Slashdot Mirror
Science and Math For Adults?
Peter Trepan writes "Like most Americans, I made it through high-school and college without a thorough understanding of major scientific and mathematical concepts. I'm trying to remedy this situation both for personal betterment and so I can supplement my *own* kids' education. The problem is, most textbooks are not designed to convey an understanding of the subject, but to squeeze in all the 'facts' required by state law. I'm looking for books that don't just tell me an equation or a concept works, but also explain *why*. Would you please list books that have helped you gain a greater understanding of the basic concepts of algebra, chemistry, calculus, physics, and other core areas of science?" This is similar to an earlier question, but with a broader focus.
The math program I was a part of in high school, at Whitney Young Magnet School in Chicago, was called IMP, or Integrated Mathematics program but it could have just as easily stood for Interactive Mathematics Program.
Basically the way it was structured was that instead of the traditional math program where one learns algebra the first year, geometry the second, trig the third and then moves onto precal, we learned a litte bit of each every year.
Furthermore, instead of them just shoving facts down our throat and saying here, memorize these (such as all the proofs from traditional geometry) we were actually guided along in discovering them for ourselves.
Every problem was given to us in word problem format. Each unit, which represented a major concept such as the quadratic equation or some of that other stuff, was presented as one big word problemm and it was broken up into smaller pieces which slowly led up to the solution of the actual problem.
So instead of coming out of it with simply memorizing the quadratic equation, pythagorean theorem, pi, geometric proofs and the like, we were actually able to discover these on our own.
It's just too bad the teachers weren't all that great and the program didn't much fit into the "flash/bang" you need to know this information right now that most high school classes are based around. God forbid students actually understand and can apply the information they are learning.
I also can't seem to recall who published the books we used but I'm sure a bit of googling can solve that.
There are several reasons for wanting to fail students, the most frequently mentioned is that theres "not enough room" in the upper courses. But the real reason is they are simply elitist bastards, they figure, "I had to go through it, you do to." The worst abuse I ever saw was a chemistry course I was in. 250 Students, the teacher spent the entire quarter lecturing about the heart medicine he was working on, and how steel refineries worked (his other interest). No problem -- if the tests are on heart medicines and steel production, but, he gave standardized tests and flunked 90% of the class.
Flunk courses also create some strange strange acedemic relationships. For instance, I was getting 15s and 16s (out of 100) on my physics tests and, with the curve I was getting a nice fat C. The problem with this is two fold ... It sounds great right? get a 15 and get a C? First problem, I'm not getting the education I paid for. Secondly, it encourages cheating because all you have to do is "beat the curve". The thrid and most intriguing problem deserves its own paragraph.
For me to get a C with 15 out of 100 points. That means, about HALF of the students scored worse then me. The students who scored WORSE then me *financed* my C by getting D's and F's. If they weren't the cannon fodder, *I* would have failed the course. Now here's where things get tricky. Sometimes, you are the sacrifical lamb, and sometimes you are the priest. If you are the lamb, you take the course over -- but this time you're the priest because you've taken the course before and it's finally starting to make sense. So the first timers are competing on a curve with people who have taken the course before. This wouldn't be a problem with a normal distribution of scores, but with poor instruction causing scores to center around 15%, that advantadge *REALLY* counts.
So now that I've written a diseratation here, what I really mean is, in your post you assume that mathbooks are even designed to help students, when most of the time, they aren't.
Religion is a gateway psychosis. -- Dave Foley
People go to community college to transfer into a good university and get cheap credits, not get an education.
If they wanted me to focus on an education perhaps they wouldnt make the GPA so damn important.
What is the point of avoiding difficult but important classes simply to preserve your GPA? Are you in school to get an education or to simply achieve some arbitrary GPA? I've been in the position of hiring people for technical positions and I've always been far more impressed by a mediocre GPA in a substantial curriculum then a high GPA in an easy curriculum.
Ok say I do take a few math classes and get a few Cs, well then my GPA goes under 3.0 and I can forget about transfering into a good 4 year university, I can also forget about scholarships and grants which also require a high GPA of above 3.0 or 3.5, I really cannot afford any Cs and I know for a fact that its simply impossible for me to get an A or B in math. I take classes which I know I can/will get an A or B in.
This isnt about the jobs, this is about getting a degree from an elite private university.
I recently returned to school myself, so I do have sympathy with amount of work required to do really well in a course, and I do understand that those planning to continue to a four year school or go on to graduate school need to match minimum requirements, but in my opinion you'll be better served by reducing the number of classes you take in a given term then by trying to ditch the challenging courses.
I never take more than 4 classes per semester, and I never get anything below a B in grades, those are the rules I follow.
Maybe if universities werent so strict and competitive on the GPA issue I could actually focus on learning but right now I have a goal, that goal is to get into Harvard, Tufts, Boston College,Boston University or North Eastern, all which are ELITE private universities which will NOT let you in with a sub 3.0 GPA, you most likely wont get in with a sub 3.5 GPA, so no its not about "learning" right now, its about moving up the ladder, it will be about learning once I get into university, thats when I'll take math clases, get a C or two, and learn something.
If you use Linux, please help development of Autopac
I confess that I made it through 3 semesters of college calculus and an engineering degree pretty much not understanding the underlying concepts of calculus. It's surprising what you can accomplish by rote. This book was a real forehead-slapper for me, and I can't recommend it highly enough. Many years after graduating, I've finally learned what I should have back then. If it were up to me, this would be the first book anyone learning calculus ever read. I wish Sylvanus Thompson were still alive (I think Calculus Made Easy was published in 1919) so I could give him a big smooch.
Area of a sphere? 4 pi r ^2...no calculus needed ;-)
:-P ::silence::
Of course a (an astute) calculus student would notice that when you derive the volume formula for a sphere (4/3 pi r^3) with respect to the radius you get the area.
My dad is an engineer (I will be too soon...hopefully ) and he has a novel way of find an oddly shaped area.
As long as what you are looking at has a scale of some kind you can actually cut out that area and weigh it on a (sensitive) scale. Then cut out a known square dimension from the same paper. Now you know what that area is relative to a certain weight...well now finding the original area just takes a little knowledge of proportions.
Granted it is not exactly going to score any points in the rigorous category, but it will get the answer with uncanny accuracy, which is the only category engineers have anyway
Yeah I am lucky they don't have -1 geek as a moderation...
--Joey
The best piece of advice I can give anyone trying to learn from a textbook is to tell them to work through the problems. Anyone should be able to pick up many of the textbooks listed below and work though as many of the problems as time allows (limited either by patience or by real life events). Most textbooks provide answers to selected problems, so you can check your progress.
Absolutely, 100%. Nobody is born with the ability to take a triple scalar product or multiply two matrices (both happening in your video card when you're playing Doom!). As a great Calculus teacher once announced to his class through a thick French Canadian accent, "Math is not a spectator sport." (Actually, it came out as "Matt ees not a spectator sport.")
Having said that, Calculus is my favorite kind of math. It's incredibly elegant and probably the most useful advanced math, as it touches everything you do. Consider your car. If you calculate your speed using a watch and the odometer, you have an idea how fast you were going, but your speedometer is actually showing you the value of the derivative at any instantaneous time. Your speedometer shows the rate of change of position (distance travelled) at any instantaneous time. That's calculus.
Don't be afraid. "Calculus" (besides being a formal term for tartar the dentist scrapes off your teeth) means small stones in Latin... small stones as used for counting.
Two *great* books on the subject:
Remember: Do the problems, succeed. Don't do the problems, fail. It's that simple.
Fire and Meat. Yummy.