Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Do the math: too much calculus? (2012)

washingtonpost.com

Post reply on HN
Print view View original

141–150 of 220 posts

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

#141

Post by novembermike »

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

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.

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

#143

Post by dredmorbius »

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.

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 in art, storytelling, maths, sciences, music, etc. An opportunity to work to those strengths might be useful.

I've also noticed that a short period of instruction at the appropriate time often seems disproportionately effective.

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

#144

Post by analog31 »

optionalparens wrote: post #123
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.…

One of my degrees is in statistics, and the others are in computer engineering, finance, and computer science. As such I not only took a ton of math, but studied and worked in the contexts you describe where stats is relevant. The problem with statistics education is that it is generally heavily watered down, particularly the classes at the university level for business, psychology, and other majors that need the kno…

For students who aren't going to learn calculus, I wonder if a better introduction to prob and stats (and perhaps math in general) would be through simulation and visualization rather than learning formulas by rote.

I had the opposite problem, which was that I learned stats as a bunch of proofs with practically no applications. I only use fairly basic stats today, but I often test my conclusions by running some sort of monte carlo analysis. I graph everything.

It sounds like a lot of what you're recommending could be described as teaching general quantitative scientific methodology.

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

#145

Post by LgWoodenBadger »

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.

One of my calculus classes in college involved calculating the required spline for a curve of a theoretical portion of interstate in order to meet the interstate requirements/regulations. It was pretty interesting.

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

#146

Post by patrickthebold »

pps43 wrote: post #133
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 is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need derivatives and integrals. These days you can solve many practical statistical problems with Monte Carlo, but understanding why those curves look the way they do is still very useful.

There's a difference between defining the integral,then taking about how it's estimated numerically and to use some software to get numbers.

Vs

Trigonometric substitute to solve analytically.

For example.

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

#147

Post by CalChris »

supahfly_remix wrote: post #25
CalChris wrote: post #9

Earlier quoted context omitted.

Berkeley EECS grad. I didn't go the device physics route but I used calculus about twice in 4 years except in physics classes.

Circuit analysis turns differential equations into algebra, so you might have been using calculus more than you realize.

Yeah, I might have been guilty of some hyperbole. I remember a nasty integral on the Linear Systems midterm. It probably would have taken an hour or so if I didn't make any mistakes; but you could transform it and solve it as a linear equation in 10 seconds.

That was the point of the class, that there area two kinds of problems, linear problems and problems you can't solve.

I'm not in the least suggesting that an engineer shouldn't go through three semesters of Calculus, Linear Algebra+DiffEq and a Discrete Math course.

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

#148

Post by montyhallstuff »

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

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 2. prize is behind B 3. prize is behind C.

In case (1) you win by staying with your choice of A. In case (2) Monty Hall must open C (by the rules), so you'll win if you switch to B and in (3) the host will open B(by the rules) and you should switch to C.

In 2 cases out of 3 (2/3) you win by switching and in only one case out of 3 (1/3) you win by staying with your first choice. Since 2/3 > 1/3, you should switch.

This problem is easy if you know the defintions of sample space, event and the Equally Likely Probability Formula.

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

#149

Post by colechristensen »

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?

The median age in 1st grade is 6.

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

#150

Post by apricot »

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…

There are good stats classes and bad stats classes, just like there are good calculus classes and bad ones. When I was a student, we spend a full term learning integration techniques, with almost no class time devoted do learning what an integral actually is. The fundamental theorem of algebra was glossed over in a way that makes me think the lecturer didn't really understand it. Differential equations was a catalog of recipes, with almost no modeling and certainly no qualitative analysis. I got an A+ in the course but learned almost nothing from it.

Fortunately, I had a great professor in Calc III who more than made up for this.

Post reply on HN