Increasing amount of Math HS students take hurts, not helps math education

Great Debates
61

"You wouldn’t believe the hoops you need to jump through to get a course added to the curriculum. "
I can see that it being hard at the high school level, but at the college level it seems you just need a professor and a room. Maybe you’d have to make it zero unit/seminar.

I take it by College Algebra you don’t mean Modern Algebra? [snotty math major]Because that’s the only Algebra a college should have.[/snotty math major] I suppose requiring every student to take Modern Algebra would be a good way to cut down on the expense of having all those people at the grduation ceremony :slight_smile: .

I read a book called “fast math” or something like that that had a bunch of tips on doing arithmetic quickly (ignore orders of magnitude until the end, divide by 2 instead of multiplying by five, etc.) Most of the stuff I looked at and said to myself “of course, that’s just common sense”. Perhaps students would benefit from learning shortcuts for arithmetic, so they don’t get bogged down in the numbers instead of learning the concepts. Something like 499*20 every high school graduate should be able to do in their head. On the hand, maybe they’ll just consider them a bunch of arbirary rules they’re supposed to learn rather than useful tools.

62

The Ryan,

I LOVED Modern Algebra. Really. :slight_smile: Groups, Rings, Fields…ahhh the memories… :slight_smile:

What’s purple and commutes? An Abelian Grape of course!

When I taught, I took a 3-week summer course every year from a professor where EVERYTHING was group theory. He was weird but good. I mean EVERYTHING was group theory. You could take a course on something you thought completely unrelated and it turned into group theory fast.

Where I was at, getting a new course into a college curriculum was not easy. If it was pure elective it was a snap, though you would have few takers. Getting it accepted as a course applicable to a major took work. Getting it to replace a all-students-must-take course like College Algebra was long and involved. Complicating it was the fact that other colleges became interested in it and needed to be informed, which lended ‘weight’ to the course I was putting together but swallowed up much more time in travel, phone meetings, putting info together, etc. It was worth it though because the students really accepted it. Hey, it got them out of College Algebra! :slight_smile:

63

Yeah, I liked it other than the fact that the professor apparently used the same syllabus for both undergraduate and graduate versions. My TA had trouble writing up the solutions, the problems were so hard. Non-Math majors were oddly unimpressed by my claim to have never gotten less than 70% on a test.

PS What’s yellow and equivalent to the axiom of choice?

64

Zorn’s lemon. Algebra is one of the areas that I’m seriously considering pursuing after I get back to school (the others are logic and combinatorics, but those are a bit more specialized).

A classic: What’s the equivalent of the axiom of choice and requests water for his school?

65

A well-ordering principal?

66

How is the Catholic Church like 1/z?

67

It has a Pole at the origin? That’s the best I can come up with, but I doubt anyone would refer to Karol Wojtyla in that manner. On the other hand, he is responsible for appointing a great many conservative Cardinals, so perhaps one could say he’s the origin of the modern Church’s reactionary stances on a great many issues.

68

I’m not sure why something like “Practical Math” is dismissed out of hand for a high school curriculum. I see “Practical” having many many implications for Algebra, and as such can be used as a theme to tie an Algebra course together. For example, trying to figure out the 1970 initial deposit for a current account balance that used compound interest of 5% as its growth rate. Or the example that someone used about if the sale price is X, what is the non-sale price? I mean, you can have very practical applications for virtually everything that is taught in Algebra 1, no?

Geometry seems less practical, especially since the main focus is on proofs (at least where I went to high school), and it is hard to show how being able to prove that opposite angles in a parellogram are equal has any real world use. I guess one could call it logical thinking with a geometric theme?

In fact, one can almost make the argument that a probability course that goes from sample spaces and sets to combinatorics and other jazz could be inserted in place of geometry, as proofs abound in probability as well. And one can give it a lot more practical spin.

With actual calculus, it isn’t too hard to make the case that it is necessary for every science, economics, statistics (well, if you want to understand statistics instead of merely using formulas), etc.

That said, I am not sure at what level math should be mandatory. Algebra should absolutely be required, but beyond that, it’s a toss-up. Some students really don’t want to learn this stuff, and if teachers are resorting to just passing everyone regardless of what’s going on, well that’s just sad.

I really wish that at some point, a teacher’s union goes on strike for the right to fail students who deserve to fail. Of course, all effort should be made to help the student catch up, but if they refuse to learn, it really hurts the whole educational system if kids know they can pass without doing anything.

Some kids may be hopeless, but some can actually get a kick in the pants when they see that big fat “F” and have to retake a class until they succeed.

69

Your idea is sound, but not practical in this culture. You really, really need to understand this…

Our culture believes that every student is capable of passing. If he/she doesn’t pass it is the teachers fault. Even if the student does not do homework or pay attention in class it is the teachers fault. A good teacher would inspire the student to work. So, if a student fails FOR ANY REASON, it is not the students fault but it is the teachers fault. I mean, they are only children!

This is what our culture believes. For the teacher unions to make a stand on flunking students would be an extremely bad stand.

70

If you were a teacher and made this statement outside of a confidential friend/colleague you probably would be in big trouble.

Again, students don’t fail. Teachers fail. All students are bright. All students are above average.