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Plus the fact that it's a bad problem. Students haven't been taught the linear algebra necessary to solve it. It's not the type of problem that generalizes into a class of problems and which can serve as a foundation for more complex ones. It stands as a "top down" approach in which in the paraphrased words of NCTM: Understanding is the foundation upon which skills are then learned.

-- BarryGarelick - 01 Jul 2005

I have to say: just reading through the problem I have no idea how to solve it using conventional high school algebra.

Doesn't it have a gazillion variables?

Can it be solved using high school-level algebra?

I've been noticing lots of problems where you have to list endless arrays of 'combinations'--that must go along with the idea that in addition to always having more than one way to solve a problem, many or most problems have more than one answer, too.

-- CatherineJohnson - 01 Jul 2005

You know, the word 'abuse' really does jump into my mind, reading this problem.

I've restrained myself from saying this so far, but I have frequently felt, listening to the problems in the grade 6 phase 4 class, that the class is 'abusive.' I have thought and said that word.

The kids are suffering. These are 6th graders crying at night because they can't do their math and they got a 60 on the last test.

Their parents are being told they 'don't belong' in advanced math, that the course is only for the most gifted students.

It's c***.

-- CatherineJohnson - 01 Jul 2005

Absolutely right. It is abuse. I talked about that very word with Sandy Sstotsky and others in talking through the op-ed that I'll write some day (!!). They agreed with me that abuse is correct, but it carries too much baggage (e.g., Michael Jackson, priests convicted as pedophiles, etc), plus it connotes that teachers are the abusers and that's unfair. Teachers are stuck with these wretched programs. So we've settled on "educational malpractice" which has opened up a very rich avenue of inquiry indeed.

As for the haybaler problem, it requires some knowledge of combinatorics and linear equations, neither of which students would have had in the 9th grade. Not to mention the fact that no farmer in his right mind would ever weigh bales of hay that way, bringing into question of how "real life" is this piece of c***? David Klein solved it and explained it to me and there is one solution. But as he says, had he been forced to do it in the 9th grade, he would have hated math.

-- BarryGarelick - 02 Jul 2005

They agreed with me that abuse is correct, but it carries too much baggage (e.g., Michael Jackson, priests convicted as pedophiles, etc)

Definitely.

Still, educational malpractice wouldn't describe the situation I've seen, 'from afar,' in the 6th grade math class this year.

The problem there isn't a constructivist text, btw.

They use Prentice-Hall.

But they have a constructivist attitude.

-- CatherineJohnson - 02 Jul 2005

My dad was a farmer.

Definitely, no one in the entire Middle West ever constructed such a table.

I probably don't know what combinatories are.

As I say, we're going to have a full month's worth of these problems thrown at us next September, if the course is not radically reformed over the summer.

My plan is to have Carolyn solve them while we carry on learning math around here.

(Hi Carolyn!)

-- CatherineJohnson - 02 Jul 2005

Barry, do you have any thoughts on Kumon Math?

Robert Talbert thinks it's probably good.

-- CatherineJohnson - 02 Jul 2005

Hi Catherine!

Now I know your nefarious plans for me.

-- CarolynJohnston - 02 Jul 2005

Since we are on the subject of educational malpractice, I want your comment on a particular situation. The first student I tutored is now going to be a senior in high school.

When she was in middle school, she got a D in pre algebra in the 8th grade. Her mother was worried about how she would do in algebra, so I tutored her over the summer. Very typically, we had to go back to fractions and teach middle school math. But she got it and did fine in algebra and geometry.

This year, she had Algebra II. She was getting an A until the final, then she got a 60. The teacher won't show her the final because she gives the same one every year. So she doesn't know if her problem was the material or some accuracy errors.

But here is the real issue: the teacher recommends that she take precalculus next year, not calculus. She want to major in some type of science in college. I say she needs to take straight calculus. If she passed all her other classes, she should be ready. All the kids that she will be competing against for college entrance will have at least calculus on their transcripts. But I think the teacher has her convinced that she can't do it.

What do you think?

-- AnneDwyer - 02 Jul 2005

The teacher should show her (and her parents) the final. This sounds fishy to me. I can see not wanting to hand out copies, but she should be able to see her final in a meeting with the teacher.

The best thing to do would be to get hold of an assessment test. Hmm... I wonder if there is a final assessment for precalculus math in the set that David Klein drew up for California... I'm going to check it out.

-- CarolynJohnston - 02 Jul 2005

No, those only go up to 8th grade. But here is a link to an assessment test specifically for placement in AP Calculus AB, which is the AP class that she'd most likely take (the other is AP Calculus BC, and I don't think most schools offer both).

-- CarolynJohnston - 02 Jul 2005

As usual, someone on this site always manages to come up with exactly what I need. I pulled off the assessment test. It will make an excellent review for me also. Then, using the test, we can make an informed decision about whether she is ready for calculus. Thanks again!!

-- AnneDwyer - 02 Jul 2005

I think Carolyn's advice is exactly right:

• the teacher needs to show the girl & her parents the test, in private if necessary. She doesn't need to give them a copy of it (I think that's obnoxious, but ok...). But she needs to give this girl feedback about what went wrong.

• I emailed with Ralph Raimi about the issue of parents being able to assess their own kids without shelling out several thousand dollars to an educational consultant. He said, absolutely, use free problems you can find online. He suggested using Singapore Math tests, but that was just off the top of his head. I'm sure he'd say the AP problems are good, too.

In short, what was reassuring to me was that he didn't see the kind of assessment we're all needing to do as anything mysterious or subtle.

Find a good, sold set of problems representing whatever level your child is or should be at, give them the problems, and see how they do.

I was very reassured by that.

-- CatherineJohnson - 02 Jul 2005

I've got to corral John to come help us out here.

John & my friend Lissa.

-- CatherineJohnson - 02 Jul 2005

Overall, I liked the assessment test. It was very heavy on calculation and very light on word problems, but it is only meant to determine if a student has enough skills to take calculus. But, in general, I don't think an assessment test should be multiple choice. It is hard to tell whether the student can do the whole problem or just enough to guess at the right answer.

When I give my tutoring clients an assessment test, I give them mostly calculation problems. I usually give four word problems: one problem is slightly below what they should be able to do. It is easy to read and very straight forward. One problem is at their grade level. It uses straight foward numbers but is multistep. If they are above 3rd grade but still in elementary school, the third word problem involves fractions. It is usually a problem from Singapore math that has several steps clearly deliniated with an a, b, and c. They should be able to get at least part of the problem. The fourth problem is a multistep problem that requires that the student have some logical way (ie bar model or equations) of keeping everything straight.

-- AnneDwyer - 04 Jul 2005