Back when I was in school we spent quite a bit of time drilling our multiplication tables. We learned long division. There were no calculators allowed in the classroom. You didn't come across any touchy-feely word problems. The teachers' goals weren't to massage our egos and pump up our self-esteem and feelings of self-worth. The name of the game was mathematics.
Today, of course, we couldn't possibly allow our children to have to figure out how to multiply or divide on paper. None of that moving the decimal point to the left. Forget about carrying over. Today's generation was raised on computers and that's what they'll be using the rest of their lives. Pencils and paper - that's so yesterday.
Really?
The other day I was in a rush when I went to Staples to pick up some file boxes. I thought I was grabbing what I needed - until I got back to the office and realized I got the wrong size. So, the next day I headed back with my boxes and my receipt so I could exchange them for the right sized boxes.
I headed back to the corner of the store and found what I needed. Then it was back to the register.
The boxes I bought the day before were $18.99. I had my Staples' reward coupon and I ended up paying about $10. The boxes I meant to buy cost $19.99. I would owe a shade over a dollar (with tax).
Imagine my surprise when the cashier (or whatever they call them over there) told me I owed almost $10. I told him the boxes I was bringing back only cost a dollar less than what I had in hand. I told him to look at my receipt. I told him I shouldn't owe but a little more than a dollar.
He tried to explain how I owed $10. So I asked him about the coupon I used the day before. I asked him if it had just vanished into thin air. He kept trying to explain to me that I owed a lot more money for the boxes.
He had absolutely no clue as to what he was doing. He was so used to scanning items at the register that he had lost the ability to do the most rudimentary math. He had lost the ability to think logically. He looked at me like I didn't know what I was talking about.
Then it struck me how when we rely on an electronic device to do our math for us that we divorce ourselves from the numbers themselves. The numbers no longer represent sets of objects and relationships. They're just blips on a screen. And when we become dependent on those blips we somehow lose the ability to know how to deal with a curveball when it's thrown our way.
Learning multiplication tables and long division can be awfully hard. It can be awfully boring. In our short attention span culture it's just not the way we do things. Kids sometimes have a hard time grasping the concepts. They might get red marks on their papers.
But they might just learn that math is more than numbers.
And these folks are going to be in your jury panel the next time you stand up to begin your voir dire. Scary, huh?
UPDATE: I went back to Staples today after leaving the courthouse and the cashier manning the booth today knew exactly what to do. I walked out with my new boxes after paying $1.08 extra.
Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts
Friday, September 7, 2012
Tuesday, August 14, 2012
In defense of learning
About two weeks ago, Scott Greenfield penned a wonderful essay in defense of algebra. His post was in response to an op/ed in the New York Times proclaiming there was no longer any reason to teach school children higher level math.
Now I wasn't the biggest fan of algebra, trigonometry and calculus when I was in high school. I got off on the wrong foot with algebra in middle school and struggled to catch up. I was quite happy at UT when I finished the one and only calculus class I had to take.
Of course now I lament my lack of knowledge about higher level math. After reading about chaos theory and economic theory I wish I had a more solid background in math. But, such is life.
Just the other day I saw a piece on NPR's website that seemed quite appropriate given the subject matter in Simple Justice. The thrust of the article was whether the piss poor job we're doing teaching our children proper grammar is ruining the English language.
The article seemed to take the side of the squishy academics who preach the whole word method and other ways of teaching language that don't require the rigid adherence to rules. And, in the long run, the lack of fundamental grammar knowledge isn't the death knell of the language - we can still understand what our children are saying even when they are too young to know the rules of construction. But there is a more fundamental issue at stake - and it's an issue that spans the gap between language and math.
Algebra and calculus teach us different ways to look at numbers and at the world around us. They take our concept of numbers as concrete objects and force us to think of numbers as concepts. We are taught various theorems and postulates that we piece together as syllogisms. It's a language all its own.
But learning that language teaches us how to analyze other concepts critically and logically. We learn how to put together arguments to support our hypotheses.
I think we would all agree that it takes a certain level of intelligence to be able to work through differential equations and conduct a regression analysis - but those topics don't usually come up during an ordinary day. The way a person speaks, however, does make an impression.
When someone makes a glaring grammatical error it just grates on the ears. When someone says "myself" instead of "me" it makes me want to scream. When I go back and reread a brief or a motion I end up trying to get rid of all the split infinitives.
How ironic it is that non-native English speakers can actually speak the language better than those of us who grew up in these United States.
These arguments against teaching higher level math and good grammar are emblematic of a deeper theoretical war. What is the purpose of education? Do our schools and universities exist to train people to earn a living as adults or do they exist to teach us how to learn and how to think critically? And what on earth is the problem of learning solely for the sake of learning? Does everything we do have to be with some end in mind?
Which brings me to one of Mr. Greenfield's pet peeves - the world of the lawprof. Yes, our law schools don't prepare students for the day-to-day reality of the practice of law. Yes, the tuition charged at most schools is beyond ridiculous. But the purpose of law school is to teach aspiring young lawyers how to think like lawyers, to provide young lawyers with a theoretical framework with which to view the world.
In the old days aspiring lawyers read the law under the tutelage of an experienced lawyer. They read treatises on evidence and property and whatever else was in the law library. They learned the theory so they could sit for the bar. At the same time they learned what a lawyer does and how to do it from their tutor.
That is the failing with our system of legal education today. But let's not get all utilitarian and turn law schools into vocational schools. And let's not turn our elementary and secondary schools into programs that do nothing more than train young people to sit behind a desk and do what they're told to do.
Now I wasn't the biggest fan of algebra, trigonometry and calculus when I was in high school. I got off on the wrong foot with algebra in middle school and struggled to catch up. I was quite happy at UT when I finished the one and only calculus class I had to take.
Of course now I lament my lack of knowledge about higher level math. After reading about chaos theory and economic theory I wish I had a more solid background in math. But, such is life.
Just the other day I saw a piece on NPR's website that seemed quite appropriate given the subject matter in Simple Justice. The thrust of the article was whether the piss poor job we're doing teaching our children proper grammar is ruining the English language.
The article seemed to take the side of the squishy academics who preach the whole word method and other ways of teaching language that don't require the rigid adherence to rules. And, in the long run, the lack of fundamental grammar knowledge isn't the death knell of the language - we can still understand what our children are saying even when they are too young to know the rules of construction. But there is a more fundamental issue at stake - and it's an issue that spans the gap between language and math.
Algebra and calculus teach us different ways to look at numbers and at the world around us. They take our concept of numbers as concrete objects and force us to think of numbers as concepts. We are taught various theorems and postulates that we piece together as syllogisms. It's a language all its own.
But learning that language teaches us how to analyze other concepts critically and logically. We learn how to put together arguments to support our hypotheses.
I think we would all agree that it takes a certain level of intelligence to be able to work through differential equations and conduct a regression analysis - but those topics don't usually come up during an ordinary day. The way a person speaks, however, does make an impression.
When someone makes a glaring grammatical error it just grates on the ears. When someone says "myself" instead of "me" it makes me want to scream. When I go back and reread a brief or a motion I end up trying to get rid of all the split infinitives.
How ironic it is that non-native English speakers can actually speak the language better than those of us who grew up in these United States.
These arguments against teaching higher level math and good grammar are emblematic of a deeper theoretical war. What is the purpose of education? Do our schools and universities exist to train people to earn a living as adults or do they exist to teach us how to learn and how to think critically? And what on earth is the problem of learning solely for the sake of learning? Does everything we do have to be with some end in mind?
Which brings me to one of Mr. Greenfield's pet peeves - the world of the lawprof. Yes, our law schools don't prepare students for the day-to-day reality of the practice of law. Yes, the tuition charged at most schools is beyond ridiculous. But the purpose of law school is to teach aspiring young lawyers how to think like lawyers, to provide young lawyers with a theoretical framework with which to view the world.
In the old days aspiring lawyers read the law under the tutelage of an experienced lawyer. They read treatises on evidence and property and whatever else was in the law library. They learned the theory so they could sit for the bar. At the same time they learned what a lawyer does and how to do it from their tutor.
That is the failing with our system of legal education today. But let's not get all utilitarian and turn law schools into vocational schools. And let's not turn our elementary and secondary schools into programs that do nothing more than train young people to sit behind a desk and do what they're told to do.
Wednesday, September 2, 2009
Math, Texans-style
Over the offseason the braintrust behind the Houston Texans decided that it would be a good idea in these hard economic times to reduce the size of the beer cups at Reliant Stadium from 24 ounces to 20 ounces while leaving the price of foamy adult beverages at $7.75.
Fans of the Texans were outraged at this egregious attempt to gouge them - nevermind they were being robbed in the first place. Hey! Where's the district attorney when you need them? Forget about this DIVERT stuff -- what about Beergate?
As a result of the fans' adverse reaction to this little ploy, the Texans' braintrust (I'm sorry, but I'm a big fan of oxymorons) decided they would reduce the price of beer at the stadium to $7. Unfortunately, their planned pacification of the masses will only work on those who are just a bit challenged in the field of mathematics.
While it might be seen as a good gesture, the reality of the situation is that the size of beer cups has been reduced by 16% but the price of beer has only been reduced by a tick under 10%. So you see, friends and Cowboys fans, that the beer-drinking public is still getting it handed to them - only not as blatantly.
Is this the way to treat your (blindly loyal) fans? I mean, let's face it, it's damn near impossible to watch the (painfully boring) Texans without copious amounts of alcohol.
Subscribe to:
Posts (Atom)