The article states:
A TYPICAL American school day finds some six million high
school students and two million college freshmen struggling with algebra. In
both high school and college, all too many students are expected to fail. Why
do we subject American students to this ordeal? I’ve found myself moving toward
the strong view that we shouldn’t.
Now, a word of history. When I first took algebra in the 9th
grade, some 60 years ago or more, I frankly did not do that well. I had no idea
what my tutor was saying and frankly I suspect neither did he. Geometry fared
slightly better. But between reading Men of Mathematics at the end of my sophomore
year and intermediate algebra I saw all the pieces come together, thus managing
to complete that and trig in some six weeks, then onto advanced algebra,
calculus, probability and even solid geometry. I may have actually been the
last student to take the solid geometry Regents exam in New York State.
Now that some sixty plus years later my two grandsons take
algebra in the eighth grade. Now that is a year earlier, and the one in New
York already has his Regents prep book.
“Struggling”, well yes if your instructor does not have a
clue and you are being taught by rote. But “subject” is a rather strong word.
In fact it is reflective of the arrogance of the ignorant. If you cannot do it
then it must be undoable. I cannot learn Czech, no problem with Russian, and I
lived in Prague, it was just that no matter how I tried it never stuck. Same
for Portuguese, but no problem with Spanish. That is my problem not a reason to
doing away with two countries.
The author continues:
This debate matters. Making mathematics mandatory
prevents us from discovering and developing young talent. In the interest of
maintaining rigor, we’re actually depleting our pool of brainpower. I say this
as a writer and social scientist whose work relies heavily on the use of
numbers. My aim is not to spare students from a difficult subject, but to call
attention to the real problems we are causing by misdirecting precious
resources.
To be educated means that one has a minimal set of skills.
Making change, understanding data, taking measurements, predicting the future.
So take global warming. This can be examined by a simple look at data. I have
data for certain daylily species going back 30 years. The date of the first
bloom is measured and then I plot that data on a graph. Now I seek to get a
simple linear regression on the days from the first of the year that the first
bloom occurs. I use a linear regression and plot the data. The result, warming!
Voila. But that simple step assumes a de minimus level of understanding of
algebra. Not much, really! But some, and if we want informed decisions rather
than just religious followings then we need an educated electorate, at least
some of them.
Or take ratios, for example, the cost per unit, the price
per unit, etc. We then look at multiples of these ratios to get other ratios. People
use these all the time. They rely on algebra.
But on the other hand many people are just dumb. Why waste
any time and money at all. So we can avoid wasting resources by just not
educating them at all. Then we can have a dual class society, the dumb ones
without jobs, and the educated ones supporting everybody!
The write continues:
California’s two university systems, for instance,
consider applications only from students who have taken three years of
mathematics and in that way exclude many applicants who might excel in fields
like art or history. Community college students face an equally prohibitive
mathematics wall. A study of two-year schools found that fewer than a quarter
of their entrants passed the algebra classes they were required to take.
It is a University, you are hopefully expected to be
educated, and that means mathematics. If an eighth grader can learn this in New
York and West Virginia, what is wrong with students elsewhere. Consider the
draftee in WW II. The Navy had a problem, it needed students who understood
math quite well. Torpedoes, 6” guns, radar, radio, fire control systems, and the
like demanded algebra and geometry and trigonometry. Many draftees had it and
thus it opened their career path after the War. Those who did not were just
seamen, doomed to stay below petty officer rated sailors. The officers,
including those with history degrees had to have even more.
As for high Math SAT scores, there is the old MIT tale,
somewhat true, when the Freshman Calculus instructor states:, “Well you all got
800 in your SATs, but you still have to earn you’re A here.”. The response to
this was to look around at the 100 or so students and think that all 800s were
here. Then the Instructor noted, “Oh, the other 100 are at Cal Tech.”
Even jobs such as an electrician or carpenter require a modicum of algebra and geometry. The thought process is essential. Trade schools teach algebra, geometry, otherwise getting licensed to practice one's trade would be impossible. Ohms law and Pythagoras' triangle would be a sine qua non. Understanding nature is predicated on measuring and predicting, in reality. Is algebra too hard, possibly with the wrong teacher, I had one. But with the right teachers it provides insight. Perhaps the problem is our educational system.
The again the world uses spreadsheets, all the time, from budgets to understanding any business structure. What is a spread sheet, a set of algebraic instructions, unless of course you use it just for entering numbers. But to learn one needs understanding of relationships. That is algebra. Word problems must become visceral, one must "feel" the system, understand the implications. If one thing gets larger does the other thing get larger or smaller, and how quickly. Judgement results.
Even jobs such as an electrician or carpenter require a modicum of algebra and geometry. The thought process is essential. Trade schools teach algebra, geometry, otherwise getting licensed to practice one's trade would be impossible. Ohms law and Pythagoras' triangle would be a sine qua non. Understanding nature is predicated on measuring and predicting, in reality. Is algebra too hard, possibly with the wrong teacher, I had one. But with the right teachers it provides insight. Perhaps the problem is our educational system.
The again the world uses spreadsheets, all the time, from budgets to understanding any business structure. What is a spread sheet, a set of algebraic instructions, unless of course you use it just for entering numbers. But to learn one needs understanding of relationships. That is algebra. Word problems must become visceral, one must "feel" the system, understand the implications. If one thing gets larger does the other thing get larger or smaller, and how quickly. Judgement results.
In today’s world we would have to add all the IITs in India,
and Tsing Hua in Beijing for starters. And by the way, how many historians do we
really need?
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