the school of lateral thinking

Through the ages, it has been thought that there are two major types of reasoning: deductive and inductive. Do we start from a general rule and apply it to new practice using deductive reasoning, or do we observe practice and state what the law could be, using inductive reasoning? Here are some examples to understand these fundamental thinking tools.

Top down thinking

All students are motivated by grades (general rule)

Lisa is a student (particular)

Therefore lisa is motivated by grades (result of deductive reasoning)

Bottom up thinking

Lisa is motivated by grades (particular)

Tracy is motivated by grades (particular)

Students are motivated by grades (result of inductive reasoning)

We are constantly applying deductive and inductive reasoning subconsciously in order to make sense of the world around us. But the results of this reasoning do not necessarily have to be true in order to be valid. While the above examples are valid forms of argumentation, they are not by definition true. In fact, you don't have to spend much time in education to realize that the first premisis (all students are motivated by grades) is not a truthful starting point. Similarly the bottom up thinking rushes to a generalization.

Edward de Bono (1933 -) came up with the notion of lateral thinking as an alternative route to the truth. It's the kind of thinking that happens 'outside the box', using less conventional means of argumentation. Some techniques to make this magic happen included:

1. challenging the current models of problem solving for the subject of concern,


2. randomly relate seemingly unrelated things to our problem solving session by looking to objects in the room or pulling labels from a hat, or


3. being provocative and discussing that which we take for granted, like circular wheels or mugs with handles. These take the form of 'what if' statements.

Applying all of this to education is fun. A school in Texas started offering students financial rewards for graduating and their success rates increased. Needless to say , the results were as contentious as their method, but it got an interesting debate rolling on the nature of motivation at school that went much further than the examples on iductive and deductive reasoning as put forth above. And speaking of financial rewards, what if we lived in a world where teachers received exorbitant salaries, like those of football stars or CEO's? Would the quality of lessons increase or decrease? This kind of thinking is not only provocative though. It sheds light on the nature of education. Here are some more examples of lateral thinking on education.

• What if every student who failed an academic year had to do community service to make up for society's lost investment in him/her?


• What if there were no attendance requirements and students were free to come and go as they pleased?


• What if students assessed themselves?

Can you add to the list?

Stepping into the river of school

Imagine two students standing side by side. The first student is taken from the opening scenes of Hard Times by Charles Dickens. He is told that he must learn facts. That's all that matters in life. Fact, facts, facts. The heads of young individuals are reciprocals to be poured full of facts. When remembered properly and regurgitated at the right time, the facts help him contribute to a period of industrial revolution. There is so much at the end of the 19th century for him to test, dissect, and measure that there is paradoxically no time for him to think.

Our second student is taken from the information technology revolution. She wears an iPod, chews gum and chats constantly on MSN, sometimes even secretly in the computer lab, while her teacher talks about project based learning. She is computer savvy but cannot type. After cramming for her A-levels by studying essays she downloaded with her mother's credit card, she scores well and helps inflate the annual increase of national averages. Her future employer will one day complain that she is unable to communicate a single sensible idea at their department meetings. She may be of the information age, but is she any smarter than our boy from the industrial age?

Both of these character sketches have been written in such a way to expose an interesting question: has education made any progress?

Heraclitus (535 - 475 BC) had an interesting philosophical insight which may help us here. He said, 'you can never step into the same river twice'. Imagine that students are stepping into the waters of education. The framework of a flowing river with two banks has always been there. There has always been an upstream and downstream. Learning institutions are these rivers. But the content is forever in a 'state of flux'. The molecules of water represent the particles of our zeitgeist, the current state of our society, the paradigm du jour. It is into this context that our students step. It is a brief, fleeting moment of young adolescence that is inextricably bound to a small period in history.

So how are we to compare two points in history to know whether education has made any progress? I have often heard statements like: 'I wish I had had it as good as our students today when I was at school,' or the opposite 'back in my day we had to do timetables by heart, spell without a spell checker, and read 12 novels a year.' But were those the good old days or the bad old days? It seems that methods have changed so much through the years that it is difficult to measure the success of failure of them.

One method claims to have measured its success today. It is known as 'direct learning', others refer to it as a form of rote learning. With the craze of standardization in these No Child Left Behind (NCLB) years, we see the rise of scripted learning again. That's right, back to old fashion repeat-after-me drills. They have measured their results against other communicative and holistic methods with startling success. Nevertheless, could these tests and lessons have been designed specifically so that their results were measurable in the first place? How do we know that this is not another trend or molecule of water flowing down our river?

Looking at our two students, we can fairly say that there is something timeless and pure about the nature of youth. No matter what the circumstances, they are dipping their toes in, about to get wet, about to get caught up in the current.

Leap of Learning

How do we learn that 2+2=4? John Stuart Mill (1806-72) philosophized on the empirical nature of mathematics, saying that a child experiences two physical objects and then another two objects before saying there are four of those objects. Parents and teachers usually grab for the first things they can find, be it pens, apples, coasters, or maybe even an abacus. But when can we start to crunch the numbers to do our tax forms, calculate China's birth rate, or figure out the ratio of ballots to seats in parliament? When can we go beyond the experience of counting physical things and make that leap of abstraction?

Platonists like to account for the learning of mathematics with this term, leap of abstraction. It gives us access to a world of ideas where perfect circles exist and reason alone leads to the truth. But critics have been quick to point out that this leap of abstraction is a very wishy-washy term, and have dismissed it as esoteric mysticism.

This problem of definition is not only characteristic of mathematics. It seems that every field of science has its unexplainable leaps and black holes. In the 1950's, for example, Noam Chomsky explained away a great deal of language learning by referring to a 'little black box' in the brain. Similarly, when Sir Isaac Newton was asked how he discovered gravity, he answered 'by thinking on it continually.' While he saw the same apples falling from the same trees as the rest of us, something intuitive enabled him of all people to relate it to orbital movement. But what was it?

In literature and religion we see similar 'leaps'. Evangelists, in their effort to convince non-believers of the strength of their religion, often refer to a 'leap of faith'. Many people are actually convinced by this argument, without asking what this 'leap' entails. In a similar fashion, Samuel Taylor Coleridge, explained reading fiction as a 'suspension of disbelief'. But is the recipe for appreciating fiction really this easy?

One must wonder what kind of 'thinking' Newton did to allow him to make such great discoveries. For if we could crack that code, we could all access great ideas, do complex arithmetic, or teach languages really efficiently. Literature teachers could hand students novels with a set of keys to unlock them, and students would automatically walk away saying, 'oh, now I get it.' A world like this, would be a world like Neo's from The Matrix, where any given set of skills, such as martial arts, could simply be downloaded from a common source and uploaded into the brain.

The question then is whether it is possible to put our finger on that moment of learning, identify it, measure it, and implement it. Or does learning require unexplainable, intuitive 'leaps' that are impossible to define?

I think therefore I am... a student

In this knowledge game called ‘school’, where we are assessed on tests and have to fulfill requirements, we tend to lose sight of the bigger picture. We often forget to ask ourselves what the purpose of all this education is. Answers to this question can vary from personal development to social security. We hear students say that they need school to achieve what they want in their lives. ‘I need mathematics to understand engineering so that I can become an architect.’ However, in some cultures, education is not about personal ambitions but family status: ‘My father has me studying medicine,’ for example.

Then there is the view that we are, ‘just another brick in the wall.’ These Pink Floyd lyrics suggest that school is society’s conspiracy against individualism. ‘Hey teacher, leave them kids alone,’ they sing, implying that school gets in the way of learning. So which is it? Are these institutionalized years of our young adolescence a kind of cultural rite of passage that we must all endure, or are we freeing our minds through education?

To answer this, we have to go back in time to the Renaissance. After all, this was a period in history when the number of schools across Europe grew exponentially. Something curious was going on that made people want to hit the books. Besides being an age of enlightenment and scientific growth, artistic achievement and charting uncharted territory, philosophy took a great leap forward. A philosopher by the name of René Descartes was born in 1596. He would change the way people looked at themselves, nature and God. And perhaps his philosophy can still affect the way we look at education.

‘Cogito, ergo sum,’ he proclaimed. ‘I think therefore I am.’ This in itself might not seem revolutionary, but the path that led him to this conclusion was important. Until that period many philosophers felt there was little we could be certain of: our senses were not to be trusted, abstract reasoning led us to an intangible world, and worst of all, thoughts could not be measured, seen or weighed. Whereas other philosopher’s threw in the towel at this point, Descartes saw this as a perfect starting point. As cheeky as it may sound, he was reassured by man’s inability to be sure. We humans seem to doubt everything, which means we are thinking. We are thinking and reflecting on a different level than animals. And if we are thinking, doing abstract reasoning, and contemplating the pros and cons of nuclear war, then we must exist. This must be what defines our existence. ‘I think therefore I am.’

The attitude taken toward education, where school is a kind of good citizen producing factory, where kids go on the conveyor belt and are stamped into a mold, is a rather Dystopian view, because there is no room for critical thinking. Perhaps we should ask ourselves if it is possible for a student to go through high school, study medicine, and become a doctor without ever learning to think critically or be skeptical. If this were the case, then this doctor may indeed just be another brick in the wall (and I don’t know if I would want him operating on me). If this were the case, then his education would have been more of an indoctrination.

But is this scenario possible? To what degree are we being educated or indoctrinated at our schools today? Is learning 2+2=4 a form of indoctrination or education? Descartes would have been proud to see us question our education. We must constantly ask in order to be good students. We must constantly think in order to be.

The paradox of cartography and school

There is an episode of Joey where he realizes he's running late for a date because he didn't calculate the distance to the restaurant properly using a good, old-fashioned map. He states in desperation, 'why don't they make life size maps so you can see how far it is!' The audience laughs. The notion of a 1:1 scale map is simply absurd, which brings us to a paradoxical truth about maps, known as the 'paradox of cartography'. They must be imperfect in order to be useful. Let's briefly look at this basic map to illustrate the point:There are three major flaws (besides the absence of the antartic).

1. It's inaccurate. Greenland looks roughly the same size as Africa, whereas in actuality Africa is 14 time larger. This problem is due to projecting round objects on flat surfaces. That's why geographers prefer the 'peeled orange' map.
   
2. It's based on arbitrary convention. Is there a sign on planet Earth that says 'this side up'? What makes north north?
   
3. It's culturally biased. This is why those who live 'down under' appreciate a good upside-down projection of Earth, preferable with the page break in the middle of the Atlantic, not the Pacific Ocean, as opposed to the Euro-centric world view which we're all so accustomed to.
   

So many students respond to these flaws of archaic mapping by pointing out that we now live in a Google Earth age, where so much more accuracy and flexibility are available on your laptop or dashboard. But these modern inventions reveal the paradox of cartography even more. Do we want the most detailed satellite pictures at our fingertips when quickly glancing at the dashboard to find that darn address? No! Our minds cannot process complex images on the fly. We want a stylized, less accurate (or at least less exact) overview for this purpose. And so for every purpose a map serves, we find that it must be tweaked a bit to function optimally.

Now let's apply the paradox of cartography to school. Is it possible that school functions as a learning tool for how to deal with the 'real world' because it provides students with an imperfect environment? In what other place do you have to raise your hand before you're allowed to speak? Where else are you asked questions that the questioner already knows the answer to (besides in a place of interrogation)? In what other world are you rewarded with report cards? Sure, these procedures resemble the real world a little bit; in normal group conversation we shouldn't speak out of line, and at the end of an average month we receive pay slips (which may even reflect our recent performance). But in essence school is filled with conventions that inaccurately represent the life 'out there.' Furthermore, to find out how culturally biased a school is, all you have to do is talk to the foreign exchange students about their frustrations adjusting to the local school culture.

An interesting phenomenon that could support this analogy is that odd moment in the adult world, when getting involved in a heated debate with a large group of friends in the pub or at the coffee machine at work. We have a sudden urge to raise our hand to request a turn to talk. Everyone laughs. And here's another odd one: Some adults who graduated long ago will still say, 'I shouldn't make it too late, it's a school night,' when in fact they mean the following day is a work day. Why is this?

Before we accept the paradox of cartography as a good analogy for school, it is worthwhile to define the term 'imperfect'. If a school loses your transcripts as you're applying to university, do they have the right to say that their imperfection is the perfect preparation for the real world, where people lose things? Or should we look at the paradox the other way around? A teacher has done a very fair job of assessing the class's tests, with equal opportunities, a transparent point scheme, and well thought out criteria. Isn't his test a perfect imperfection because the world is hardly ever 'fair', 'equal', 'transparent' or 'well thought out'. Here the map has a guiding function.

Does the paradox of cartography show us how the imperfections of school life are actually perfect for young learners?

Is school a cave?

We all love to entertain the notion that our sense of reality is actually a dream. What’s to prevent us from believing that our ‘dreams’ are not actually reality? Who is to say that our brains are not just organs in a vat, receiving certain stimuli, convincing us that all these sensory perceptions are real?

This is the stuff of The Matrix or The Truman Show. Hollywood loves it and so do high school students. The idea is as old as the word ‘idea’ itself. 400 years before Christ, Plato accounted for this sense of another reality in his ‘Allegory of the Cave’. According to this view on reality, we are prisoners in a cave, looking at the shadows of puppets on the cave wall. That is to say everything we see around us is just a illusion. We may think we see trees and cats and BMWs, but in fact they are only shadows, projected by the light of a fire and some fancy puppeteers. Outside the cave are the true trees and cats and BMWs, or the pure ‘idea’ of these, which would hurt our eyes to look at.

Whether or not we should believe in this allegory is impossible to determine, but it does supply us with an interesting thought tool for looking at school. Have you ever felt like school is a cave? The students are the prisoners. The teachers (or puppeteers) project their lessons up on the blackboard, giving their version of the ‘truth’. And what is the fire they use to make students believe, or perhaps pay attention in class for that matter? Is it their charisma? Is it the notion of getting grades? And what about that exit door that leads to the light? Is that graduation? Is that what teachers are referring to when they tell students about life in ‘the real world’?

Is this allegory of the cave a fair analogy for school? Is school a cave?