I think a Physics course taught with "Just in Time" Calculus would be fruitful for motivating the Calculus. Calculus was invented to do Physics.
Do the math: too much calculus? (2012)
71–80 of 220 posts
Re: Do the math: too much calculus? (2012)
#72Earlier quoted context omitted.
>BUT people are always afraid of anything past 4th grade math! Then the solution is simple! We teach calculus to 3rd graders, then no one will be afraid of it! But seriously, I agree that calculus is taught way to late. I wasn't introduce to calculus until college, and if I had been even by senior year of high school, I would probably be a mathematician right now.
In the US, problem #1 is that it is very hard to find people who understand Mathematics sufficiently well to teach it effectively, who are willing to work for the salary typically paid to a teacher. For example, my 8th grader is being taught "Higher School Algebra" by a teacher who last year taught 5th grade and by all accounts has to leave the classroom often to get tips on the material from the 7th grade math teach…
the other criteria that kicks some people out are the requirements for a K-12 "teaching certificate". if you don't get a degree in education, it can be difficult and time consuming to get a teaching certificate. a friend of mine some years back desperately wanted to teach high school math, and had a bachelor's in pure math, tutored for years and was well loved, but couldn't surmount the teaching certificate hurdles. so now he works in software QA.
Re: Do the math: too much calculus? (2012)
#73I 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.
If it was a quadratic, you could (in effect) complete the square and thereby get it to a form like
a(x - b)^2 + c
In lucky cases, fourth-order polynomials could be put in such a form. Odd-degree polynomials will not have a unique maximum.
Re: Do the math: too much calculus? (2012)
#74Earlier 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.
The beauty of calculus is that you actually understand the Real World. For example I taught my daughter factions this way. Me: "These factions you see them? Now see these decimal points?" Her: "Yeah I hate factions they are stupid!" Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333." Her: "I always thought it was the otehr…
The first sentence in Your last statement in your conversation to your daughter is profoundly wrong. Your daughter was not in any way made to better understand fractions by this interaction. By the way, .3333 is a rational number and therefore equal to a fraction.
Re: Do the math: too much calculus? (2012)
#75Sample size of one: I think I understand calculus, the needs of calculus, and how it is profoundly meaning to understanding things around me. Can I do calculus? no. I couldn't do calculus because I really couldn't do algebra. I think that if I had been taught the concept and relevance of calculus earlier, and only had to worry about the execution of calculus later, I would have been much better off.
understanding what derivatives and integrals and trig functions mean should come before we are forced to execute their use, or learn proofs, or even really go beyond basic notation.
Re: Do the math: too much calculus? (2012)
#76Earlier quoted context omitted.
> Most universities aren't primarily focused on research. Where are you getting "many" (rather than "some")? The page you link to discusses colleges in addition to universities, and it's well known that colleges exist primarily to educate students. > Even if you subtract the research budget out first you will still arrive at a figure less than 50% for most universities. Where is that numbers coming form?
Universities are composed of colleges in USA. You seem to have more of a 'Canadian' definition, where college means something like "community college" in USA.
I am not using such a definition. I am an American, and I am thinking of American places like Kenyon College, Hamilton College, Harvey Mudd College, Union College, Claremont College, etc., etc.
> Universities are composed of colleges in USA.
This is pretty rare terminology in the US, being mostly found in Ivy league or other old schools. Most "colleges" in the US are independent institutions.
https://studyusa.com/en/a/107/what-is-the-difference-between...
Re: Do the math: too much calculus? (2012)
#77I 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. It's also useful for citizens to understand statistics better - and educating citizens is truly one of the purposes of public education.
Re: Do the math: too much calculus? (2012)
#78I 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,…
I think that a student not well versed in how to perform calculations will not do well with the theory. Last night in the calculus class I am currently teaching a student could not correctly translate the fact that f is increasing where f' > 0. This on a problem where f' was linear. He just stared blankly at the inequality 2x-3>0. Anyone well versed in this sort of calculation is not going to fumble around at this problem. He thinks calculus is the problem when it's his knowledge of algebra that hinders him.
Re: Do the math: too much calculus? (2012)
#79Earlier quoted context omitted.
>BUT people are always afraid of anything past 4th grade math! Then the solution is simple! We teach calculus to 3rd graders, then no one will be afraid of it! But seriously, I agree that calculus is taught way to late. I wasn't introduce to calculus until college, and if I had been even by senior year of high school, I would probably be a mathematician right now.
In the US, problem #1 is that it is very hard to find people who understand Mathematics sufficiently well to teach it effectively, who are willing to work for the salary typically paid to a teacher. For example, my 8th grader is being taught "Higher School Algebra" by a teacher who last year taught 5th grade and by all accounts has to leave the classroom often to get tips on the material from the 7th grade math teach…
Yeah, the line in the article about demand for calc teachers outstripping the supply suggests an obvious remedy...
Unfortunately, the fragmented (ie, redlined) us public school system means that higher teacher play is impossible in lower income areas. So private schools will pay more for the calculus teachers, and the low income public schools will continue multi-classing pe teachers for the task. And in another twenty years we will continue to lament the increasing lack of social mobility in this country...
Re: Do the math: too much calculus? (2012)
#80Earlier 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.
The beauty of calculus is that you actually understand the Real World. For example I taught my daughter factions this way. Me: "These factions you see them? Now see these decimal points?" Her: "Yeah I hate factions they are stupid!" Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333." Her: "I always thought it was the otehr…
is there a reason you call them factions and not fractions?