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19 Dec 2005 - 02:08

## death march to Algebra

Christopher's class took the Chapter Three test on November 30.

They will take the Chapter Five (Rational Numbers and Expressions, aka fractions & decimals) test on Tuesday, December 20.

Chapter 5 content:

5-1 equivalent fractions and lowest terms
5-2 fractions and decimals
5-3 rational numbers
5-4 comparing and ordering rational numbers
5-5 adding and subtracting rational numbers
5-6 working backwards
5-7 multiplying and dividing rational numbers
5-8 rational numbers with exponents
5-10 multiplication equations
5-11 the stock market

After tomorrow, the kids will have had thirteen school days to study Chapter 5.

Of these, one was a snow day, and they had a substitute teacher on Friday.

So, 11 days of instruction to cover....11 huge topics. Fractions. Decimals. Equations with fractions and decimals. In 11 days.

Judging by the homework Christopher has brought home, and by what Christopher himself says, they've only gotten as far as 5-7.

That leaves three units, 5-8: rational numbers with exponents, 5-9: addition and subtraction equations, and 5-10: multiplication equations, to get through tomorrow, one day before the test.

They've had some coverage of addition and subtraction of fractions. I know this because Christopher told me yesterday that Ms. Kahl had showed them how to borrow, but it was confusing everyone, so she said they should just convert the mixed number(s) to improper fraction(s) and do the subtraction that way. That's what he was planning to do for the rest of his life.

I told Ed to tell Christopher he was going to have to learn to borrow no matter what Ms. Kahl said. Ed did, and Christopher cheerfully agreed. Boys love their dads.

We are in rote-land. Tonight Ed gave Christopher a problem like this one:

2/3 x 5/6 x 3/10

Christopher knew that he could cross out the 2 and the 10, and write a 5 next to the 10. Ed was thrilled.

Then he asked Christopher why he could do this, and Christopher said, "Ms. Kahl told us we could." They studied the properties in Chapter One, but Ms. Kahl does not seem to have pointed out in class that the commutative property and the multiplicative identity property make it possible to 'cancel' numerators and denominators. If she did tell them this, and she may have, she did no formative assessment to discover whether Christopher either heard or understood.

Apparently she keeps early office hours every day so kids can come in for extra help. I didn't know this. You'd think this information might be pointed out, stressed, and underlined for the parents, but no. The kids are, as their Grade Contract states, 'fully responsible' for their grades.....so nobody told me about it. At least, I don't remember it if they did.

I'm not that interested in 'extra help' in any case. We're way past 'extra help.'

It's obvious that the only way to get him through this is to begin serious study for the Chapter Test the minute the previous chapter test is done. We started doing fairly serious extra problems 5 days ago, but that wasn't nearly enough. I suggested to Christopher that he stay home tomorrow to study for the test. He doesn't want to.

But things may yet come to that.

pre-algebra is bunk
death march to algebra
NYU ed textbooks; NY math test

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OT question: how is Christopher liking his new Language Arts class?

-- CarolynJohnston - 19 Dec 2005

The stock market? What's the stock market doing in there?

I mean, there is lots of maths around the stock market. But most of it is a rather more advanced level than fractions and decimals.

Perhaps they are referring to the points language used in stocks.

-- TracyW - 19 Dec 2005

He's not in the class yet.

I hope they change him this week; the kids are teasing him mercilessly.

It's a dreadful situation for everyone. The fact that the principal, one of the few men in the place, is moving Christopher out of the class is a clear vote of no confidence; at least, it is to the kids.

So now the kids are riled up about that. One of his closest friends is especially upset, I think. He's constantly telling Christopher that the principal is 'bad' because he moved Christopher; Mrs. Roth is a good teacher, etc.

The other day they had a sub, and the kids were going on and on about Christopher, so Christopher got up and left to go to the bathroom, and told everyone he was going to stay in the bathroom.

(Where was the sub during all this? I don't know.)

While he was away another friend bawled out all the kids and made them apologize when Christopher finally came back.

That was good, but he needs to move to the new class. At this point, it's bad for the other kids.

-- CatherineJohnson - 19 Dec 2005

She needs to go.

We found out from another dad (I think I mentioned this) that his son reported to him that Mrs. Roth has specific kids she picks on.

Christopher was one.

-- 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.

Christopher does essentially zero word problems in this course. I'm not kidding when I say rote.

During the course of a chapter he might do 1 or 2 word problems; then she might spring 1 on the chapter test.

Even KUMON does more word problems than that, and they're integrated into the practice; they come at the exact point they should come to illustrate why we would do the operations we're practicing.

However, Christopher's class isn't going to do the Stock Market section. I don't think they did the 'Work Backwards' section, either.

-- CatherineJohnson - 19 Dec 2005

I've completely changed my view of word problems.

When I was a kid, I thought they were hard.

Now I think they're essential—and if they're hard, it's because they haven't assigned the right story problems to the right material. Obviously, word problems become hard as you advance. But the word problems you begin with should clearly and simply illustrate the material the student is learning.

Word problems are the real 'manipulatives'; they're the concrete illustration of why a person multiplies or divides fractions.

-- CatherineJohnson - 19 Dec 2005

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

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.

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

here's another thing......Ed and I were talking about the one boy in the math class who aces all the tests. His mom told me he doesn't even like math.

We were wondering how he was getting all those 96s and 98s.

Ed said, 'His parents are probably helping him. They're both really smart.'

This is one of those HUGE misconceptions about what it takes to teach well.

Being smart is, at best, a help.

I'm plenty smart; I'm as smart as that kid's parents, and so is Ed (and Ed has actually taught high school math to GED students in Newark).

I would have to be an expert in curriculum design to do what I need to do with Christopher.

I'm not an expert, and I'm not going to be.

-- CatherineJohnson - 20 Dec 2005

I'm going to hound this school district about formative assessment until they either establish a district-wide policy of formative assessment or my kids graduate out of the school.

Then I'll keep on hounding them as a Concerned Taxpayer.

-- CatherineJohnson - 20 Dec 2005

I don't want to hear, EVER, that a teacher challenged my kid.

I want to hear if a teacher actually taught my kid.

Teach him first.

-- CatherineJohnson - 20 Dec 2005

I ordered the DI math book.....

-- CatherineJohnson - 20 Dec 2005

We talk about the difference between Saxon & Connected Math.

It's night and day.

The difference between Saxon & Prentice Hall is night and day, too.

-- CatherineJohnson - 20 Dec 2005

I've got one of the KUMON word problem sheets scanned in; I'll get it posted.

You'll see what I mean. KUMON is all about practice, overlearning, and automaticity.

But the procedures aren't tricks.

-- CatherineJohnson - 20 Dec 2005

I ordered the DI math book.....

It's a shame that only about 1/4 or 1/3 will be useful to you at this point.

-- KDeRosa - 20 Dec 2005

Well, I think there's a case for challenging kids occasionally - Friday afternoons, towards the end of term ...

But not on something that will be on the test.

-- TracyW - 20 Dec 2005

I've got to get a new compare-and-contrast post put together one of these days.

All you need to do is take one look at the way Russian Math handles a topic versus the way Prentice-Hall does, and you're done.

Basically, the difference is: Russian Math has actual math.

-- CatherineJohnson - 20 Dec 2005

How about a compare and contrast post pertaining to objectives.

Here's an example of a longterm objective from the DI curriculum book:

"Given a worksheet with 20 addition problems up to 3D + 3D + 3D with and without regrouping, the student will write correct answers with 90% accuracy on three consecutive weekly classroom exercises."

That's downright Kumonesque.

Good luck trying to find an objective to compare this to for the fuzzy curricula.

-- KDeRosa - 20 Dec 2005

"Given a worksheet with 20 addition problems up to 3D + 3D + 3D with and without regrouping, the student will write correct answers with 90% accuracy on three consecutive weekly classroom exercises."

That's downright Kumonesque.

Yup

That's KUMON

90% is ALWAYS defined as mastery

the folks here are going to fall out of their chairs when they realize that 'teach to mastery' means 'everybody gets an A'

-- CatherineJohnson - 20 Dec 2005