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Do the math: too much calculus? (2012)

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Re: Do the math: too much calculus? (2012)

#101

Post by asimeqi »

abecedarius wrote: post #82
dredmorbius wrote: post #48

Earlier quoted context omitted.

Source?

A U.S. elementary school principal in the 20th C. got his school to try leaving out any math in the first three grades (iirc), and the kids reportedly came out fine. I can't remember his name, and I'd like to be reminded too.

It was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who experimented with teaching no math in the first five grades in the early 1930s. See for example https://www.psychologytoday.com/blog/freedom-learn/201003/wh...

Re: Do the math: too much calculus? (2012)

#102

Post by douche »

jimmydddd wrote: post #13

For lower level math, my kids seemed to revisit the same subjects over and over from k-9th grades. For example, mean, median and mode, year after year. The first few years it was just robotic problem solving. After a few years, they started to get a broader understanding. Maybe some people need to take several passes through the higher level stuff too.I guess the problem is that there is not enough time.

What infuriates me, looking back on it, was simply how much of my time the educational system was allowed to waste. Thousands and thousands of lost hours, some of them filled with pointless busy-work, but many more just squandered on inanity. At least some of the teachers would let you finish the daily penance quickly, and sit quietly in the corner reading something interesting. Too few, though.

Re: Do the math: too much calculus? (2012)

#103

Post by douche »

AstralStorm wrote: post #17

Personally, I have always wondered about the prominent position trigonometry and geometry get. As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus. From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry. The rationale is probably history.

I always found trig and geometry to be the most interesting and useful part of math. It maps pretty well onto real things that you might have to do. Maybe this is more relevant in the rural area I grew up in, but geometry and trig is really useful when you're trying to do carpentry, or figure out if you've got room enough to chop down a tree, pathfinding on a map, etc.

Re: Do the math: too much calculus? (2012)

#104

Post by 0xCMP »

ThrustVectoring wrote: post #62
0xCMP wrote: post #44

Earlier quoted context omitted.

Good ones at least.

Don't quote me on this since I don't remember why I believe it, but I think it's part of the legally mandated design requirements for the US interstate system.

No I'm sure there are requirements, but sometimes there are also space or budget constraints (I assume) since some curves are definitely safer and easier than others for the same highway (I-95 for me).

I wished they were more consistent

Re: Do the math: too much calculus? (2012)

#105

Post by spynxic »

krschultz wrote: post #77

I graduated with a mechanical engineering degree, meaning I took 3 semesters worth of Calc and 3 more semesters worth of differential equations. So I'm not one to hate on math or calculus specifically. But I think high schools should focus more on statistics. Statistics is relevant to more fields than calc. It matters a lot more in business and in all the jobs where you use calc you will also have to use statistics.…

I don't think it's possible to make the assertion that one branch of math is more relevant than another, given that the set of students have diverse interests.

From a computer science, more specifically programming, background I find linear algebra, logic, calculus and the combination thereof to be more insightful when handling abstract ideas.

I fear that if too much focus is put on statistics then we many end up with another generation of heavy statistical machine learning (and programs that consume high amounts of power to function).

Re: Do the math: too much calculus? (2012)

#106

Post by elihu »

AstralStorm wrote: post #17

Personally, I have always wondered about the prominent position trigonometry and geometry get. As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus. From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry. The rationale is probably history.

For a lot of people, geometry is their primary or perhaps only exposure to proofs. Not that everyone needs to understand proofs in their day-to-day lives, but it's a good mental discipline to at least be exposed to, and geometry proofs are fairly straightforward and relate to things that many people will have a good intuition to convince them that the thing proved by each correctly-constructed proof is really true.

Also, geometry gives students something concrete to visualize, and so might be easier for some to understand than more abstract kinds of math.

Maybe trig is over-emphasized at the high school level, but it is pretty useful in a lot of real-world situations, and it's easy to apply without having to know a lot of other stuff.

Re: Do the math: too much calculus? (2012)

#108

Post by noobiemcfoob »

I feared calculus, right up until circumstances forced me to not only take calc in high school but to take the hardest level of calc my school offered (AP BC Calculus, counted as 2 semesters of college calculus). I was greatly benefited by an amazing teacher.

I've always felt that calculus is one of the most important branches of mathematics for the simple insight it should hammer home time and again: An infinite amount of infinitely small things can and will add to infinity. All too often, humans fail to see the cumulative effect of an integral.

Every branch of math has these types of insights built into them. Calc the power of instantaneous change. Geometry shows the beauty of a proof - and if you scratch a little bit, the shattering epiphany that triangles are literally the same everywhere, always and forever. The reality is that many of these concepts are simply absorbed into our culture, and we fail to realize it until someone explains that it took centuries of work to formulate the concept of 0.

When it comes to education, I believe the struggle has far more to do with testing standards than the material. It's easy to teach to process, much harder to teach insight and further harder to test. In reality, none of this matters until your institution decides and commits to truly educating its students.

tldr - None of this matters until your institution decides to truly educate its students.

Re: Do the math: too much calculus? (2012)

#109

Post by eanzenberg »

castratikron wrote: post #10

AP Calculus was the most useful course I took in high school. It was rigorous, and I scored high enough on the exam to get two free college classes and start freshman year at the sophomore level, which left room at the end of my college career for more specialized courses. There should be some vetting process for the students who want to take AP classes. A lot of the students in my AP Calculus class had no business b…

Same here. I took both AP Stats and AP Calc BC in high school and I'd be more worried about stats being taught wrong to a bunch of teenagers than calculus.

Re: Do the math: too much calculus? (2012)

#110

Post by cozzyd »

jameshart wrote: post #100
greendragon wrote: post #45

Earlier quoted context omitted.

They're not always required, but they try to bridge what you already know (or are supposed to know) with what is to come and move at a slower pace. It's also sometimes like an extra option for the less mathematically inclined who are still required to take such a number of math courses. On the other hand the only 'pre-' course I ever took (I tested out of pre-algebra somehow) was 'pre-calculus with honors'. I don't r…

There's a difference between AP calculus in Alberta and British Columbia? :)

Yes. In Alberta, all you care about is the rate of change of the the price of oil and computing the volume of manure, so only the basics about derivatives and integrals are needed. In British Columbia, you have to worry about how to fit your oddly-shaped modern furniture into your tiny Vancouver apartment and find the region of convergence for your mortgage, so more advanced techniques are necessary.
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