The best thing about learning calculus is that you see how everything you have learned so far - algebra, geometry, trigonometry - everything comes together and becomes equally useful and important. This is, in fact, what mathematics is all about.
Do the math: too much calculus? (2012)
61–70 of 220 posts
Re: Do the math: too much calculus? (2012)
#62Earlier quoted context omitted.
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.
Don't quote me on this since I don't remember why I believe it, but I think it's part of the legally mandated design requirements for the US interstate system.
Re: Do the math: too much calculus? (2012)
#63Earlier quoted context omitted.
We should teach early calculus along with entry-level SR/GTR instead of rehashed Newtonian crap. Unite math and physics for a while, and kids might actually see the point of it.
Exactly. Physics becomes so much simpler with calculus. Once you realize e.g. the relationship between position, velocity and acceleration you don't need to memorize 20 different equations for all the different flavours of problems that are basically down to integrating or differentiating ...
I held off taking physics in college until my senior year because I dreaded the 3 hour labs. By the time I got there I had 3 levels of calculus (and linear algebra, and plenty of proof based CS classes) under my belt, and it turned out to be one of the easiest classes I've taken.
Like you said, I didn't have to bother memorizing anything, because everything could pretty much be done with simple integration or differentiation.
Re: Do the math: too much calculus? (2012)
#64Earlier 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…
... Ohhhhhh.
I wish you would teach me calculus =)
Re: Do the math: too much calculus? (2012)
#65>This is not true for students who take Advanced Placement calculus I hated BC calc. Bad teacher. I learned the same material at the same time in AP Physics, and loved it. I think a related issue to the author's point, though, is that students are taught in a way that implicitly suggests that calculus is the pinnacle of mathematics. Which is blatantly wrong.
I have had the pleasure of pushing many female students into taking calculus but my success rate was about 50%. Each one of my children's friends LOVED STEM and were thinking about going into engineering. All of them said that they were the only girl in the class and were intimidated and the other said it was REALLY boring. Calculus should be easily made fun just exploring the actual concepts in real life similar to…
As it happens, my teacher was female.
She was a firm believer in "teach to the test", "do these exercises and follow the magic rules of differentiation, shut up and just do it don't ask why it works".
That's not my jam.
Re: Do the math: too much calculus? (2012)
#66Personally, 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.
IMHO, high school math misses the one course that would be most useful to the students. Statistics. While there are a LOT of statistical models that aren't especially useful in every day life, knowing the most common ones can be a big help.
Of all the math classes I took in college the only one I use on a regular basis is statistics. Thinking back on high school I spent a whole lot of time on basically calculus prep and in the end I hardly ever take a derivative or integral of anything.
Re: Do the math: too much calculus? (2012)
#67I think linear algebra is a much more valuable and general-purpose math tool. I'm not sure how feasible it would be to teach linear algebra topics "properly" to high schoolers, but even a half-assed linear algebra would be more useful than calculus. The connections to geometry, general systems thinking, formal math methods, and countless applications of linear algebra are just the kind of thing students need to get t…
Thinking in matrices and vectors is much more complicated and abstract than calculus.
Re: Do the math: too much calculus? (2012)
#68I 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,…
Berkeley EECS grad. I didn't go the device physics route but I used calculus about twice in 4 years except in physics classes.
Berkeley's a really good university.
Re: Do the math: too much calculus? (2012)
#69AP 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…
> another guy didn't even take the AP exam, and another guy just put his head down on the desk during the AP exam. I don't know anything about these people but there's two "good" reasons for this: * Some colleges don't take certain AP credits e.g. the college I went to didn't take AP Bio credit, so I didn't take the exam for it when I took the class * Some high schools give GPA boosts for AP classes. For example, an…
How do you cheat at Calculus? Asking for a friend.
Re: Do the math: too much calculus? (2012)
#70Earlier 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.
That really makes no sense, unless the "EE" part was optional in your case.
There are different "tracks", and some of them have very little EE (with way more CS focus). I think I only took two EE courses IIRC..