Notice, too, that the Prentice Hall book has word problems separated out into separate sections, rather than integrated into all the lessons.

Procedures are taught separately from the purposes for which these procedures are used.

-- CatherineJohnson - 19 Dec 2005

I just looked at the stock market section.

It's actually a good idea, probably. The point is to do story problems involving mixed numbers, because stock prices are written as mixed numbers.

That's dated information. The NYSE and NASDAQ switched to using decimals some time in the late 1990s, i.e. 5-7 years ago.

So when I buy WMT, I can put in a limit order for 10 shares at $45.67 per share. You're not limited to 1/16ths (or was it 1/64ths) anymore.

-- KtmGuest - 19 Dec 2005

That's dated information. The NYSE and NASDAQ switched to using decimals some time in the late 1990s, i.e. 5-7 years ago.

good grief

I looked at it very quickly.....but I know they said 'mixed numbers.'

btw, I have an old copy of the book. They may have changed it by now.

-- CatherineJohnson - 19 Dec 2005

Thanks!

-- CatherineJohnson - 19 Dec 2005

Why does the stock market use fractions?

In 1997, the Common Cents Stock Pricing Act was signed to simplify the stock market by converting the fractions to decimal. This decimalization of the stock market began in August 2000 and will continue until all the stocks and markets are converted. Besides simplifying the market, decimalization will dramatically change the spread for many stocks with the potential to have a spread of just a penny (.01) under the new system.

Hmm, here's a lesson called Stock Market Math.

"Students will be able to use fractions and decimals to calculate the cost to buy or sell various stocks using the stock market quotes high and low listings."

Is that the sort of thing you were thinking of?

-- KtmGuest - 19 Dec 2005

I wouldn't say it's anything that complex.

It was just a way to have the kids multiply a mixed number for a reason.

-- CatherineJohnson - 19 Dec 2005

Hi Catherine,

It's okay to be in rote-land, for awhile. He won't be there forever. Yes, it's a deep, dark forest, and very scary, but it's a place where you should not look up, not even for a moment, to look at the trees, let alone the forest.

Christopher needs to keep his head down, eyes on the path, and follow the path out. He needs to memorize the rules, and you & Ed check to see he's understood all the rules. Don't sweat the conceptual understanding in this circumstance -- if he's memorized the rules CORRECTLY, understanding CAN COME.

Don't beat yourself up over the lack of time to explain the "why" of the rules. Emphasize the UNCHANGEABLE NATURE of the rules, as cheerfully as you can. Good Luck!

-- BeckyC - 19 Dec 2005

Christopher needs to keep his head down, eyes on the path, and follow the path out. He needs to memorize the rules, and you & Ed check to see he's understood all the rules. Don't sweat the conceptual understanding in this circumstance -- if he's memorized the rules CORRECTLY, understanding CAN COME.

Don't beat yourself up over the lack of time to explain the "why" of the rules. Emphasize the UNCHANGEABLE NATURE of the rules, as cheerfully as you can. Good Luck!

OK, I am taking this to heart!

Also, I'm going to tattoo it to my forehead.

-- CatherineJohnson - 20 Dec 2005

Actually, I was feeling a little better tonight.

Christopher is now working much more cooperatively with me, and the 'timed-practice' business is good so far.....and tonight I saw that he does have some of his skills down.

We've been dealing with severely shaky skills AND no conceptual knowledge. I'm realizing that if you're going to have not-enough time to practice the skills to mastery, then I want conceptual knowledge, the kind of conceptual knowledge you can have without strong technical skills.....Conceptual knowledge does seem to help with memory. If he's going to remember nothing of the procedures and have no conceptual knowledge, the whole year is going to be like a blackout.

So.....I was thinking: we have to at least have some conceptual knowledge.

But in fact, tonight I could see that his fraction skills—purely technical—aren't half bad.

If that's the case, then yes, I can live with picking up understanding later.

-- CatherineJohnson - 20 Dec 2005

Thanks!

-- CatherineJohnson - 20 Dec 2005

While on the train ride up to NYC today, I read the DI math curriculum book's chapter on fractions. The book focuses on teaching and mastering the procedures and only gives enough conceptual understanding necessary for the kids to understand why they are using the procedure taught and if that would be too complicated they skip it. Here's what they say about dividing fractions, "Because a lengthy explanation for this procedure, we recommend presenting the strategy in the elementary grades without rationale."

Done and done.

The teacher merely presents the rules: "We cannot divide by a fractionnumber; we must change the problem to a multiplication problem. Here's how we do that: We invert the second fraction and change the sign."

Now practice until mastery

I'm thinking it's better to have the rule be automatic than to understand conceptually why the rule is applied. I can do these types of problems in my sleep now even with complicated algebraid expressions and even though I understand the rule conceptually that understanding almost never comes into play when I'm actually dividing fractions. It's all about the procedure.

And, by the way, I've yet to see any more than one procedure taught in the DI curriculum for any particular math problem. You want to divide two numbers? Great! Use the standard algorithm. Better to know one algorithm to mastery than five half-fast.

-- KDeRosa - 20 Dec 2005

I'm thinking it's better to have the rule be automatic than to understand conceptually why the rule is applied. I can do these types of problems in my sleep now even with complicated algebraid expressions and even though I understand the rule conceptually that understanding almost never comes into play when I'm actually dividing fractions.

I know that's what we've all been thinking.

But it's different when you see it in real life. It's not just the constructivists who are suffering a 'lost in translation' problem.

First of all, there's no practicing to mastery. None, zero. There's no time, because they have to go so fast and math is just one subject in school.

AND neither the textbook nor the teacher are organized to provide such practice, as Saxon does.

I'm not a curriculum creator/writer, and I'm not prepared to create this practice for Christopher myself. I'm trying, but I'm not there.

The level of 'rote' we're talking about—and I use the word purposely—is the level of teaching only the shortcuts. We're not having good teaching of procedures; we're having bad teaching of procedures.

Christopher is learning learning math tricks without word problems. No word problems.

Oh, except when a difficult word problem turns up on the test. That's the first time they see a word problem using the tricks they've halfway learned.

KUMON HAS WORD PROBLEMS.

Remember Steve saying that his algebra teacher required them to write each step along with the property that justified that step?

Christopher's teacher hasn't even taught them how to write a series of steps in line, each step below the step before. I've had a slugfest with him trying to get him to do this. Now that Ed's on the case, I'm making some headway, but it's still a struggle.

Writing out the steps for solving an equation or simplifying an expression should be overlearned by now. He thinks it's craziness, and doesn't know how to do it.

Given his lousy handwriting, which all the kids have because they've never been practiced to mastery on handwriting (another failed effort on my part, as well) he desperately needs practice writing the steps IN LINE, EACH BELOW THE OTHER.

nope, doesn't get it

I'm serious, you guys.

'Traditional math taught badly': this is what got us into the mess we're in in the first place.

-- CatherineJohnson - 20 Dec 2005

preview of Coming Attractions

Our neighbor, who's in 7th grade, says his teacher puts trick questions on her test.

I'm already mad about that one, and I'm not even there yet.

This is the teacher who justified last year's lousy Phase 4 class test averages of 74 by saying, 'I want to challenge your children.'

Fine.

Don't bother teaching them; forget about mastery, overlearning, and automaticity.

Challenge them.

TRICK THEM.

That's money well spent.

-- CatherineJohnson - 20 Dec 2005