Changing the Mathematics curriculum

[ThisCouldBeHeavn]

S1's AP stat was quite good and comprehensive. All must not be taught in the same way.

Probably true. Mine was an online class that stuck rigidly to the AP outline.

[marite]

VP"

That's the problem, isn't it? Students take classes they don't need or particularly enjoy because it will look good to admissions officers (who may not have taken the courses themselves--the mania for AP Calc is fairly recent). They could instead take courses they really enjoy and would be of use to them in college and thereafter.
Arthur Benjamin and others are trying to get colleges and high schools to think differently. Benjamin is very well known and respected, so perhaps he will be able to get his message across.

[chashaobao]

I watched the video again, more carefully this time. He did not directly attack arithmetic and algebra as I first thought. But based solely on this video clip, my opinion of the speaker remains the same.

Just listen to what was said: “If president Obama invited me to be the next czar of mathematics, then I would have a suggestion for him that I think would vastly improved the mathematics education in this country, and that it would be easy to implement and inexpensive.”

Haven’t we been down this road before, again and again? The New Math, the New New Math, and here comes the New New New Math. It sounds so eerily like the New Economy we had been promised, which led to dot com bubble and housing bubble.

But only if Prof. Benjamin had been our math czar, all these economic calamities would have been completely avoided. That’s right, all we needed was to teach statistics to every high school student. I didn’t make this up, this is what he said in the video: “… if our students, our high school students – if all the American citizens – knew about probability and statistics, we wouldn’t be in the economic mess that we’re in today.”

Really? I don’t know what teaching statistics will do for our national economy, but two of my close friends happen to be professors of statistics. From what I can tell, their investment portfolios and 401k/403b did not fair much better than that of the art history professors or the secretaries, their expertise in statistics notwithstanding.

I find the claim that statistics is more useful than calculus in daily lives somewhat amusing. Not that I have ever used calculus in my daily life, neither can I recall ever having a need to use Pythagorean theorem or to solve a quadratic equation. But I am also hard pressed to come up with a single daily situation (outside work) where I need to calculate a variance, do a t-test, or estimate the odds of getting hit by passing vehicles when I step onto the crosswalk.

I am all for teaching combinatorics/probability in high schools, but it requires a good grasp of algebra. And without learning calculus, a student won’t understand the underlining principles of statistics, simply memorizing a few formulas won’t help him/her to reliably apply statistics in real life situations. There have been too many examples of misuse of statistics, even in academia, because of the lack of understanding of statistics principles.

The ability to state the meaning of “two standard deviations from the means” without knowing how the result comes about isn’t any more impressive than the recitation of a few bible passages. It does not convey any deeper meaning that cannot be expressed using simple English language sans the jargons, nor does it required a whole semester or a whole year course. The numerous chance threads on CC show that students do not need AP statistics to understand the concept of randomness and odds.

Prof. Benjamin advocates a new “modern, discrete mathematics … of randomness, of data” as opposed to the “classical, continuous mathematics”. I don’t know what he exactly means, but it sounds like a frontal attack on the more traditional rigorous math education that includes the teaching of trigonometry and analytical geometry (pre-calculus). While these topics are important for learning calculus, they are indispensable for learning physics, which is a subject far more useful in our understanding of the world and our day to day lives than calculus AND statistics.

Prof. Benjamin proclaims “…the world has changed from analog to digital. And it’s time for our mathematics curriculum to change from analog to digital.” Ironically, the microprocessors that power our digital world are built from resistors, capacitors, and transistors, all of which are analog components. And statistics, the summit of this “digital mathematics curriculum”, is built on the foundation of calculus.

People who argue for more “useful” math subjects and against the more abstract and rigorous math curriculum that covers geometry proofs and conic sections have completely missed one of its most fundamental purposes. The abilities to deduce the similarity of two triangles or to figure out the trajectory of a thrown football are probably useless to most people. But the most important aspect of a rigorous math education is that it teaches abstract, rigorous, and logical reasoning, the power of induction and deduction, the frame of references, and the understanding that all conclusions/results reached depend on their initial conditions and constraints.

[dshinka]

Well analog is continuous and digital is discrete. I get what he's saying.

Continuous math courses deal with infinities - infinitely close, plotting curves with an infinite number of points between 0 and 1, etc. Discrete math courses deal with with finite math - generally integers but basically things that are rational and nowhere near transcendental.

While it's true that electronics appear to be continuous they act as discrete. They're either on, or off, even though on has varying degrees of on and sometimes can be misread (very very rarely).

But discrete vs. continuous is an old, old debate. The Greeks questioned whether or not one could infinitely divide up stuff or not - if one could, then the universe is continuous. If there was a smallest something - whether it be water, air or the "infinite", then the universe is discrete. Thousands of years later, quantum physics thinks of the world as discrete, but relativity thinks of the world as smooth, continuous and geometric.

I think that too much importance is given to continuous math in grades K-12 - I personally dislike discrete math and probability and statistics but I certainly agree that we stress continuous math too much and should cover: discrete, combinatorics and ESPECIALLY logic.