Skip to comments.Teens criticize 'CHIMP' math (fuzzy math alert)
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
Thank God for homeschooling and SAXON math.
But then again, the NEA follows the liberal guidelines of form over substance. Why are we experiencing a math and science curriculum crisis?
I pointed out to my daughter that this is the same problem that doomed the prior NASA Mars probe. Oh the FORMulae were correct! It was the insertion of English rather than metric variables that caused the loss. Ergo the FORMulae worked but the Answer did not. $40 Million down the ole crapper!
Social/socialist math. In a few years they can meet as a group when they try to calculate change for a dollar at McDonalds.
Hey, I was homeschooled, and my ma threw Saxon books at my head, and I taught myself advanced algebra and calculus as a highschooler. I was a darn good student if I do say so myself, and not turned off to it in the least. Heckuvalot more interesting than history or lit...
The above is anecdotal and I was the exception rather than the rule because I was a frickin' geek, but I disagree with your assessment in general. High school math is not supposed to be FUN. It is supposed to be functional, and if that means grueling and repetitive to get the message across, then so be it. Good students will hack through it and do what they must to get to more interesting stuff.
Actually I deal with this all the time. Consider the following:
You and three buds go to the bar. By two o'clock in the morning, as you are getting kicked out, the tab is shown to be $113.78. Bud #1 drank four beers and a shot of jag. Bud #2 drank five shots of jag. Bud #3 drank 9 beers and mooched jag off somebody else. You drank 5 beers and three shots of tequila. If jag is $5/shot and tequila is $4/shot, what does everybody owe?
And then you set up your equation, assuming you can see straight--
4b + 1($5) + 5($5) + 9b + 5b + 3($4) = 113.78, where b = price of one beer. Solve for b, and tote up the rest. (Actually I am getting b ~ $4, which probably means that the bartender figured y'all were too wasted to notice and stiffed ya for an extra $20 or so, so that is something else that you will have to deal with...)
And don't forget tip...
/p> I've always wondered why people complain about cash registers. Do you really expect people to add up numbers in their head all day and memorize the price of every single item? Any way, I wouldn't be bothered by this if they simply asking seniors to apply what they have learned. One of the things that stands out in mind from the statistics classes I took in college was how much trouble people had with word problems. If you can't read a paragraph and draw on the body of knowledge you've acquired then that learning is largely wasted.
Amen, friend. The founder of Saxon Publishing was confrontational with the 'mainstream' educational establishment. He would challenge any school system to compare results with his methods versus any other -- free of charge. With his death, the children now run the company, and they're now just trying to 'get along' with the Socialist math claque -- unfortunate.
When attempting to learn math the ability to organize information is VERY important. Higher order problems often involve many different calculations. The teacher may simply be trying to teach his students to organize their problem in an effective manner. If they aren't organized, their chances of success are greatly reduced.
Tell that to the homeschool population where Saxon is the main math text. We are currently using Saxon 54 (4th/5th grade) and Saxon 76 (6th/7th grade) with impressive results. If my kids were Einsteins, Saxon wouldn't work. But my kids are normal to bright, and the repetition/incremental approach is providing them with a solid grounding. It's a damn sight more than I got in my government school education.
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.
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!
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...
Make that 60.
Learned responses can lead to creative and inventive outcomes. We know that Edison wasn't the "genius" that is portrayed in the movie, "Beautiful Mind". But Edison did invent the 20th Century. I visited that little lab in New Jersey as a high school student. What a marvelous place!
He gave the world light, sound, camera, and action!!!! His talent was to surround himself with intelligent and creative individuals and then he made his dreams a reality!
Social/socialist math. In a few years they can meet as a group when they try to calculate change for a dollar at McDonalds.
And in a few more after that they'll meet as a group to calculate what your allotment of McDonalds Vegan Delux Gruel should be based upon your race, enthusiasm for social justice, and footprint upon the earth mother...
He dropped out of school in the 3rd or 4th grade. His mother DID educated him for some limited period of time.
My daughter, last year in 8th grade, spent two weeks writing an essay for her math class. Why? I never quite figured that out.
This same school, a Catholic elementary school, wasted years of these students lives with the Univ of Chicago Math books. My youngest had it from 1st grade, by the 4th grade could not even add single digit numbers. And she was the norm for the class. They did finally get rid of this stuff, but it took a lot of complaining. My hubby and I went to a kids' book store that carried homeschooling supplies and got Saxon math books to get her up to speed.
Okay; but his mother's participation in his education was also fairly limited in the sense that he was doing experiments on his own at a very young age, building telegraphs and such, and was employed by the Railroad by the age of 12. Beyond the first few years, he was for all practical purposes self-educated.
I "figured" that you would be interested in this.