Gifted Issues Discussion homepage Forums Parenting and Advocacy Question about algebra and radical acceleration

Well...I think it's like Texas Summer wrote some time ago: there are 2 sets of skills you need for math--the "tools," which are the rote knowledge of math facts, and the "concepts" which are more like the way things are done and why you're doing them. Two separate parts, and often two different ways of learning the parts.

Repetition is usually required for memorization of math facts. In our case, DS6 has mastered virtually every part of the *concept* of even multiple-digit multiplication--that it's about multiple sets of like groupings, carrying, etc.--but he currently lacks the *tools* because he's not yet ready to memorize his times tables. He needs both to progress (or at least a good work-around until he does the memorization). Repetition would/will help him learn those tools when he's ready.

OTOH, repetition was NOT necessary to help him with the concepts. He picked those up right away. Some kids can probably come to understand the concepts through repetition of the tools. But I don't think that this is most kids. I do think the way math concepts are usually taught is to have the class do multiplication problems ad nauseum and hope the child gets why things are done that way. But I do NOT think it is very effective.

For example, when my father was a very young child, he could do multi-digit math problems of all sorts in his head, giving the answer the second you finished saying the problem. Wow, right? But he did it backwards, starting with the 1000s (or millions, or whatever) place instead of the 1s place. When he got to school, the teachers saw that he was using the tools "wrong" (never mind that his conceptual grasp was ideal and that he always got the right answer fast!), so they drummed it out of his head. He can't do it anymore. They focused on the tools, not on the concepts.

For my part, I don't recall anyone explaining to me why we did math, say long division, the way we did. We were just expected to "follow the leader." The better you were at imitating the teacher exactly, the better your grade. When I got to calculus, I was a goner because we were expected to think, not to imitate, and I had no idea how to do that in a math class. It had never been asked of me before.

Of course, these are non-NCLB examples--two old ones and one from home school. Maybe things in school are different now? I just still don't understand what, exactly, is different. Please forgive my denseness, but I really would like to know!

K-

Maybe the more successful students in your calculus class were homeschooled!


hee hee hee hee

LOL neato!!!!

I do think things are different now in school. My children have been up and performing in front of their peers since kindergarten and have no fear of public speaking whereas I never did an oral report until 7th grade and about DIED to be in front of people for the first time. Also, in kindy last year, my DS now 7 was doing some pre-algebra type work!!! I asked the teacher about it and she said they were introducing the concepts at that age to get them ready for more difficult pre-algebra/algebra conceps later on. My DS10 has already done some algebra type work this year also. I don't believe I saw an "x" or a "y" until I was in 8th grade when I took algebra.

I honestly think my kids are doing much harder work at an earlier age than I did (of course that was a long time ago so maybe I can't remember everything ).

Oh yea this is soooo true. My DS10 has a math test pretty much every 4 days on some new concept. They move very, very, very fast in math. Luckily he catches on pretty easily and the teacher does do comprehensive tests every few weeks to make sure they are getting it, but there is virtually no drill involved. You have to move fast to keep up!

But WHAT is different? Can you give me a specific example? HOW are they making it conceptual? To be honest, what it sounds like is that they just aren't doing much teaching at all, either of tools or of concepts. Navel-gazing isn't teaching, and that's the impression I'm getting of it (albeit perhaps wrongly).

I don't call word problems conceptual (and those have always been around anyway). Is there more to it than that?

FWIW, DS6's workbook from 1st grade was no different than the ones we used when I was in school from what I could see. Not conceptual at all. Lots of repetition of the tools. I saw there were maybe more manipulatives in class than we used, but nothing else seemed significantly different. Certainly nothing "on its head" about the math he was doing. But that was only 1st grade, so I realize I don't know much here...

Do you know what curriculum it is? We are using 1st grade Everyday Math and it does have this kind of model. But it still seems very slow. And the spiraling! I swear it was after x-mas break when we actually got a NEW concept. I got a note today that it was a goal by the end of the year to have the kids memorize a small sub set of single digit addition. I'm quite sure we knew the whole addition table in first grade. I did go to an extremely kill and drill private Catholic school. We memorized incessantly without reason - all the presidents, countries and capitols, etc etc etc. So great for visual spatial me. I'm saying this as a mathy person with a mathy kid that goes to a very NCLB test score focused school. This is a school that hired a full time teacher this year just to focus on bringing up math scores for the bottom third of the class.

I remember sitting and learning long division trying to figure out WHY it worked. When I taught DS addition and subtraction with renaming I had to come up with a proof with manipulatives why this really worked. Once we did that, he was good to go. But before that, he didn't want anything to do with it. That and he can do a lot of 2 and 3 digit addition and subtration in his head.

Thanks, Dottie. That helps. I see now. It doesn't seem like navel-gazing (smirk), and it does seem better than the old-school method overall.

I guess I like the more intuitive start, but then I'd also want to make sure they drill sufficiently on the tools. I don't know why they can't do both. Neither is sufficient on its own, I don't think. Though 6 problems is a lot better than the 50+ we'd have to do...and none of that "do the last 10 that are hardest and skip the rest" stuff for us either. Ugh. That right there was enough to make me hate math forever. Calculus just put the nail in the coffin!

A more conceptual tack would have appealed to me, for sure.

We crossed paths, kimck, but as usual, I agree with you. The WHY would have made a big difference to me, as it does with DS6.

LOL! Concepts, tools, or both?

Are you guys talking about reform math? Hasn't that been around conceptually since the late 60's or something like that?
This is oversimplifying it, but it's about taking numbers apart and putting them back together. Playing with the numbers as opposed to straight memorization, if you will. I warned you, oversimplification! I've seen that instead of memorization they teach the itty bitty's to add/subtract using manipulatives, number lines, hundred's graph etc.

Even peeking over my shoulder at DD8 doing aleks, they teach quotient and remainder totally different then I remember.
I never remember doing estimating a sum. Doing a larger calculation in your head by rounding up to the larger numbers, adding/subtracting, etc. than subtracting away the number you added by rounding up to get the answer.

I kind of wish they taught math like that when I was younger, it seems more fun.

I think DD's favorite part of the day is the mental math test they have everyday. I agree with Kriston, drills have their use but mix it up, people, please!