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Do the math: too much calculus? (2012)

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

#191

Post by lordnacho »

gohrt wrote: post #186
lordnacho wrote: post #93

Earlier quoted context omitted.

Same experience here. I went to international school, so I often ended up with American friends who'd talk about Algebra 1/2/3, pre-calc, trig, geometry, etc. Makes no sense to me. All those things are related. There's a picture that shows you why Pythagoras' Theorem is true. And why the difference of two squares is never prime. You'll have had a whole summer holiday between trig and algebra if they're separate thing…

Did you learn all of K-12 math in one year? Which year?

You certainly can't learn it as separate things. I had classes called "Mathematics" every year, all the way to the end of high school.

Got a bit more separate at university, but not really.

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

#192

Post by [deleted] »

SiVal wrote: post #173
amluto wrote: post #139

Earlier quoted context omitted.

I would love to see statistics taught more universally. But there's statistics and statistics. I took a fantastic one-off class as an undergraduate called, IIRC, "Statistics for Physicists". The class taught us Bayes' Law, what tests were, what significance was, and how one might go about deriving and using simple tests. Everyone came out of the class with a very clear understanding of what statistics meant , and no…

This is an area where I think the usual proper math approach of abstract patterns and theorems and proofs is all wrong for the general public (the ones in a general public school). They should teach it from the perspective of what problems you are trying to solve, what your options are, and how those options work in practice. The "in practice" part should be lots of simulations with something like a ChromeBook, so pe…

[deleted]

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

#193

Post by inimino »

posterboy wrote: post #121
lordnacho wrote: post #91

Earlier quoted context omitted.

I second that. Stats is so much more applicable, and it is also the area where common sense will fail you the most. Simple things like birthday paradoxes, Gambler's fallacy, Monty Hall problem, and so on are all contrary to common sense yet not taught in schools. And you need stats all the time. Every time someone says crime has never been worse, you need to know how to decide if you believe it. When someone says fly…

As if algebra or calc was common sense. I did learn about the Monty Hall Paradox but I'm still doubting it

I think there is an easy and intuitive explanation:

Two thirds of the time, you pick the wrong door on your first choice. So far, so obvious. Now, you picked a wrong door, Monty opens the other wrong door, and there are only three doors. Obviously the remaining door has the prize.

Every time you pick the wrong door, and then switch, you win. That means two thirds of time, if you switch, you win. That makes switching the right strategy.

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

#194

Post by [deleted] »

retsibsi wrote: post #174
montyhallstuff wrote: post #165

Earlier quoted context omitted.

Just in case.... A sample space is the set of all possible outcomes of a random experiment. An event is a subset of a sample space. Let S be the finite sample space with equally likely outcomes in it. Let E be an event. Then the probability of E is the number of outcomes in E over the total number of outcomes in S. Now consider 52 cards in a deck. The sample space of outcomes here are the 52 cards. What is the event…

As I mentioned in another comment, it's important to note that Monty Hall is guaranteed to open a door with a goat behind it (a losing door). If he chose randomly and just happened to reveal a goat, the answer would be different.

[deleted]

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

#195

Post by kol »

ivansavz wrote: post #170
japhyr wrote: post #41

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 hav…

I don't have kids, but if I had a 5 year old, I'd sure get them some of these: https://en.wikipedia.org/wiki/Cuisenaire_rods I've often thought about inventing math toys, e.g., group theory for toddler: S_3 = triangle toy, S_4 square toy, etc. I'm sure there are many advanced math topics that could be turned into toys. No symbols, no equations, just toys, but subtly you're getting kids familiar with important math st…

Rubik's cube can be used to teach group theory, see http://geometer.org/rubik/group.pdf or http://www.math.harvard.edu/~jjchen/docs/Group%20Theory%20an...

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

#196

Post by thearn4 »

As someone currently teaching college calculus on the side this semester & works in aerospace engineering, I agree. The two math subjects that I notice most people are deficient in post-college are statistics, and linear algebra. In my opinion, we teach way, way too much calculus.

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

#197

Post by TheOtherHobbes »

danielmorozoff wrote: post #131
ghaff wrote: post #98

Earlier quoted context omitted.

I suspect calculus is less commonsensical to most people than you think :-) That said, I've argued the parent's point for years. Basic stats/probability/economic biases are really fundamental stuff and don't require a lot of complicated math if you don't want them to. There are some basic calculus concepts that are useful. Area under a curve. Basic derivatives (for finding maxima/minima, etc.). But the truth is that…

I think the reason calc is preferred, to prob/stats is because the intuition is much more visual than the latter. Furthermore, students up until that point spend the majority of their time studying various functional forms (conic fxns, exps/logs etc.) Functional analysis seems like an obvious next step. Though stats/prob are perhaps more 'useful' in non-academic life. Imparting the notion of what probability actually…

In the UK high school math is really a preparation for a hard science/engineering degree, and there's a lot more calc than stats in hard science/engineering.

That's why calc is central. I wouldn't be surprised if it's the same in the US.

This means most people have no idea what the math they learn is used for, because they never reach a level where they have to use it.

So they leave school with the idea that math is annoying bullshit that they don't understand and can't use.

I think it would be better to stream math by ability much earlier. Make everyday math compulsory for everyone - interest rates and loans, basic stats, currency rates, areas/volumes, simple trig, maybe some slightly more advanced finance, perhaps touch on some calc ideas.

Only teach calc and scientific math to those with the talent and interest for it. Give everyone else a taste so they understand a little, but don't try and get them ready for a career they'll never go into.

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

#198

Post by baldfat »

eanzenberg wrote: post #97
rconti wrote: post #84

Earlier quoted context omitted.

IME the #1 problem is the failure to teach anything WELL. I took AP Calculus in high school, and today, as a 35-year-old, I'm still continually surprising myself with the problems I realize must be related to Calculus-- but nobody bothered to tell me. Things like the 'ol speed vs acceleration vs jerk kind of problems. All calculus ever taught me was to apply these formulas to those problems (for some reason) and that…

Dude, the "with respect to" clause is a pretty deep idea in calculus that really matters in multi-variate but not so much in uni-variate. I keep seeing how society needs better math education, whether it be statistics or calculus. Well no shit. Unfortunately those are extremely hard subjects to teach in high school. I'd argue statistics is harder to teach than calculus. In calculus you usually derive things by follow…

Looking at Common Core anything besides old arcane way of math will never be accepted :(

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

#199

Post by arethuza »

jameshart wrote: post #138
pirocks wrote: post #128

Earlier quoted context omitted.

Just in case you didn't know calculus BC is considered the harder AP calculus while AB is considered the easier.

So I went to school in a country that is notorious for forcing kids to specialize early - the UK. In my age cohort, at age sixteen we had to pick just three subjects to study for the next two years. I chose 'pure and applied mathematics' as one of those three subjects. Some people chose 'pure mathematics' and 'applied mathematics' as Two of their subjects. I guess, vaguely, that doing the expanded applied maths would…

Worth noting that the Scottish education system is different - people do 5 or 6 highers at 16/17 and those are used for university entrance rather than 3 A-levels at 17/18.

Scottish first degrees are 4 years rather than 3 in England - presumably to allow for this.

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

#200

Post by Oletros »

Oletros wrote: post #53
euroclydon wrote: post #26

I have a 5th and a 6th grader. I'm going to buy them an educational copy of Maple soon, so they can have a beautiful platform to plot 2-D and 3-D graphs, solve equations, do derivatives and integrals, and factor algebraic expressions. I want them to do all this in high school, whether or not they take Calculus, so they can get an intuition for it. Then they can memorize the trig rules in college.

AS an Spanish not knowing the US education system, at what age one kid goes to 5th grade?

Thanks to both of you
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