Posted on 12/04/2002 9:41:55 AM PST by Lizavetta
Goshen – A new math curriculum plus confused students equals angry parents. At least when that new math curriculum is the Interactive Mathematics Program.
Under IMP, high school students learn from books that have more word problems than equations. Instead of traditional math instruction, IMP emphasizes students working in groups to solve a problem over the course of a few weeks.
Goshen has been using IMP for the past three years in its freshman, sophomore and junior classes. The district plans to add it to its 12th-grade curriculum next year.
But some parents want it gone.
"The whole program is a travesty," said parent Traude Ellert, who has made it her personal mission to convince the district to ax IMP. "It's like a cancer. We are using language arts books to teach math. I'm outraged as a taxpayer. Part of my money was used here."
IMP replaces the algebra, geometry, trigonometry and pre-calculus found in traditional math, where students are taught in a more structured setting and a teacher drills formulas. Students of IMP are taught in groups and spend weeks on one central problem or theme.
An IMP textbook states that it "does not teach directly." There is no index in the book for math concepts. Called "fuzzy math," IMP has received mixed reviews. In 1999, the U.S. Department of Education named it one of the nation's top five exemplary math programs in the country. But some Web sites call it a scam that frustrates parents and turns A and B students into C and D students.
Math is an exact science and IMP makes it cloudy, Ellert said.
"Don't mess with math," she said. "They messed with math and that's not OK."
Ellert, who teaches pre-GED courses at a state prison, began her own math group. Every Tuesday night for 90 minutes, she teaches math to a group of 16 freshmen, including her daughter, from a Math A Barron's Review Book.
The students meet in the art room of the high school, where Ellert gives homework assignments and rewards them with saltine crackers for correct answers. She doesn't get paid to teach and the students go on their own time, many sacrificing extra-curricular activities.
But they don't mind. It's better than learning what they call "CHIMP" math. "We call it CHIMP because it's so easy monkeys could do it," said freshman Katey Bischof, 14, an honors student. "We learned more in three weeks here (with Ellert) than we learned in three months in IMP class," said freshman Hillary Quinn, 14.
The students complain that there are no lessons, just stories; parents can't help them if they have questions because the book does not explain the math problems and the Math A Regents exam has nothing to do with IMP.
Goshen isn't the only school district with IMP. Newburgh also has the program but it is under review, said spokeswoman Rebecca Foster. By the end of next year, the Goshen School District will have spent about $65,000 funding IMP, said Superintendent James Langlois. The district added the program to adapt to changing Regents requirements.
By the time current freshmen graduate, they will have to pass English, U.S. history and global studies, math and science.
"We can no longer allow kids to slide by with the same understanding of math as they did in the past," Langlois said. "Everyone has to pass the Math A (Regents) exam." And that concerns parents.
"We're giving the tutors in the area a lot of business," said a mother, whose son is part of Ellert's group. "As soon as I saw the book, I saw a problem. I said, 'This is not math.' We need a blending of the old math and new math. I don't think anyone is against new and innovative ideas. But you need a basis."
But for Ellert, it's become a personal goal to get rid of the program. "I'm not stopping until this is gone," she said. "It's a travesty to the Goshen School District."
IMP word problem
IMP was created in 1989 by San Francisco State University professors Dan Fendel and Diane Resek. The program uses an integrated problem-based approach to teach algebra, geometry, trigonometry, probability and statistics. It is used in more than 350 schools across the country.
For more information, visit the IMP Web site at www.mathimp.org or contact Dan Fendel at 415-338-1805 or Diane Resek at 415-338-2071.
This is an example of an IMP word problem:
"Pick any answer"
Lai Yee has a new trick. He tells someone:
--Pick any number.
--Multiply by 2.
--Now add 8.
--Divide by 2.
--Subtract the number you started with.
--Your answer is 4.
1. Try out Lai Yee's trick. Is the answer always 4? If you think it always is, explain why. If not, explain why it sometimes will be something else.
2. Make up a trick whose answer will always be 5.
3. Pretend that someone gives you a number that he or she wants to be the answer. Using the variable A to stand for that number, make up a trick whose answer will always be A.
Source: Interactive Mathematics Program text book
The problem with "the problem" is that it tries to get the kids to "learn" something backwards from the way it would normally be done. Specifically, the problem is designed to get the students to "infer" some of the rules (Axioms) of arithmetic from the example given. Of course, in the real world of Mathematics (as taught in decent Universities), the first thing you are given is the Axioms of the MAthematical system you are working in, and then you DEDUCE various principles (Theorems) FROM THE AXIOMS, not the other way around!
In the example, the problem reduces down to the algebraic expression:
Which when you apply the axioms for arithmetic, reduces down to
In which the variable "x" always cancels out of the equation, leaving "4" no matter what you started with.
A house is built from the foundation up, not from the roof or living room down. Mathematics works the same way; you start with the axioms (foundation) and derive the rest of the structure therefrom. You don't start from a black box and infer what the rules (axioms) are, which is what this problem is doing.
This problem would be useful ONCE the student has learned the rules of Arithmetic, but is a waste of time as a mechanism for the student to learn the rules.
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Few people here under the age of 50 have probably had real "real math" as it was once taught in this country. In 5th grade we measured and calculated the area of the schoolground in acres. In high school I had the problem, "If you drop a ball off a cliff and hear it hit 20 seconds later, how high is the cliff?" With my old math I was able to write a 1,000 line computer program to analyze horse races. I was able to derive some of the fundamenal equations of calculus such as pi Rsquared before reading that chapter in the book. I can derive a Pearson product moment around a curvilinear form.
The reason for this is that these teachers don't like the subject of mathematics, they never have (that's why they became teachers instead of, say, engineers), and consequently they find it difficult and painful to teach. They don't even understand what they are teaching well enough to do so in an interesting way, so the students lose interest.
Of course, from such a teacher's point of view, the problem must be the textbook and the "way" in which the mathematics is being taught, and the textbooks. It couldn't possibly be that the teacher is a bonehead at mathematics. Nope.
The sample question was a fine word problem for students who have already learned the basic underlying algebra concepts.
I shudder to think what goes on in regular (not the smartest) students' minds if this problem is shoved in their face before they've learned to grasp equations like "x+4=10", however.
Fuzzy math isn't about correct form but correct answers! Fuzzy math algorythms are used in the auto focus function on you camcorder. Real world correct answers are more important than form! I've seen/created great business models. I've also seen the failure of the enterprise regardless. I worked for a company which used my budget models to chart its course from a $100K/month revenue stream to $30 Million per month. We lost focus and just before a downsizing, (and eventual hostile buy out by the competitor who had forced this issue), our VP of Sales/Marketing owed up to his inattention and stated, "Well, I guess I'll have to give up my Friday Golf Games!!!"
He had mucho salary,commissions and stock options and he fled before the fall. The models were good the execution was crap!
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Amen. It's converting math to a group-think love-in with people dependent upon each other producing answers equal to the sum of their individual fears and incompetences.
Sadly this is sometimes true - especially in elementary school. Elementary teachers are often language arts people, not math. I am a math teacher. My son-in-law is an engineer. I love math for being math, he loves math to use it.
The one reason more teachers don't love/teach math is money. After 20 years, my salary as a classroom teacher is less than half of his with less experience.
My niece was having trouble with math (she was in 3rd grade, now 4th), and her mother asked me to help out. One "problem" was that she still used her fingers for math problems. Her mother wasn't too pleased when I encouraged her to continue with this - use the tools you've got at hand, so to speak... Anyway, the trick was, as I saw it, to let her use her fingers, just make the problems more difficult, so you've got to be creative.
To put this in perspective, I have a doctorate in physics, but I still use my fingers regularly when solving cross products, just to see the right-hand rule. I almost always wrap my fingers around when doing E&M problems to figure out how the magnetic field will affect things, etc. This is common in physics, we see it all the time. I see no reason a grade school student can't use the same tools.
Anyway, now she's in 4th grade, and we play a game called Nemo. Here's how it goes: Take toothpicks, as many as you want. Make an arbitrary number of piles of toothpicks, with as many as you'd like in each pile (hopefully none more than 31, or you'll need both hands for the solution). On your turn, you may remove as many toothpicks as you would like, but only from a single pile. The winner is the person to pick up the last toothpick.
Now, if you're good enough at math, adding and multiplying by 2, you can solve the problem right from the beginning, ang guarantee a win. Here's how: For each pile, figure out how many toothpicks are in the pile, and break it down into powers of 2. For instance, a pile with 19 toothpicks would be 16 + 2 + 1, or 2^4 + 2^1 + 2^0. Now, let each finger on your hand represent one of the powers of two - we usually let the thumb be 0, and the pinky 4. Put down each finger represented in that sum. Now move to the next pile, and do the same thing. Only, this time, when you're moving your fingers, put it down if it was up, and up if it was down. For instance, say our second pile has 7 toothpicks, or 4 + 2 + 1, or 2^2 + 2^1 + 2^0. Then, our thumb and index finger, which were down, go back up, and our middle finger, which was up, goes down. Continue this until you have "done" every pile this way.
If all your fingers are up, and it is your turn, you will lose unless your opponent makes a mistake. Period. If you have any fingers down, you will be able to win. To figure out your move, do the calculation again, excluding the largest group. See which fingers you have down, and use the sum above. That's how many you want to leave in the largest group. So, using the above examples, where we had 19 and 7, we would just do the 7 - leaving out first 3 fingers down. Adding them up leaves 7 (this is a simple example, we usually play with 5-20 piles), so that's how many we want to leave. We remove 12 from the larger pile, leaving 7, and will win the game. In future turns, you always want to leave your opponent with the symmetric solution (all fingers up.) At some point, he will have to leave you with all the toothpicks in 1 pile, which you then pick up and claim victory.
This makes heavy use of your fingers for doing the math, but you can't just count. My niece plays quite well, and she's also doing great in math now, since she gets so much practice. So don't knock using your fingers...
Drew Garrett
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Make that 60.
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