’s about the child. If there is one thing that all of the supremely talented educators that we work with here at the Extraordinary Learning Foundation™ would agree on, it is that we teach children; we teach situated, contextualised, definitional children (apart from those of us involved in adult education).

When I read of some of the ‘reforms’ that are taking place in the global edusphere, I sometimes worry about the children. I wonder if they are front and centre of our concerns. Am I alone?

I don’t think so! As Dyer explains, children are definitely at the top of his list.

“One of the strategies that we’ve been working on with the Extraordinary Learning Foundation™ is a model based upon Talk-it-out™ with a particular focus on the pre-cognitive/recognitive stage.”

Talk-it-out™ is one of the successful Extraordinary Learning Foundation™ strategies that we have action-researched across a number of contexts and situations, finding it to be extraordinarily powerful and effective.

Talk-it-outClayton Dyer and his colleagues at the William Rodgers Middle School have been successfully trialling and researching a modification of this model with a particular emphasis on the mentalistic elements.

“What we found,” Explains Dyer, “Was that, when presented with standard curriculum content, children would typically try to work out what it was; describe it, list it, recall it and so on. But they did not interact with it critically. They would not ask how these knowledges related to the reigning hegemony and therefore whether they were disputable or at least coalesced into different patterns from alternative, diverse, inclusive perspectives.”

This is a problematisation that I am familiar with from many multi-layered contexts.

Dyer continues, “We used the architecture of Talk-it-out™ to help formulate some of the critical vocabulary. But vocabulary are still just words. We needed students to speak for meaning rather than just speak. And so we decided to spend more time in the pre-cognitive/recognitive in order to give them tools to add meaning to their own thoughts.”

This is the model that Dyer and his colleagues developed:

Think-it-out“The value of the model,” Continues Dyer, “Is that it enables students to independently develop a superluminal mass of capacity for criticality.”

The benefits could not be clearer than that.

Ductile Thinkpoints

I am sat at the back of Virginia George’s classroom in the Jose Manuel Garcia Rodriguez Memorial International School in Baichek, UA.

“I want you to think about how you could get that heavy chest from one side of the ThinkLab™ to the other,” She tells her group of smiling sixth graders.

They all know the score! Each child turns to their thinking collaborators for a quick discussion. This is not the hard part and the students know it. After a short time, they use their elbows to indicate that they are ready to contribute.

“Okay, wow!” Exclaims Virginia George, “You guys are fast! Now, tell me your answer. Kelly?”

A little blond girl with plaits confidently states her solution, “We think that Gerry and Khaim and I can do it if we co-operate.”

“Hey, that’s great,” Says Virginia George. We are now about to witness the pivotal moment, “That sounds like a cool strategy to me. Now let’s go back to our thinking collaborators and answer the question; what other problem could we solve with this solution? We may need to stretch it a little. The details maybe won’t stay the same.”

A short flurry of activity follows while the children talk loudly and animatedly to each other. Virginia George doesn’t say anything at all – a key feature of this process. After a longer while than last time, the students again indicate that they are ready to contribute.

Virginia George nods towards a boy with olive skin and soulful, brown eyes, “We think that you would need to maybe co-operate to solve something like global warming.”

“Oh wow,” Virginia George nods, “What a cool idea.”

Virginia George is working on a strategy that we have been developing for some time at the Extraordinary Learning Foundation™. The notion centres on ductile thinking and the need to develop ductile thinkpoints within the normal class structure.

Brittle and Ductile Thinking

In nature, there are brittle materials that fracture easily and there are ductile materials that can be shaped to suit different purposes. The traditional approach to learning, with its emphasis on the rote memorisation of disconnected facts, promotes brittle types of thinking. However, in order to be ready for the challenges of the 21st century, students need to develop ductile forms of thinking; durable thinking that can be shaped to fit new challenges. The careers of the future do not involve standing at a single loom for forty-years, thinking exactly the same thoughts, day after day. In fact, we don’t even know what the careers of the future will be yet because we can’t see into the future. We therefore need to prepare our students by developing their ductile thinking.

In nature, you can take any brittle material and form it into a ductile material by repeatedly stretching it. This is the revolutionary concept behind the idea of introducing ductile thinkpoints. Instead of a standard teacher-student interaction where a teacher asks a low-level question, expecting the student to answer with the simple recall of a discrete fact, the technique takes the question from where the solution lands and works it back from there; like the ball in a cricket game.

In fact, the magic of the approach is that it takes a solution and stretches it to suit a different problem. This is exactly the sort of exercise that will develop ductile thinking and promote transfer; the ability to solve problems in different areas based upon the same root solution strategy. This is precisely the kind of skill that businesses that don’t yet exist are demanding education to deliver right now; an education fit for not just the 21st century, but for most of the centuries beyond.

As I left Virginia George’s class, I had one final question. “Hey everyone,” I asked, “What’s the coolest solution that you know.”

One young man could not wait to contribute, “The one with the fish and the bamboo.”

I didn’t know what he meant, but I did know from Extraordinary Learning Foundation™ research that he would be able to use that solution in a wider range of contexts than 87% of European Union residents aged 21 – 57. It makes you think.