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Do the math: too much calculus? (2012)

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

#41

Post by japhyr »

I have a 5 year old, and I was talking to some acquaintances who also have a kindergartener. The kids are learning math, by playing with manipulatives. It's great; they're learning mathematical concepts, and they have no idea anyone in the world doesn't like "math". They don't know what "math" is, they are just starting to discover that the world is made up of interesting but identifiable shapes, and that numbers have some really interesting patterns as well.

These parents, however, don't see anything they recognize as "math". They're afraid their kid is going to fall behind, so they're giving their kid worksheets at home focusing on two-digit addition and subtraction. Their kid doesn't like math already, because at home math is just writing things on a piece of paper with little meaning. This is sad to me, because there are so many interesting things you can do with your kids at home to help them develop their mathematical understanding.

Our educational issues with math start young, and they come from adults. I'm fortunate to work in a small high school where I get to treat each kid individually. It's wonderful to meet kids where they're at, and help them move forward and start to enjoy math again.

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

#42

Post by hossbeast »

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.

You can't possibly understand calculus without first understanding trigonometry and, to a lesser extent, geometry

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

#43

Post by sotojuan »

wutbrodo wrote: post #27
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…

> There should be some vetting process for the students who want to take AP classes. Is this not usually the case? My high school used to make you fill out a short form and make the case for why you should be allowed in the AP class, and my senior year I had to go in and speak with a counselor who was concerned that I was taking too many. Sure, it was a pointless hurdle for me personally, but I can see how it would b…

Depends on the school district and size of the school. For example, Texas high schools are for the most part huge and can accommodate anyone who wants to take AP classes without question. We did check with our counselor but they were more than happy students took AP classes.

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

#44

Post by 0xCMP »

ThrustVectoring wrote: post #33
hanoz wrote: post #30

I remember once when when driving I was pleased when it occurred to me that I should be seeking to minimise the third derivative of distance with respect to time for the comfort of my passengers. That was the sum total of calculus's contribution to my adult life. Not sure it was worth it.

Curves in freeways are designed that way as well - they don't just start turning suddenly, but gradually transition into and out of the curvature.

Good ones at least.

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

#45

Post by greendragon »

jameshart wrote: post #23
rhizome wrote: post #19

Earlier quoted context omitted.

I would have done much better in math if the class after Geometry was something other than pre-trig.

As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.

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 remember it much but I think it was mostly reviewing the harder topics from intermediate algebra aka 'algebra 2', which included trig (no separate trig course in my system), introduction to limits, and toward the end differentiation and maybe discrete summation. The 'honors' variant was also geared toward students who were planning on taking the more comprehensive 'AP Calculus BC' variant rather than the 'AB' variant.

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

#46

Post by jpfed »

ThatGeoGuy wrote: post #31

I am not sure how much of this is specific to the American education system, as I am Canadian, and have not experienced it, but my own take after going through high school to my current graduate studies is that 1) We teach algebra, geometry, and their relationship wrong in many ways 2) We don't teach enough calculus at lower levels of mathematics, instead opting to prefer a "poor man's" algebra. I'm sure there's too…

>Finding the maximum of a relation using Calculus is much easier than strictly using algebra for this reason

I recently-ish helped my stepdaughter with an algebra assignment where she was asked to find the maximum of some polynomial. I totally blanked on how to do this with only the tools that she was supposed to have. I didn't know how to do it or explain it without calculus.

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

#47

Post by mmmpop »

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.

So I guess you've never framed up a house have you? Basic trig is so incredibly important to anyone that ever desires to build a thing. Don't you remember learning the unit circle in Calc 2??

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

#48

Post by dredmorbius »

cgag wrote: post #28
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.

I believe there's decent support for the idea that you could just teach them nothing until they reached the age of understanding, and theyd pick it up pretty much just as quick without the years of rote.

Source?

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

#49

Post by dboreham »

ThatGeoGuy wrote: post #31

I am not sure how much of this is specific to the American education system, as I am Canadian, and have not experienced it, but my own take after going through high school to my current graduate studies is that 1) We teach algebra, geometry, and their relationship wrong in many ways 2) We don't teach enough calculus at lower levels of mathematics, instead opting to prefer a "poor man's" algebra. I'm sure there's too…

I came to the US (where I have children in school) from Scotland (where I obtained my education). US K-12 Mathematics education drives me nuts. Peeve #1 is the idea that the subject should be divided into these seemingly separate subjects : Algebra, Geometry, Calculus and so on. These are not different subjects -- they're all deeply interconnected, and furthermore : observing the connected nature of seemingly disparate areas in Mathematics is one of the key insights to be had.

To be honest I don't really care what kind of Mathematics they teach: I just want it to be taught with passion and rigor such that the students gain insight and a better understanding of how the world is put together; how to solve problems and express ideas.

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

#50

Post by baq »

smallnamespace wrote: post #4
spike021 wrote: post #2

I think this is just another example of standardized testing (specifically AP course exams in this story) almost creating a niche-like education for students. Maybe that's an odd way to put it, but some students wind up spending hours and hours studying AP/SAT/ACT/etc.-specific materials (literally 500+ page textbooks for each type of standardized test). Sure this method of studying helps them achieve great scores on…

A pattern that you see almost everywhere is: imperfect incentives/objectives + strong competition = perverse outcomes Over the last decades, we're increasingly seeing this in academia (publish or perish), the corporate world (boost the bottom-line at the expense of everything else), politics (win the election even if you have to burn your own party to the ground), and many other walks of life, as the world has gotten…

> imperfect incentives/objectives + strong competition = perverse outcomes

if you think about it, it's just a rephrasing of 'survival of the fittest'.

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