Changing the Mathematics curriculum

[BP-TheGuy88]

Arthur Benjamin's formula for changing math education:
Arthur Benjamin's formula for changing math education | Video on TED.com

Good short video. The guy says that currently the math curriculum builds up to calculus, but that it should in fact build up to statistics/probability. The reason being that calculus rarely has everyday use application whereas statistics/probability can be used every day. I thought it was interesting. In a class I took this past semester, my professor had this reading which said that humans in general are naturally just poor statisticians, and he's right. I wouldn't even consider myself to be a good one, though I understand certain basic concepts. But it is a tough thing to comprehend initially and maybe it's because it isn't thought enough at school. What do you guys think?

[chashaobao]

Is this guy really a professor of mathematics?

He sounded so much like guys on late night TV hawking detergents and cookware, but that would be an insult to the infomercial guys. Those other guys at least sell things that could be useful to some people, if at inflated prices. This guy is just full of hot air and harmful ideas.

He claims that our math curriculum is too focused on arithmetic and algebra and we should teach probability and statistics instead.

There is nothing wrong with teaching games and rudimentary game theory to high school or even elementary school students, some of the concepts are easily understandable. But how can a student have a good appreciation of the fundamentals of probability without a solid foundation in algebra? And to truly understand statistics, one has to have a good knowledge of calculus.

The problem with our math curriculum is not too much arithmetic and algebra being taught but rather that the curriculum allows too many of our students to be so poorly trained in the very basics of mathematics: arithmetic, geometry, and algebra, which prevents them to successfully move on to more advanced subjects such as trigonometry, probability, etc. Many studies have shown that U.S. students (including many of our best students) are woefully behind our competitors in math education.

Let me give an example. In China, every student who wants to go to college, including those only interested in humanities and social sciences, is required to study algebra, trigonometry, theory of probability, solid geometry, and pre-calculus (analytical geometry). Everyone will be tested on these topics and some differential calculus (though I don't believe humanity students are required to study calculus) in the college entrance exam (gaokao).

[toadstool]

Heartily agree with post above; American schools are skipping basic computational skills in favor of conceptual or theory skills. The results are showing up in upper level classes at our school in a big way. Advanced students clearly understand trig and calculus, but fail at tests because they can't manipulate the number reliably.

Teachers who lambaste parents for teaching long division and who don't bother teaching multiplication tables need to be re-focused to teach both theory and practice.

[originaloog]

chas, did you watch the video? He is not suggesting scrapping arthmetic and algebra but substituting statistics for calculus in hs. He also acknowledges that calc is necessary for those students studying scienc, engineering, econ, etc,

What he suggests make total sense and anyone wo has read Innemeracy will agree with what he is suggesting. Stats&probability have usage in many facets of everyday life whereas calc rarely does so. One of Innumeracey's main points is how ignorant we are to place common news into proper perspective. A cursory knowledge of probability would help enormously.

For example many environmental disasters send people into a panic. But even a carcinogen such as PCP's poses little individual risk. That is not to say that the risk should be ignored or that there will not be some community wide consequences. But an individual should not panic and merely take reasonable precautions to minimize or eliminate the already minimal individual risk. Calc would be of no value to properly understand this.

[marite]

I agree with Originaloog, and I'm the parent of a math graduate. For most people, statistics is more useful than calculus.

[tokenadult]

He really is a math professor. I have seen him speak at a conference. He doesn't disparage knowing arithmetic at all.

[BP-TheGuy88]

chashaobao, where in the world did you get that he wanted to get rid of calculus, algebra, trig, etc. he's saying that students should be taking those courses (except for calc) and then in the end when they're in high school have it build up to statistics/probability rather than calc. as it stands if you're going into the math/sciences field for a career you WILL have to take calc. but most people aren't going into that field and can't make much everyday use of calc. statistics was offered at my high school but wasn't not required and was considered an elective. that's a shame.

[marite]

Arthur Benjamin is a highly respected math prof at Harvey Mudd College who has written several books, one of which, Mathemagics, was my S's favorite in grade school. He has thought and written a lot about the math curriculum.

I tried to make the same argument to my HS about the value of statistics, and asking the school to consider introducing AP-Stats for those who were not going into math or math-heavy fields. But the principal thought that AP-Calc looked more impressive to college admissions committees, even though up to 2/3 of the students at those colleges will not need calc, but would benefit from greater familiarity with statistics and probability.

[Dad_of_3]

Agree with him. As one who went to engineering school and has a son who's doing the same, nobody needs to sell me the importance of calculus; but for all of those who go in a different line, I believe stats is far more useful than calc.

[wis75]

Another math topic I had in HS as part of another course was logic with formal equation-like rules. Basic statistics and probability should be part of every cuuriculum- either part of more basic math courses or other required ones so everyone gets some.

[dntw8up]

Arthur Benjamin rocks! And he's right about math as it's taught in the U.S. We treat every kid as if s/he should be going to college, and eliminate vocational training and trade schools to reinforce our stance. Calculus is useless for most people, whereas training in statistics would help people understand information. It seems like we've increased accessibility to information, but haven't likewise increased people's facility to comprehend the information they ingest.

[dshinka]

I'm a math major who has a bias towards pure, geometrical and continuous maths contrasted to the other genres.

I think a course in the fundamentals of formal logic and philosophy are in due order for high school education. We spend all our time teaching rhetoric and soft argumentation tactics - reminiscent of the Sophists from Ancient Greece - how are people supposed to make informed voting choices if they cannot identify a logical fallacy and are swayed by charisma?

I also think Linear Algebra is more important for most people than multi-variable calculus. I'm biased against probability and discrete math since I'm not as good at it, but I think a rudimentary knowledge of discrete math/combinatorial math in starting as early as middle school would be useful... Also much of geometry is useless for most people - constructing things with a ruler and compass and geometry proofs.

I also think more schools should offer a practical math course - one that teaches how to balance a checkbook and whatnot...

[vicariousparent]

But the principal thought that AP-Calc looked more impressive to college admissions committees

This is the only reason my D (a humanities kid) will be taking BC Calc next year as a senior instead of AP Stat. She already got a 5 in AB this year and Stat would have been a much better class for her but she wants to leave no doubt that she is taking the "most rigorous curriculum".

[geek_mom]

"Back in the day," I took three semesters of calculus, plus diff.eq and linear algebra. They had their place in my program (especially linear, because in graphics we worked on this new thing out of BYU called "Windows"), but stats (the one class not required, which meant I had to pick it up on my own as an undergrad) was far more useful to me than calculus in science classes, grad school, work, and life. IMHO just about any grad student in any field will benefit from statistics.

And after his presentations at HMC pre-frosh orientation, Art Benjamin is my son's hero.

[bluebayou]

What do you guys think?

Take both; that's what many of our top kids do -- they double with precalc. AP Stats only requires a strong background in Algebra I (not even II). While a great course, it ain't conceptually difficult.