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Do the math: too much calculus? (2012)

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

#151

Post by russellspitzer »

montyhallstuff wrote: post #148
posterboy wrote: post #121

Earlier quoted context omitted.

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

Consider 3 doors: A, B, C. If you pick the right one you win the prize. Say you pick door A. Monty Hall opens B or C and reveals that there's nothing behind. Now he asks if you want to stay with A or switch to the closed door. What should you do to maximize your chances of winning? Right before any of the doors is opened we have no idea what to expect, so there are 3 equaly likely possibilities: 1. prize is behind A…

I prefer thinking about the 100 doors case.

You are shown 100 doors 1 ... 100. Imagine you pick 1 door.

Of the other 99 doors Monty tells you which 98 of them don't have the prize.

He now asks if you want to switch to the 99th door that he didn't cancel out.

Intuitively that seems to make much more sense to me.

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

#152

Post by orangutango »

amluto wrote: post #139
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 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…

Completely agree, and this hits close to home.

I was a very math oriented student at a high school with a heavy bias towards liberal arts ... So when it came to picking senior year electives, I was delighted to enroll in AP statistics.

The classes turned out to be tutorials on the built-in TI-83 stats functions, with step-by-step instructions on how to answer the various types of questions we would encounter on the test. I forgot everything and gained virtually no statistical intuition.

Thankfully I had a similar experience to you ("Probability and Statistics for Engineers") with a fantastic professor who researched computer networks. His lectures were sprinkled with tangents tying the current topic back to his own field / research, which to me made the biggest impact. Contextualizing a taught subject markedly improves the course experience.

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

#153

Post by eli_gottlieb »

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.…

The problem with trying to teach statistics, to anyone really, is that once you get past the very basics, you have to stop every time the lecturer/textbook invokes measure theory and figure out how to explain the concepts without just making everyone sit through two to three semesters of real analysis.

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

#154

Post by posterboy »

novembermike wrote: post #141
posterboy wrote: post #121

Earlier quoted context omitted.

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

The Monty Hall problem is about being given two sets of information. First they give you a 33% shot, then they give you a 50% shot. Take the 50% shot.

No, the second chance is supposed to be better than a 0.5 and I could outline the argument, but I don't trust it.

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

#155

Post by debacle »

baldfat wrote: post #6

I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of anything past 4th grade math! "A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math. But this progression actually “has nothing to do with how people think,…

> BUT people are always afraid of anything past 4th grade math!

The problem is that elementary and middle school math teachers can't teach except out of a book. Your child's math teacher isn't teaching your child math, she is just the proctor for their math textbook, which isn't teaching them anything at all really.

This is not a dig on (all) teachers. These workbook-driven curriculum are a band-aid for bad teachers, and all they really do is harm good teachers and students.

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

#156

Post by hilop »

novembermike wrote: post #141
posterboy wrote: post #121

Earlier quoted context omitted.

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

The Monty Hall problem is about being given two sets of information. First they give you a 33% shot, then they give you a 50% shot. Take the 50% shot.

That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.

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

#157

Post by hilop »

novembermike wrote: post #141
posterboy wrote: post #121

Earlier quoted context omitted.

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

The Monty Hall problem is about being given two sets of information. First they give you a 33% shot, then they give you a 50% shot. Take the 50% shot.

That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.

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

#158

Post by hilop »

eli_gottlieb wrote: post #153
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.…

The problem with trying to teach statistics, to anyone really, is that once you get past the very basics, you have to stop every time the lecturer/textbook invokes measure theory and figure out how to explain the concepts without just making everyone sit through two to three semesters of real analysis.

You just use discrete scenarios, not continuous. Same concepts, easier math.

same way you can do linear geometry without calculus.

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

#159

Post by posterboy »

russellspitzer wrote: post #151
montyhallstuff wrote: post #148

Earlier quoted context omitted.

Consider 3 doors: A, B, C. If you pick the right one you win the prize. Say you pick door A. Monty Hall opens B or C and reveals that there's nothing behind. Now he asks if you want to stay with A or switch to the closed door. What should you do to maximize your chances of winning? Right before any of the doors is opened we have no idea what to expect, so there are 3 equaly likely possibilities: 1. prize is behind A…

I prefer thinking about the 100 doors case. You are shown 100 doors 1 ... 100. Imagine you pick 1 door. Of the other 99 doors Monty tells you which 98 of them don't have the prize. He now asks if you want to switch to the 99th door that he didn't cancel out. Intuitively that seems to make much more sense to me.

Yes, indeed it did for me, as well, but then I'm not trusting my intuition that failed me for the three door version, and I'm desperately trying to prove it wrong, because I'm biased by my first commitment to an answer.

I think that commitment bias or what it's called is also an explanation for the misunderstanding in the first place. The argument against the increased chance, as I would use, works both ways and that is much more apparent the smaller the initial chance is. But I only intuitively used it to defend my position.

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

#160

Post by abecedarius »

dredmorbius wrote: post #143
abecedarius wrote: post #82

Earlier quoted context omitted.

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.

Interesting. I've been thinking about education and a few dynamics of it, including human cognitive development and individual differences. 1. Young children seem to have the biggest capability in learning languages. 2. There's the John Stuart Mill example -- homeschooled by his father in the classics and philosophy. Interesting biography (Wikipedia has a fair account). 3. There are children who are naturally skilled…

My guess is that math teaching can be a benefit to anyone at any age, but the usual curriculum on average mainly teaches people to hate math. (That's what's happening with my niece in grade school right now.) For some kids arithmetic may be boring, but at least it's easy, and they suffer less of this damage. If you start it later when they're readier, more of them will be open to learning a little actual math, not just gritting through baffling seemingly-arbitrary procedures.

Montessori schools are said to be better on this score, though I haven't looked into them.

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