Gifted Issues Discussion homepage Forums Age or Ability Specific Forums Math acceleration - forward or sideways ?

I have been re-reading some of the posts last night and this am (as I have indicated I would )and I have one observation that I decided to share here, since it might help some of you in understanding your mathematically gifted kids.
We seem to worry here about those kids being bored to death in regular classes and our advocating is generally able to push the process ahead - by this I mean acceleration and grade skips, if not accross the board than at least in math. This leads us to the problems of accomodation high achieving math students in regular classrooms. It has happened to us. My DS has been placed in Algebra 1 in 5th grade.
The problems of this decision, as seen through my eyes today:
1. The teacher who is a very good lecturer of Algebra 1 might not be so good for Geometry and Algebra 2, since those are generally subjects not taught till HS. Keep this in mind. I am not even mentioning Calculus.
2. The acelerated child is still at the top of his class. He is learning more advanced material but his peers, even though years older, are still struggling, just the same as the peers in his regular, same age classroom were.
3. The fact that the accelerated student is collecting A+ does not mean that he is a problem solver. What is being taught in the classroom is just very basic touching of some of the basic ideas. More difficult problems are almost never introduced, there is no time, there is no interest, there are no incentives - only easy problems are on end of levels, after all, right ?

So do make sure that you involve your precocious mathematician in a LOT of problem solving contests. You will be shocked how poorly they are performing if they haven't been "trained" in solving more complex problems. DO NOT sit happy if your child is the best mathematician in his class/school. DO worry.
I am going to make a separate thread listing math contest/competitions avalable out there.
But here is a link to my favourite article - yes , AGAIN.
I somehow feel like I have a right to say it since I drasctically accelerated my child in math.
http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php

Well put, Ania! It's the PACE and DEPTH that also need to be changed for talented students. I see my oldest working problems every night for Alg 2. There are tons of them and they're very similar. I am not convinced this is teaching him much (other than obedience). In fact he could not solve the AoPS problems in the Intro course his brother was taking. In high school, there is less free time, so I would encourage addressing their needs early-on. Now I'll try to figure out if DS will have enough free time to take a community college course.

I'm still at the low end w/ a 2nd grader. They've done two digit addition w/ regrouping over and over, then w/ 4 digits over and over (numbers then w/ money)...problem after problem. My son could do that 2yrs ago. The teacher expressed SHOCK that she gave him some problems to solve that were 2 step problems and he did them all mentally and got them right. It was only one sheet however for the whole year for his portfolio she is compiling for GT program. Why can't they give multi-step problems using 2-4 digit addition/subtraction that make the kids think? All the kids could benefit from that!!!!!

Also, whereas from doing RS math and some SM math, DS would read the problem and think about what they were asking, the teacher is now emphasizing looking for keywords to determine whether you need to add or sub. He was confused on a problem b/c it deviated from the keyword list on the top that said "If it says X, then do Y; if it says Z then do A." I told him to ignore that, re-read the problem and think about what it was asking. Of course he said "oh I need to subtract." I feel like I"ll spend the summer undoing the damage that school inflicts all year.

So to answer the ?, my novice opinion is pace needs to be faster and depth needs to be deeper.

You have to bear with me here, sometimes words do not come easily in a second language I do not like that "forward or sideways " thing but could not think of anything else at the time.
I believe there is always going to be PACE problems for GT students, and there is really not much we can do about it. Even if our kids were placed in the classroom of five mathematically gifted kids, their pace would be all over the place. This is my son's biggest problem so far. This year he was finally mature enough to propose to his math teacher that he will be working on his own, ahead of the class. It was not perfect, but it was better than following the class pace. The class was small, but I imagine that other kids were also working at different pace. It is difficult to find a solution to pace problem. The ideal situation would be to work independently with a tutor.
I believe we can more easily find solutions to depth problem. Math contests.
We are frequently lamenting on this board that our kids are not challenged ,that everything is too easy, they are getting easy A's and not really learning the value of studying. Why aren't you guys signing them up for contests that will realy challenge them? Chances are, they are not going to be the winners (well, I am talking outside of class/school), they will learn some humility, they will see that they NEED to study way more than what is in the book.

If I was given a chance to do this over, I would have made sure that my kids were exposed to MathCounts and MOEMS since grade 4 at the latest, preferably sooner, and to AMC since grade 6.

Hi Ania,

I agree with you 100%. My dd8 suplements her school work with problems from CML and mathcounts. Some of those problems are very challenging, but she actually enjoys doing them. This summer she will also be working on JHU Distance Education - Math Olympiad.

What they learn in their class is definitely not enough. She came home with her last test results last week. She received a 131% (she did all the extra credit problems). She was happy, I was not. She is +2 years in math and still not challenged at all. Next year she will be able to compete in CML and maybe even Mathcounts depending on her beginning of the year assessment. Until then, I just have to provide her with extra challenge at home.

Must be some good news about math for you, Dottie, if you're "Feeling + about public school" right now.

Good!

I agree completely that deeper not faster is the ideal. But I also think that at younger ages, that's a lot harder to do.

We did the challenging word problems and the intensive math to ramp up the problem solving and slow down the speed. It was okay for a while, but there are only so many ways you can add 2+2 or 55+78 or whatever. Eventually, even that "challenging" stuff just isn't very interesting. Same stuff, different day, you know?

As long as the kids are still only getting calculation and haven't been allowed to dig into concepts (beyond the basics of sets and arrays and that sort of number concept stuff that kids do get in 1st or second grade), I really haven't seen much deeper you can go. (And I've been looking!) A little deeper than just a page of problems, sure, and every little bit helps. I am certainly a firm believer that problem solving is the way to approach pretty much *ALL* math. Word problems and tricky thought experiments are GREAT! But I'm not sure I believe that you *can* effectively go a whole lot deeper than the norm in early math without going pretty far from the normal ways to teach math. Calculation is calculation is calculation...

OTOH, so far geometry is a smashing success for DS6. Seriously, it's been tremendous! He *adores* doing the thought experiments that geometry require--and I'm approaching it from a problem-solving/experimental angle, so he has to figure stuff out for himself--and it seems to be precisely where his head is right now. He just shines when we work on it.

As for next year...Well, we'll see how things go with our goofy physics/calculus experiment. DH and I are kind of excited to give it a try, and if the geometry work from this year is any indication--and that seemed pretty outlandish when we first considered it--we may be on to something for our particular kid, But at least I know that what we're planning WILL be problem solving, with actual, real world problems, and that it WILL be deeper, conceptual math, not merely a faster sheet of the next kind of problems.

I'm babbling...Can you tell that I'm thinking a lot about next year's plans?

It's exciting, though, isn't it? When it finally seems to gel and it's working and you see your child shining?
I've seen it a little with DD8, let's hope we can get there with DD5!
Dottie, glad to see your excitement about school for the kids!

A friend of mine with a GT child several years ahead of mine talks about wanting to get her child through the elementary years as fast as possible, because that's where the spark usually gets snuffed. She says there's more "deep" to be had once you get out of the near perma-shallows of the primary grades. I didn't really get that until this year...

This is the way to go. Believe me , you want to do this now and not in high school, when your child begins to fail!

Another Bravo - I envy you being able to have a private teacher. How did you go about finding one?