Gifted Issues Discussion homepage Forums General Discussion APS article on math ed: A Math Paradox

Yes, I was schooled in Europe but it was many years ago and it is different now. What I said above comes from observing the behavior of US schools/parents over the last few years. Not from my past schooling experience.

Then again, Ania, I've been doing my darndest to slow DS8 down in math. I've not wanted to let him move past pre-algebra this year. Serious foot-dragging on my part...

But he started acting up. Bored. Cranky. All his usual signs of underchallenge. I can't stay put, no matter how much I want to.

My plan is to move slowly through a simple version of algebra (the "Key to" series) and then have him take the AoPS version next year. I'm hoping that in this way I can keep him challenged, plug any gaps in "the basics" for him (I'm not seeing many), and still slow him down at least a little. (Not as much as I would like!)

But I don't see a way to keep him from algebra right now. It's where we are.

Its a lot faster to do computations in your head for many numbers rather than use a calculator. Its also a lot easier to check work if you know numbers well. There are the basic number things like multiplication tables and division - memorization of up to 20 x 20 or 99 x 99 is not a bad goal. Beyond that, knowing the log tables for base 10 and e will allow you to do division and multiplication for much larger number sets. Knowing sine ( and by implication - cosine ) by tenths of a radian is a good target as well. Knowing the numerical methods to derive other numbers is a good target, too. Knowing primes between 1 and 1000. I could go on. You just never know where you will find a number that you know..

When to use calculators? I say from the very beginning. But with the caveat that you should be able to walk away from the calculator and still be able to do the numbers to a good approximation quickly as a rough estimate at least. Calculators will have to be used if there are a lot of numbers to process - ie stats or a very long problem.

Can most adults do calculus? The answer is no. By calculus I mean a word problem involving rates that must be solved using integration. One needs to know Geometry, Analytical Geometry, and Algebra fairly well to even set up and solve most problems. And one must be able to hold all this information in one's mind and decide from the list of stuff what to use and how to use it.

Calculus is just one small branch of Mathematics, too. Most mathematicians consider Calculus to be trivial.

What is developmentally appropriate? If someone is good at the basic prerequisites for that subject, then they are ready for the subject. Some kids are ready for Algebra when they are nine and others when they are 14 - and others when they are 18. Some - never. Once one has Algebra down and Geometry down, then Analytical Geometry comes next, then Calculus. Mathematically mature students could jump Analytical Geometry and do Logic then go into Real Analysis then back track to Calculus.

Two of our retired PEs teach remedial math and Calculus as insructors at our local Community College. They get pretty high marks. So based on this, I'd have to disagree.

Just one other thing - if some has a very high verbal ability, then they will do very well at math. They just need the exposure. The real mathy stuff like proofs may be more accessible to them than the highly visual stuff in Calculus. Just something to think about.

http://www.megsss.org/index.php?option=com_content&task=view&id=31&Itemid=62

Here is the curriculum for an organization established in 1978 by mathematicians, scientists and engineers to challenge and train (only) the most highly able math students beginning when they are as young as 4th grade. The organization�s mission is to identify and instruct the most promising future scientists. At least in the St. Louis area, far more than 1 in 1000 kids qualify for the lessons based on their results after a battery of math achievement, math aptitude, logic and reasoning tests. Many graduates of this three-year program do test into pre-calc as freshmen when they enter either public or private high schools and continue on to prestigious universities.

I wish I had known about it earlier for my son.

Kristen, I had thought this might be a good home school curriculum for your son. I don�t know if you can buy the books anywhere though.

Interesting that you mention this as one of the initial qualifiers for the program mentioned above is reading scores at the 95th percentile.

That's good to hear. Don't get me wrong, it's critical that the teacher get math but it's even better if he/she gets why some students don't get math. Unfortunately, many of the engineers I know don't get why other people don't get math.

For example, I'd be in class following along in lecture with one of my engineering professors. All of sudden he'd stop deriving the equation and just say "the rest is obvious." Well, it usually wasn't obvious to me.

It's the same with grammar though, so don't feel too guilty. It can be hard for English-y types to explain why something is incorrect or inelegantly written. It just is. I think that's just the nature of being more-or-less a natural at something.

delbows, thanks for the link! I really appreciate your thinking of me! I'm looking at it now...

I owe you one!

Hi Ania,
It's late and perhaps I'm misreading your post but I'm not understanding why you regret early AlgI for your DS? Is he having problems now or is it b/c of the effect it had on the school in placing other kids in early AlgebraI who don't belong there?

^^ CFK is right on the dot. It has to do mostly with logistics.
And you really do not know where you are going to be until you are there, unfortunately.
To be more specific - University is far away from us, classes have to be taken in the evening as freshman and sophomores have to have a full load of classes at school, which really means doubling up on workload. Having U classes in the evening takes away some extracurriculars. He doubled up on science this year and even though he is doing physics, not normally taken by freshman, it is still not calc based, which turns to be really tedious for him. Again - do not get me wrong - this is honors physics and he will most likely switch to AP Physics in a couple of weeks, and he is learning tons of new things, but doing it based on calc would have been so much easier for DS!
What can you do not to rush ahead? Spend 2 years on Geometry! Geometry is not really taught in american schools. One year of basics. Never returning to it again. Kids do not know how to write proofs. Even the smart ones do not know! So if you kid tells you that he knows or understands something intuitevily tell him to prove it. Prove it in two or three different ways!
That should cure any boredom...