Orangpples

Today I went to help an 8^th grader with his math assignment. He had to use a compass and straight edge to make angle bisectors, perpendicular bisectors, altitudes, and midpoint lines on triangles making inscribed and circumscribed circles. I was excited since I had loved doing this exact same stuff way back in 9^th grade. Unfortunately it turned out to be a much more painful process than I ever could have imagined. We would read the instructions in the book on how to bisect an angle but then when I drew an angle and asked him to bisect it he had no idea where to start. I then demonstrated how to do it; pointing out how each action corresponded to the instruction in the book which he had read and then drew another angle and ask him to bisect it. Still no idea where to start. I would literally have to hold his hand and place the compass in the correct spot and if I didn’t tell him which direction he needed to go, he’d go the wrong way (mysteriously way more than half the time) and have to make an entire circle before getting to the right spot when all that was needed was a small mark in the opposite direction. And after doing three angles like this I expected him to be able to do one on his own. Nope no success. Still no idea where to start, though this time he did understand that he was supposed to draw arcs on the paper and did so at random points along the line.

I don’t want to put to much blame on this one kid for I could go on and on describing similar anecdotes from the last several months. The 12^th grader who had to make chicken scratches for 3×3, the blank stares I got today when asking what the x and y coordinates of a point were (they were (1,0) and the point was on the unit circle and the students were supposed to graph cos(θ)), the total inability to pick any meaning out of word problem unless I explicitly explain it. The level of mathematical literacy is so frustrating below the level of understanding the curriculum requests that it makes me slightly mad just to think about it. I’ve decided to make it my battle for the next 18 months to do my part in helping improve mathematical understanding, intuition, and problem solving at all grade levels. I feel that math is a good thing to pick because you can do it with out any fancy equipment, the critical thinking skills required to solve math problems can be translated to other areas of school as well as life, and math is easy to teach because it has concrete principles that you can fall back on (remember those chicken scratches to multiply). I have lots of great ideas on how to do that, but nothing that is making any progress as of the moment. I hope in the next few months to have something productive started with that regard.

But none of that is what I’ve been thinking about tonight. While I was watching this kid attempt to bisect an angle and find the midpoints of lines I started thinking how the Ancient Greeks could make regular pentagons with just a straight edge and ruler over 2,500 years and yet this kid was struggling with something so much simpler. At the same time, several times while helping him I saw him pull out a cell phone capable of 3G data access. The juxtaposition of those two events really got me thinking that not much about human cognition or intelligence has really changed since the dawning of civilization. The simple key to all the great successes we credit to the human mind is a memory of what came before and the ingenuity to go further. In the 12^th century Bernard of Chartres wrote

We are like dwarfs on the shoulders of giants, so that we can see more than they, and things at a greater distance, not by virtue of any sharpness of sight on our part, or any physical distinction, but because we are carried high and raised up by their giant size

Just think how much the collective human mind has created, invented and discovered in the 9 centuries since that was written. Just think how much its done in the last century alone. Just think how much has happened in my short life time of 22 years. The computer world has a very famous axiom of growth first quantified by Intel co-founder Gordon Moore in the mid 1960’s which basically states that the number of transistors that can economically be placed on an integrated circuit grows exponential to time – double approximately every two years to be moore exact. Such exponential growth is only made possible because each generation of integrated circuit stands on the shoulders of the last. And this analogy can be extended to technological change anywhere and at anytime because one change leads to two more changes which lead to four more changes ad infinitum. The whole process is due to the fact that knowledge does not have to be reinvented and each generation sits upon the mighty progress of the last. It is interesting to observe the effects of that cycle being broken as happened in South Africa during the years of Apartheid. How it only takes a few generations of cruelty, hatred and fear for a society to lose its collective conscience and how hard it is to restart the engines of human creativity, inspiration and ingenuity as this countries school system has been trying to do virtually over night.

I think its also important to note that the only thing that has changed in the last 5000 years is the amount of collective knowledge and technological prowess. I doubt the basic intelligence of the average human has changed very much in the last 3000 years. Our capacity to feel and be loved hasn’t grown in the last 2000 years. The desires and needs of a new born infant are still almost the same as they must have been a few million years ago. So while technological change is exponential biological change is relatively constant. This is why technology without foresight and vision is so dangerous. Technology breaks barriers. It shortens time and distance. It is the great instant pill reducing the amount of physical labor necessary to live. But its also blind. The chain saw doesn’t care if it cuts down every tree. The TV doesn’t care if it shows WWE or Sesame Street to a generation of South African kids. The cell phone doesn’t care if its used as the detonating device in a large bomb or to call 911 once the bomb explodes.

We are basically large apes running really fast to change the world but staying in the someplace because we can’t change ourselves.

“Well, in our country,” said Alice, still panting a little, “you’d generally get to somewhere else — if you run very fast for a long time, as we’ve been doing.”

“A slow sort of country!” said the Queen. “Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!”

We are like the Red Queen in Through The Looking Glass and the only solution we can think of is to run faster, when maybe the right choice is to slow down and make sure we’re not running in circles. Its easy to change the world with our technology but much much harder to change ourselves so we can use it efficiently, effectively and ethically.

Its interesting the places you mind can go when set out to help an 8^th grade student with maths. Just imagine all the places it can go when you set out to explore the world.