ummm ... convert everything to decimal
and eyeball it (with a millimeter ruler).
anyhow, that's the "real world" solution ...

-- VlorbikDotCom - 14 Nov 2005

RUSSIAN MATH has some whoppers....but frankly I don't think any of them is this baroque.

Actually, this problem goes beyond barogue to Rococco.

RUSSIAN MATH has students do quite complex circle graphs—but students construct the graph themselves.

They don't turn somersaults just trying to read a chart someone else has constructed.

I'll find the ocean problem & post it later...

-- CatherineJohnson - 14 Nov 2005

Catherine,

The thermometers and the red bar on each of them (representing dollars raised) are a given.

My head is beginning to spin thinking about this elaborate task.

I don't think this task or exercise is bad in itself. It's exciting for people who like to puzzle thinks out and who have the necessary math knowledge. The problem whith fuzzy math is that it doesn't give pupils the necessary math knowledge (computational skills, math facts, algorithms, etc.)

The compromise in the math wars I could see is giving pupils a sound math foundation along with elaborate tasks like this.

-- CharlesH - 14 Nov 2005

Here's what's still stumping me.

Who puts the dollar amounts on the thermometer in the first place?

(Or is the thermometer a given....is this an elaborate exercise in figuring out how to read a graphic illustration?)

-- CatherineJohnson - 14 Nov 2005

"Fraction rulers whose units are given by the 8 1/2?

That much I can see, but I'm not then following the second half of the assignment, which is to convert everything and plot it on a graph...."

Yes, I guess you could call the student-made strips fraction rulers.

If you have trouble following the assignment, imagine what the kid is facing.

The goal of the assignment is to come up with dollar amounts derived from the thermometers and then to plot these amounts over time (fundraising progress).

How are you going to derive dollar amounts if all you have is an 8 1/2 in long thermometer (representing $300) and a red bar on the thermometer (equivalent to the money raised so far)?

You could measure the red bar in inches, form a ratio, calculate the decimal, multiply the decimal by 300.

The assignment calls for measuring the red bar with the "fraction ruler". Then you would know what fraction of 8 1/2 the red bar represents. Then form the ratio with this fraction, come up with a decimal to calculate the dollar amount. All very complicated even if you are a ratio wiz.

I totally agree with your statement:

"These math programs are ludicrously low-level & ludicrously high-level at the same time."

-- CharlesH - 13 Nov 2005

I first noticed this at the big Phase 4 math meeting last year.

There was zero talk of teaching & learning to mastery.

Everything was 'challenge.'

'I want to challenge your child.'

They were giving the kids problems that were way over their heads, and hadn't been taught in class, but that could be justified as a challenge—which, yes indeed, it surely was.

-- CatherineJohnson - 13 Nov 2005

This is exactly what you see when there are no boundaries.

These math programs are ludicrously low-level & ludicrously high-level at the same time.

-- CatherineJohnson - 13 Nov 2005

Boy.

I'm not following this assignment.

The point of the fraction folding was to create 'fraction rulers'?

Is that right?

Fraction rulers whose units are given by the 8 1/2?

That much I can see, but I'm not then following the second half of the assignment, which is to convert everything and plot it on a graph....

-- CatherineJohnson - 13 Nov 2005

I just confirmed that is was Scott Foresman Addison Wesley. Go figure.

-- NicksMama - 13 Nov 2005

He is currently using Everyday Math. I'm not sure what he was using last year when I saw the lattice work.

-- NicksMama - 13 Nov 2005

Nicks Mama

Which text is the 5th grader you're tutoring using?

-- CatherineJohnson - 13 Nov 2005

Many thanks for putting this up front.

I need to make a correction on making these fraction strips.

Where I said:

"Or you could divide 8 1/2 by the various fractions..."

it should have read: Or you could divide 8 1/2 by the INVERSE of the various fractions.

This adds another layer of complexity far beyond the capabilities of the mathematically crippled kid. Dividing by the fractions tells you how many fractions should be on the strip, e.g. 8 1/2 divided by 1/5 gives you 42.5

Dividing by the inverse gives you the length of the fraction (1.7). Now convert 1.7 to 1/16's so you can use the inch ruler!!!

Now try doing this with the remaining fractions up to 1/12's as required by the CMP task used as a homework assignment!

-- CharlesH - 13 Nov 2005

Yes, I recently tutored a 5th grader victim of fuzzy math. At 10 years old, he can't divide 150 by 2 in his head.

I recalled that he spent a great deal of time drawing grids for a unit on lattice multiplication last year. Maybe he should have been working on the basics?

-- NicksMama - 13 Nov 2005

another connected math story

This was posted on the PenfieldInTheNewYorkTimes thread today by CharlesH.

In the spectrum of mistakes made in the Connected Math series, this is at the other end from MySpecialNumber: projects that are so difficult and time-consuming that, in the end, the child learns nothing from having done them.

Here's Charles:

Giving people a choice is the democratic thing to do and is also a good political strategy. It should satisfy everyone. It's an inoffensive offensive. But I doubt that zealous educationists in a position of power will go along. Being responsive to reasonable popular wishes is not their thing. I also suspect that many parents are not conversant with the math issues and won't know what to do with choice.

Just yesterday I talked to a parent of a sixth grader I am tutoring in math who had no clue of fuzzy math. (I tutor disadvantaged kids after hours in addition to my regular classes.)

I was helping the kid do homework. Part of the homework required the kid to cut a sheet of paper into strips to make various fractions. The parent was aghast and thought it was a time-waster. I had to explain the purpose of the exercise. It was all news to her.

The school the kid is in uses the fuzzy series Connected Math. The homework assignment was quite demanding and way beyond the kids abilities. She had neither a conceptual understanding of the task nor the requisite tools (computational skills, procedural knowledge, math facts) to accomplish the task had she had a conceptual understanding of the problem. This is a key problem with fuzzy math. It is quite pretentious on the one hand, and refuses to teach the necessary skills on the other. The result: the kid was hopelessly drowning and getting straight F's.

Now what was the task? It was a real-world problem.

A class was holding a fundraiser to raise $300.00 in ten days. The progress was shown in the form of thermometers showing progress in two-day increments. The thermometers were all 8 1/2 inches long and showed the money raised so far on the various days in red. The fraction strips were to be used to determine the amount of money raised so far on the various days and then to plot the progress in a coordinate plane. The kid was to make the strips and mark fractions from 1/2 to 1/12 on the various strips.

Making fractions strips of 1/2, 1/4 and 1/8 is of course easy. It's not so easy to come up with 1/3, 1/5, 1/12. You could do time-consuming trial-and-error folding. Or you could divide 8 1/2 by the INVERSE of the various fractions. This adds another layer of complexity far beyond the capabilities of the mathematically crippled kid.

Dividing by the fractions tells you how many fractions should be on the strip, e.g. 8 1/2 divided by 1/5 gives you 42.5

Dividing by the inverse gives you the length of the fraction (1.7). Now convert 1.7 to 1/16's so you can use the inch ruler!!!

Now try doing this with the remaining fractions up to 1/12's as required by the CMP task used as a homework assignment!

Even if you can get the numbers they don't work well with an inch ruler. You could approximate. Suppose you (meaning the kid) could accomplish all that. Then what? She was supposed to find the strip with the right fractions and measure the red thermometer bar (money raised). Then she had to add the fractions and know how to calculate the decimal from the red bar to total thermometer length ratio to finally determine the amount raised to begin plotting. All this without instructions in CMP and without computational skills and procedural knowledge.

No wonder the kid is drowning. What a tragedy.

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• Posted by: CarolynJohnston
• LogDate: Nov 12, 2005 @ 23:30

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