Steve H

This is my one objection to Math Olympiads.

A lot of schools are obsessed with those questions today, and the whole point of them is to be 'trick.'

I'm going to write about this at some point, but a lot of schools will have kids spend days laboring over one Math Olympiad question on grounds that it is challenging.

This is the flip side of watered-down fuzzy math: problems that are way too easy and problems that are way too hard.

The whole concept of teaching one step ahead of the child's actual level is gone.

-- CatherineJohnson - 27 Jun 2005

Carolyn's right: in this case I misread the question.

It's a standard misreading an adult would make, but it's still a misreading. (It's true, though, that the precise word would be 'separating,' not 'dividing.')

I think the activity is terrific, now that I know what it is.

I keep mentioning that I've been reteaching myself elementary math, and going through these basic exercises of 'disaggregating' numbers, sums, products, & quotients has been important.

It's also led to confusion in the realm of multiplication and division that I can't capture in words, but that I think is 'good' confusion, meaning I'm eventually going to have better understanding because of it.

-- CatherineJohnson - 27 Jun 2005

Yes, I'm sorry that I've gotten into this discussion a bit late -- busy day! The "adult" in us will read the word "equal" into that sentence "find various ways to divide 10 cubes into two groups". We just assume it means "into two 'equal' groups" because that is what a divisor does -- it divides a large group into smaller, equal groups. Well-taught, older students who understand division, will also make this assumption of "equal" groups.

It's not a bad activity -- I did this with my first grade students 40 years ago. However, each student had his own sticks for sorting into sub-groups and there was none of this "group" work.

More specific information must be given to the students by the teacher, and as suggested, the word needs to be changed from "divide" to "separate" or "sort".

-- CarolynMorgan - 27 Jun 2005

The silver lining of Everyday Math, which my son uses in school, is that he gets lots of practice with vague or trick questions. I don't want him to be unprepared later on when his math ability is tested with these stupid questions. If he sees a "rule box" question, he will know what to do. Unfortunately, some feel that answering vague, misleading, or trick questions is an indication of intelligence. I think it is more a matter of whether you have seen it before.

-- SteveH - 27 Jun 2005

Isn't it beautiful!???

-- CarolynJohnston - 27 Jun 2005

Yes, JD has it right. It's an ill posed problem of which there are many in the world of "real life" math. One problem in a 2nd grade math text asks the students to compare another classroom to yours and tell if it is bigger. It fails to define what is meant by bigger: more volume, more floor space, more seats? Of course, kids will come up with various answers to which the teachers will be delighted--just what they learned in ed school, there's more than one right answer.

-- BarryGarelick - 27 Jun 2005

oh JD!

That's exactly right!

I was feeling like a dunce ... but then I was thinking, Well if I made that mistake, isn't a 7 year old going to make it?

Of course, given that a 7-year old doesn't know how to divide yet, probably he isn't going to make the mistake I did -- but then why encourage him to think of 'dividing' as 'separating.'

(btw, it may have been the journalist who chose the term 'dividing.')

Saxon Math always uses the word 'separating' to speak of subtraction, and it's been incredibly helpful.

Let's see.

He'll contrast 'problems about separating' with 'problems about combining.'

Thank you.

I feel better.

-- CatherineJohnson - 27 Jun 2005

Sounds like a bad choice of words. They are not 'dividing' 10 cubes into two groups; they are 'separating' them into two groups--1 + 9, 2 + 8, 3 + 7, etc.

-- JdFisher - 26 Jun 2005

What does this mean?

Just back from Washington & am addled (hot there & hot here--)

I'm hot, tired, & cranky enough to feel I'm missing something here:

One second-grade lesson encourages students to work with a partner to find various ways to divide 10 cubes into two groups. This lesson helps students identify sums that equal 10, an essential component of addition that will help them later with more-complicated calculations.

Isn't 10 divided by 2 always 5?

What do you think this activity involves?

Are the cubes different colors?

Does anybody know?




source:
Bitter Single Guy

Duval gives 'new math' good grade
(no longer available online 5-14-06)

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