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Day’s Verses:
Your boasting is not good. Don’t you know that a little yeast works through the whole batch of dough? Get rid of the old yeast that you may be a new batch without yeast–as you really are.
1 Cor. 5:6-7
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Teaching summer school keeps me modest; the constant act of balancing what I know and what they ask— two rarely-congruent situations — forces me to occasionally honestly reply, “You know, I’m not sure about that.” Which is very humbling, since these kids were born in 1990 and have had at least six years less schooling than I have. Age doesn’t mean that they cannot ask perceptive questions occasionally—something of a gem in the rough situation, since the vast majority of their questions run along the lines of, “I don’t get this,” with “this” referring to a question of this type: “Simplify (2(a^6)b)/(4(a^2)b^3)” or “For all a ? 0, what does the graph of ax^2+bx+c look like?” Worse still, I want to smack somebody in the head when they don’t know how to solve such algebraic equations as 30x+15 = 10x – 5. Come on, people! You can’t subtract the 10 from the x because it’s “attached by multiplication.” I say that at least five times a day, often more. Enough venting. God is good, providing us with a condo right near BCS to stay in, with money to buy fresh half-flats of raspberries from a farmer’s across the street, with warm lazy summer afternoons to doze and pet the dog in. Every morning we wake up with the sun shining through the kitchen window and enjoy the fact that we’re not sleeping on the floor. We have access to big TVs, a car, and plentiful food, as well as loving family and friends. We attend schools in America, land of excellent (if expensive) educations. I could go on and on, but the point is: if many of my comments are complaining, they aren’t the full spectrum of life. I doubt there’s anybody who reads this blog who truly has more to complain about than offer thanks for. We live in America, land of the free and home of the brave; though we all complain about our country’s leaders and its policies, who among us would give up the blessings that come with an American citizenship?
I think that greed, like the yeast in today’s verse, has insinuated its way into American culture until we cannot but gripe about the hardships we “endure”—if indeed endurance even need be applied to our troubles. We don’t starve or freeze to death, our physical needs are over-abundantly met, we pay less for gas than nearly anybody in the world, we enjoy some of the world’s finest technology at great prices… Maybe it’s time to get rid of the easily-accepted “I Deserve All” mindset and give thanks for what we’ve been given—everything.
– KF –
I totally hear you on the feeling incompetent thing w/ teaching. I TAed this last year in the intro Bio classes, and there were definatly times when they asked me Q’s that I had no idea about. It can get to feeling pretty stupifying. And I agree about our complaining attitude. We have this idea that we are “entitled” to things here in America, that we have these things called “rights,” which very often are more illusion of rights than actual rights in the pure sense of the word.
Remind your students that there are so many worse algebras they could be working inside of, where ax^2 + bx + c looks like roadkill, and the answer to 20x = -20 is garbage. Then they’ll realize how silly they are being and instantly see their work as easy.
I don’t think math is being taught well much anymore. It’s about memorizing rules and facts and learning about this mystical world called math. It’s really just about learning about things that make sense, you just hadn’t thought about it in that way or that abstractly before. If kids took the time to think about what 2 step algebra really means in real life and what the concept actually is, it’d be easy to realize why the 10 and the x are “attached” and need to be dealt with as one. It’s all common sense dressed up in the cult of mathematics textbooks.
And while I’m on the subject, isn’t math nowadays a big old pyramid scheme? I’m sure John could inform me differently, but right now my ignorant opinion is that you go into math to become a math professor who teaches other people how to become math professors. I’d like to meet the Mathmaster general who’s running this joint.
I’ve started trying to address their questions in terms of real-life experiences they might have had (ie, relating rates, distance, and time by asking “If you’re going 20 mph for 2 hours, how far have you driven?” then asking them to explain how they got 40 miles). I challenge you to think of a real-life situation that could be used to explain why polynomials should be listed in a certain order (biggest exponents first), or what (120x^5)/(60x^3) means.
I’m not going to disagree with Klon; to a certain extent that pyramid scheme is what it’s all about. Ignorant? No way. There are the basics to be learned in any subject, so in that respect, (to pick English as an example) every english professor is teaching the same base stuff to every other one, in preperation for them to pass this onward to their own students, until the end of people (or English!). But, there’s more to English than just the basics, or else every writer would be constructing the same work over and over. There is a personal element everyone brings to their art. This personal element isn’t very easy to see within the very very finite, logical bounds of theoretical mathematics, because those personal creations are a part of the basics as soon as they’re founded.
George Boole creates the Boolean algebra, and now there isn’t a computer scientist without the fundamental knowlege of the subject. It’s all pretty and stuff, and I admit makes a whole lota sense, but one guy had to sit down and actually say “here are the rules, here’s how it works, which comes from what we know already”, and nobody had done this before him. I think that’s as close as anybody gets, here: the tools are always there, but somebody must formulate them into creation (and then get their names be mentioned forever to bored schoolchildren). Somebody has to take the string and the pole, and create the bow.
But are those personal elements ever as strong as the styles of Shakespeare or Aristotle or Da Vinci or others? Nope, there’s no means of making mathematics “personal”. Two people can devise the same theory simultaneously (Newton, Leibniz, and calculus), and yet they’re fundamentally the same. Would two people told to paint a picture of a single object generate the same exact creation? Unlikely. Would two people asked to write about a subject, generate the same exact piece? Impossible. Would two people, given a, b, and c of a quadratic, generate the same (or equivalent) formula for finding the roots of x? They had better!
Mathematics = creations without opportunity of creativity??? Can’t say. I know that math wouldn’t be math if we all didn’t see the world the same way, but art is art because we all see the world differently.
Paul Erdös once said “A mathematician is a machine for turning coffee into theorems.” A machine with no room for creativity, it seems.
The question lends itself to the concept of mythos (versus logos), that the overall base knowlege of mankind is growing, keeping people, who are born not knowning more than a neanderthal, out of the stone age. What is common sense to ourselves, may not have been to even our past generation, let alone those several centuries past. The Copernican Revolution is the classic example.