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Criticize This Idea Concerning Math!
Posted August 22nd, 2012 at 12:37 AM by Godot17
What if we combined Logic, Algebra, Geometry, Precalculus, Calculus, and Physics and put them into a godforsaken kitchen blender to create this 5year long 9hour/week concentrated course in Natural Philosophy?
Or maybe just Algebra and Calculus. With a little ingenuity, introducing calculus after introducing functions in general as well as polynomials could work very well. Now you just turn the math course mostly into a catalog of functions and their applications and calculus.
But I prefer my former idea because calculus is motivated a lot more strongly from problems that arise in physics. I have in mind a long and hard course that introduces mathematics as an art of proofs, starting at the lower level, to develop mathematical proof abilities concurrently with algebraic reasoning. This would make introductory geometry go along smoothly. So with complete abilities in proofs, geometry, and simple algebra, the student goes on to advanced algebra along with some calculus. Physical problems are interwoven and soon enough, after trigonometry and vectors are out of the way, we do some physics honors style. We can also naturally build vector calculus along with electromagnetism. And if series is introduced early enough, transcendental functions could be somewhat more motivated...
Of course, I do know there is a major flaw with this natural philosophy course that I conceive of: It's pretty allornothing. You can't drop into an algebra or calculus class if its aborted, and you can't just jump right in after some algebra.
And obviously, the endeavors required by such a course could only be undertaken by the students motivated by mathematics, also being able to see amazement with both the world within their mind and the world around them.
But I guess I'm just dreaming as long as I'm in the states. I can't expect anything out of the education system here anymore with a straight face. So I think I'll stick with writing an algebra book. Maybe later I'll work on a massive monster collection of math books from MiddleSchool math to Vector Calculus, but I'll probably have to put a small price tag on those if I want to have enough for when I'm retired or stuck as a badly paid and unappreciated teacher like all the teachers in this damned country.
Maybe I'll just start my own private school. It'll be like Hogwarts, but you learn some freaking cool math and science instead of magic. I'll call it: Mathwarts.
Or maybe just Algebra and Calculus. With a little ingenuity, introducing calculus after introducing functions in general as well as polynomials could work very well. Now you just turn the math course mostly into a catalog of functions and their applications and calculus.
But I prefer my former idea because calculus is motivated a lot more strongly from problems that arise in physics. I have in mind a long and hard course that introduces mathematics as an art of proofs, starting at the lower level, to develop mathematical proof abilities concurrently with algebraic reasoning. This would make introductory geometry go along smoothly. So with complete abilities in proofs, geometry, and simple algebra, the student goes on to advanced algebra along with some calculus. Physical problems are interwoven and soon enough, after trigonometry and vectors are out of the way, we do some physics honors style. We can also naturally build vector calculus along with electromagnetism. And if series is introduced early enough, transcendental functions could be somewhat more motivated...
Of course, I do know there is a major flaw with this natural philosophy course that I conceive of: It's pretty allornothing. You can't drop into an algebra or calculus class if its aborted, and you can't just jump right in after some algebra.
And obviously, the endeavors required by such a course could only be undertaken by the students motivated by mathematics, also being able to see amazement with both the world within their mind and the world around them.
But I guess I'm just dreaming as long as I'm in the states. I can't expect anything out of the education system here anymore with a straight face. So I think I'll stick with writing an algebra book. Maybe later I'll work on a massive monster collection of math books from MiddleSchool math to Vector Calculus, but I'll probably have to put a small price tag on those if I want to have enough for when I'm retired or stuck as a badly paid and unappreciated teacher like all the teachers in this damned country.
Maybe I'll just start my own private school. It'll be like Hogwarts, but you learn some freaking cool math and science instead of magic. I'll call it: Mathwarts.
Total Comments 14
Comments

Posted August 22nd, 2012 at 12:44 AM by Overlord Drakow 
Posted August 22nd, 2012 at 12:58 AM by Mariah Carey 
Posted August 22nd, 2012 at 01:46 AM by Banjora Marxvile 
Posted August 22nd, 2012 at 06:16 AM by Toujours 
Posted August 22nd, 2012 at 06:29 AM by Vader 
Quote:
Math is satan? Screw you guys, I'm studying Differential Equations.Posted August 22nd, 2012 at 07:15 AM by Godot17 
Posted August 22nd, 2012 at 07:33 AM by Overlord Drakow 
The only reason people hate math is because schools don't even teach the basics well so they're bad at it. Typically the only people who don't hate the subject are either so naturally gifted in it that they figure things out on their own (because they have a natural aptitude for it) or actually had decent teachers which is much rarer.
So essentially your course would only be for a small subset of the population. And completely altering the mathematical education of such a small class just wouldn't be worth it because it would take too many of a school's resources to do. Especially since, as you said, there's no backup plan if this route turns out to be the wrong one for someone. So unless someone is 100% sure that they can handle it for the whole 5 years, they'd probably be reluctant to sign on. (And someone at age 1213 who thinks they can handle it could have a very different opinion on academics and the like only a few years later.)
Besides that, most schools are tiered, as in, separated by grade. It's different everywhere, but typically you have elementary school, possibly middle school, and high school. No matter how you look at it, a 5year course would be split up between elementary/middle and high school because the latter is only ever 3 or 4 years long. And again, school quality comes into play. If your feeder school is just awful and didn't teach the course right, you're gonna flounder when you hit the high school parts of the course. And vice versa, even if you have a good background in the early content, if your high school has horrible math teachers, you're also kind of screwed. Also, I've found that when a faculty has low resources and some teachers are better than others, they usually assign the better teachers to the worse students hoping they'll balance out. So the people who actually want to take more advanced courses get shafted.
Also agreeing that if Physics is getting added in, other applied areas of math need to go in the course. Physics may be applied Calculus but it has a lot of other things in it that aren't necessarily centred in math or, looking at it from the other way, most of the theory in math (which is what you're emphasizing if you want logic to be a part of your math course all the way through) is entirely unaffected by physics. I'd leave them separate or introduce applied versions of most math subjects included in the curriculum. :PPosted August 22nd, 2012 at 08:04 AM by Cherrim 
Keeping Erica's post in mind, would this be more useful as a group of higher math courses, taught in college for a degree higher than a Bachelor's? I know my best friends is currently in a program where she gives up all her summers after her first one and goes to school for 5 academic years to graduate with a Master's instead of a Bachelor's, in situations like that a set of 5 years of math designed to feed one into the other might work out well. Or even just 5 semesters.
Then again that's a ton of math for any college student that isn't in the business of math. Even the engineers at my school maxed out at 5 semesters of math.Posted August 22nd, 2012 at 10:37 AM by Toujours 
P1: oh gawd no.
P2: That's pretty much GeometryAlgebra II, as Geometry also introduces one from Algebra into more advanced concepts arriving at Calculus.
P3: This is already how school mathematics standards work here in California.
P4: That's why it's broken up into seven years and is standardized, with multiple paths for underperforming, average, and honors/advanced mathematics. Everyone chooses their own path so they won't have to be forced into the middle of a course with no previous understanding of foundation concepts.
P5:That's why we have underperforming math, average math, and honors math course paths. One can choose how they would like to use math based on their own will and awe of math.
P6:As far as I can tell Foothill High School in freaking California USA kicks ass with amazing teachers, so I suggest moving around to different states and school districts to see if you like it. Generally though I think California has the best balance between hard work and fun, though you might want to check out the East Coast for advanced classes.
P7: Good public schools exist, no need to make one unless you want money.
All in all: your state sucks at education, I feel bad for ya.Posted August 22nd, 2012 at 11:21 AM by dʒɹʌmpfʼt̚ 
Posted August 22nd, 2012 at 11:24 AM by dʒɹʌmpfʼt̚ 
You guys are such naysayers
Each AP class is already for a small subset of the population. So I'm not concerned about my idea being a saviour to the education system. I could conceive of it lasting 4 years instead, with a 5th year being optional with partial differential equations and the like.
It's a course taught in high school, but it'd probably be worth a few college credits.
@Erica Of course, physics won't be the only application of the mathematics, but it's very emphasized to motivate calculus. The logic part is only dominant early in the course, and the applications part come later.
@Toujours Maybe a shorter version of this could serve as a twoyearlong "STEMMajorBasicsInABox" honors course. But then again it might not be too convenient to have an 8hour chunk in your schedule for 4 semesters, especially if you already took some AP exams.
@droomph Meh, don't advertise your state's education system. On the average, it's bad just like the other 49. And your college admission system is weird too. >__>Posted August 23rd, 2012 at 10:43 AM by Godot17 
I don't think physics is required to motivate calculus. I rather enjoyed Calculus (not assignments but tests, at the very least) when I took it in university and it had almost no application whatsoever. But physics? I hate it with almost all of my being now, even the university course I took where it was just applied calculus. It's just... ugh. :( Definitely not required to "motivate". I'd keep them separate and just use physics problems here and there as word problems on assignments as needed.
I don't know much about AP classes though so if that's what all this is based on, that's probably where my negativity comes from. :/ AP is only offered in certain schools here and only for schools that have a gifted program (which is usually one or two per district). And you don't get a university credit for taking an AP class here or anything, iirc, so they're kind of pointless in Canada to begin with.Posted August 23rd, 2012 at 11:24 AM by Cherrim 
I'm only saying what I know. All I'm saying is that as far as I know not every state sucks. I even said go to Massachusetts for a better education. I don't particularly agree with some schools in California either, but I'm just saying you have to shop around. I believe there's a school rating system somewhere? Use those things to your advantage, don't move to California (or any state for that matter) if you don't want to. And if you really cared reading a couple online articles on whatever you want to learn is a good alternative too. I believe I've learned a lot of things that way (eg derivation of formula for volume of spheres, cones, etc) and none of them were particularly from any state afaik. If you want a good education you're gonna have to look around. The Internet is here for a reason. I look up random math topics all the time on Google, and 99% of the time I learn stuff better on the Internet than at school.
Basically, work for education, don't expect it to be handed to you on a silver platter. The joy of knowledge is the journey to knowledge.
I love learning because of this. You have to find what you want to learn yourself. If you expect the diploma just to come to you you might as well drop out. The school system is only there to aid you on your journey to knowledge, not to take you on its back and bring you there.
I hope these concepts make sense to you. The Internet is an alternative to school, if you can't find vector calculus or whatever you wanted in a school course.
And screw college pffffPosted August 23rd, 2012 at 11:41 AM by dʒɹʌmpfʼt̚