Saturday, April 26, 2008
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.
Friday, April 4, 2008
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?