In the morning, rather than doing a train switch to my bus stop, I walk the extra two blocks from where the Red Line leaves off. It is uphill, and with my backpack it provides a good workout.
In both cases, I could travel the extra distance by car or train, but I am choosing to hoof it instead. I am about to turn 43, and I am not getting any thinner. It is quicker and easier to travel by motorized wheel, but I need to burn the calories. My hobbies are all rather sedentary, so I take the movement where I can get it.
I was considering this as I was in my Math Assessment class tonight. So often in our schools, we encourage kids to pull out the calculator. It is faster, less tedious, and more accurate. Add a couple of parents recounting their difficulties in math at a school board meeting, and suddenly the little keypads are getting worked in everywhere.
Here is the problem though:
Wall-E.
You know, the prophetic movie where in the future all humans are obese and cannot hold a coherent thought past the next 5 seconds?
Everything we do seems to be about making things easier. We will loop the parking lot 5 times to get four spaces closer. God forbid we walk that extra 50 feet.
Our bodies are getting soft, and so are our minds... because we keep looking for short cuts and leisure. Contrast that with JFK's attitude that it is the difficulty that makes something worth doing.
We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too. ~ President Kennedy
2 comments:
I love math. I am studying to be an astronomer and learning advanced mathematics is essential. You cannot do any science with math.
As you pointed out, calculators are a short cut. They makes things easy. In the long run, however, they can actually make things harder. While learning how to use a calculator well might get you through all your math classes until you graduate high school, if you are planning on any career which requires knowledge of advanced mathematics (calculus and beyond), over-reliance on a calculator will cripple you.
I have studied differential, integral, and multivariable calculus, linear algebra, and ordinary and partial differential equations, all of which I found difficult, despite having some natural talent at math. Even worse are the complex derivations of custom formulas I have had to do in my advanced physics and astronomy classes.
Unless you are willing to shell out hundreds of dollars, calculators cannot solve problems in these branches of math. You're on your own. Even if you did buy one of the super expensive advanced calculators, they can only take you so far. At the end, you are once again on your own.
A major problem I have observed is that people who have become completely dependent on calculators really struggle in advanced math and science classes. They might have passed their high school math classes, but since they used the calculator for everything, they did not actually understand the concepts behind the math.
I'm not saying calculators are all bad. I myself have a nice graphing calculator and I use it to check my work, draw three dimensional graphs (as I cannot picture them in my head) and do the tedious arithmetic (addition, subtraction, multiplication, division) which can sometimes be found in advanced math problems (especially in Linear Algebra) and where it is very easy to make a mistake.
Everything I do on a calculator is something I know I can do on my own. I use it as a tool, not as a crutch.
I think JFK said it perfectly. The challenge is what makes something worth doing. I love coming up against a difficult math problem that takes hours to solve because, once I do finally solve it, I have a sense of accomplishment. Sometimes shortcuts are helpful or necessary. But, if we get over-reliant on them, our bodies and minds get soft and we lose the joy of accomplishing something ourselves.
I agree Sammy. Calculators should let you do faster what you can already do... not bridge what one can't do.
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