Posted on 08/08/2012 4:34:06 AM PDT by SeekAndFind
America has a math problem. We've had a math problem for at least fifty years - since the Soviets launched Sputnik, if not before. Our high school students have trouble competing with those raised in considerably poorer nations, and we aren't producing enough talented scientists and engineers to ensure our nation a leadership position in the twenty-first century knowledge economy.
If you think about it the right way, that's not just one math problem - it's two. You might think of improving math skills of both "average" students and the nation's top students as two birds that could be killed with one stone. But they aren't - in fact, some of the easiest ways to solve one problem make the other one worse. Our failure to recognize the distinction between these two problems helps explain why we've managed to spend so much time worrying about math in this country without ever improving the situation.
The tragedy of American mathematics can be told through the history of a single course: algebra. Two generations ago, algebra was a course reserved for elite students - perhaps the top 10%. It was taught exclusively in high school. The educators who designed the curriculum saw little point in teaching the abstract subject to students destined for careers in manual labor. A large proportion of those students who took the course would go on to use math in their careers: among male college students who graduated in the 1940s, for example, about 3 in 10 majored in a mathematically intense subject.
The pragmatic attitude towards mathematics for the masses gave way in the post-World War II era. Successive waves of curricular reforms sought to improve the mathematical skills of ordinary students. The "New Math" movement of the 1950s and early ‘60s tried to beef up the curriculum for all students, with disastrous results. By steering the curriculum away from practical application to a focus on fundamentals, new math managed to turn a generation of students off from math. Male college graduates raised in the new math era chose math-intensive majors at a rate of 20% -- down a third relative to the prior generation.
The new math movement waned, but an intense interest in improving the math performance of ordinary students persisted for more than a generation, culminating in the "No Child Left Behind" movement of the past decade. We now instruct our schools to prioritize the performance of the worst students, and impose no penalty if they neglect their top achievers in the process. Recent studies have confirmed that schools respond to these incentives.
Today, algebra is considered a "gateway" course seen as the most critical step toward college-readiness, rather than an abstract course useful only to a select few. About one-third of American students take algebra as eighth graders. In some states, more than half of all students take algebra in middle school. A few years ago, the California State Board of Education attempted to mandate that all students take algebra in eighth grade. Proponents of early algebra point out that students who complete the course at an earlier age are more likely to do all sorts of wonderful things later in their lives. While this observation is true, it best serves to illustrate the difference between correlations and cause-and-effect relationships. Presumably, the students who take algebra at a young age were precocious even before they took the course - that's how they ended up there in the first place.
Unfortunately, the misguided transformation of algebra into a course for the masses has proven to be a cure worse than the disease. The transformation has resulted in a less rigorous course. Introductory textbooks have slimmed down considerably over the past century, omitting some subjects entirely. The primary victims of this dumbing-down are the elite students themselves. Among the most recent cohorts of college graduates, the proportion of male students majoring in math-intensive subjects has continued to hover in the 20% range. If we compare this to the historical 30% rate of two generations ago, we lose about 100,000 mathematicians, scientists, and engineers every year - enough to replace every American employee of both Microsoft and Google and still have tens of thousands to spare.
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I, too, possess a copy of that book. I acquired it back in the eighties, faced with an interesting problem in database marketing. We had a list of several million consumers who were good prospects of our client, who had a network of retail outlets. The idea was, let's send out computer letters to the consumers, informing them where the nearest outlets were. But that would have needed a table of nearest stores by zipcode. Which we didn't have.
However, someone on our team latched onto a database linking five-digit zip codes to latitude / longitude pairs (trivial in the Google age, but required connections of the non-ISP variety in the eighties). Obviously, the answer was to compile a list of nearest stores based on zipcode and use that. Simple: just calculate the distance from the customer's zip to the nearest outlets' by zip. That's where Bowditch (and the IBM 360 floating point instruction set and Fortran 4H libraries) came in (with some assembly language trig simplifications in the interest of computational efficiency).
Of course, it didn't work out too well. Some of the results were positively embarrassing. E.g., folks on Long Island needed boats to reach those near stores in Connecticut. But, for most of the country, it was fine, and the marketing campaign was judged successful.
You never know when you're going to need a new skill. The trick is to know when you need a new skill and to have what it takes to add the skill to yourself or buy it from whomever (the judgement between those two choices being yet another skill, LOL).
>> Nope, not in the software industry.
That’s funny given all the symbols, statements, and functions.
That’s funny given all the symbols, statements, and functions.
It depends on what you do. If you are working on top of the stack building web pages or user interfaces, he's mostly right. If you are further down in the stack developing interfaces or function libraries, less so. And if you are programming at the base you must live and breathe higher math. I spend my time in the middle writing stored procedures and data mining functions. The math is frequently challenging.
Are they hiring at your concrete batch plant? My husband was a foreman for wetcast and drycast; form construction, reading blueprints, the fineries of concrete—until the worldwide company got smart and closed their plant in upstate NY. He left about a year before they closed for good and is now doing HVAC.
I think there are two kinds of people in the world - those who like algebra and those who like geometry.
I loved algebra. Loved doing the homework. It was so much fun. Geometry on the other hand I didn’t like. It seemed to me all about putting numbers into formulas. Very boring but probably useful if you’re going to sell carpet for a living.
I have never used geometry since high school. I use algebra every day.
I just went to my mailbox and found an article that’s relevant to this discussion.
Here is a link to the article: http://www.mauldineconomics.com/frontlinethoughts/where-will-the-jobs-come-from
John Mauldin writes some interesting articles.
When I took algebra I hated the “mixture” problems. That is, combining various materials to achieve the right mixture at the optimal price. I got out of school and then spent the next 7 years doing those. Ouch.
We are seasonally shutting down in a week or two, and will open back up for a limted basis after the first of the year. The season for us here in Alaska usually starts in may until november.
The US Department of Education has said that it is a violation of civil rights to divide students according to abilities. Seriously.
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