Conics and Geometric Proofs

As I tutor for high school math students in the New York City area, I've noticed that most of the Conic sections (mainly the ellipse and hyperbola) have been taken out of the curriculum. I have also noticed that high schools, in general, are not concentrating too much on the importance of geometric proofs.

Why would that be? Why have they taken this course of action?

You may also note that fractions (the messy guts of common denominators, etc) are not taught, nor is long division, nor many other topics. The current educationist philosophy, at least in the US, is that students shouldn't be "burdened" with actual computations. Anything that the calculator can do, it should do; in particular, the student should not do, as it would be bad for the student's self esteem (it is alleged).

Instead, students play with blocks ("tiles", "cubes", etc) and other "manipulatives", "discovering their own mathematics" (as there is, of course, no objective standard or reality). The "best" methods involve not teaching the students anything at all, leaving them to flounder about, lost, trying to rediscover millenia of mathematics on their own.

Assigning "no right answer" weeks-long projects (especially if one doesn't tell the students that there is no answer) is believed to enable the students to "grow their love of mathematics" and "discover their inner mathematician". By these "methods", educationists claim to enable students to "do 'real' mathematics", as the students are now utterly unencumbered by any actual arithemetical or algorithmic knowledge.

Please don't ask me why anybody actually thinks this makes sense. :roll:

Eliz.

Liz,

Hello. I thank you for your reply. I agree with you 100 percent. In today's world, students are not taught math the right way. The results: we have an adult population of illerates who can't who solve for x samples like x + 5 = 10. Theyalso have no idea that this is an equation.

In fact, 5 + 5 = 10 is an equation but elementary school teachers today are concentrating too much on math games with cards, cubes manipulatives and other junk that does nothing for the students mathematical thinking. As a sub teacher, I get heavily criticized in the public schools when I try teaching an old fashioned math lesson. They call it "abusing the kids mentally."

As a private high school math tutor, the parents of the kids thank me for using old fashioned methods that are not abusive, in the least. For example, I have a 9-year old son. He already knows the ENTIRE multiplication table. He learned it using something God has given
to us all--->THE BRAIN. The result: he has the best math grades in his fourth grade class. I don't know where you live but in NYC, anyone can pass the high school regents in math. I believe the passing score is now 39 percent. It's a joke! When I went to school here, the passing grade for ALL regent exams was 65 percent but it has been going down hill year after year because teachers are "too demanding" of students and thus "abusing" their precious little minds.

In terms of trig, for example, I tell students to memorize the Unit Circle because it can make their trig experience easier and more pleasant. Those who listen, thank me for a million years; those who don't listen are still trying to figure out how to write the word trigonometry.

What is your reply?

Thanks

Let's just say that my time spent studying in an education department and working with education majors was a big part of convincing me to home-educate my own child. He's using Singapore Math, thank you very much! :wink:

Eliz.

When I retired from teaching (in 1999, after 35 years), I was SO frustrated about the inability of kids to do basic arithmetic and their total reliance on calculators (fostered by their elementary school teachers!).

I'm still frustrated. I tutored a very bright girl for 5 years....from 8th grade until her high school graduation. She had never memorized the multiplication facts...didn't think they were important, and neither did her mom. So, we'd get to a problem like (5/28) + (4/35) and she was lost if she couldn't give a decimal answer. For 5 years I tried to impress on the kid and the mom that learning basic facts was important.....to no avail.

The student (who wasn't really a "math person") got a scholarship to Cornell....

Elementary school teachers and curriculum coordinators don't have a clue about how important some basic concepts are. A 5th grade teacher may not realize that somewhere down the line, some of these kids may have to deal with things like [(1) / (cos x + 1) + (sin x) / (cos x - 1)]......can't use a calculator on that one!