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Greg Barlow, an Air Force officer in the defense secretary's office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?
The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school's new math textbook, "Investigations in Number, Data, and Space," Christian tried breaking the problem into easier-to-digest numbers.
But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. "How would you do that another way?" Barlow asked.
What a horror show.
Here's a picture of Greg.
Anyone recognize that expression of exasperation?
This'll make him feel better.
"I don't know what happened in Prince William. Have the parents visited the classrooms? This has to be a decision made by everyone that's affected by it," said Cathie Dillender, a senior Pearson executive who handles math issues. "We have a lot of happy customers out there. We're all educators, too, and we certainly wouldn't publish a program that would not work with the kids."
Sure you wouldn't.
As for Greg Barlow in Prince William, the former fighter pilot with college degrees in aeronautics and astronautics, he finds himself in a new role: home-school dad. He has spent about $100 at Sam's Club and Costco on math textbooks.
Poor bastard.
The engineers and scientists are always the canaries in the coalmine.
25 comments:
KEN!
Sometimes I wonder if schools honestly don't understand the criticism leveled against fuzzy math. Then I get over it.
You would think their response would be that they understand that some don't like it, but they feel that these programs are best for all kids. They don't say that. They say that they are better.
The school educrats are more concerned about rewards and awards for innovation than they are for the achievements of each individual child. Very few educrats were proficient at math as students - they would have chosen another field of study if they could understand real math.
That would be Prince William County, not Prince George. Very different places.
Amy P
From the article...
"Knight said Prince William revamped its elementary math in part to raise "embarrassing" SAT scores that were below national and state averages last year."
Does anyone really believe that imposing TERC on K-3 is going to improve SAT scores 10 years down the road?
BURNSY
What about the kids whose parents' math skills aren't as strong as an engineer's? If they can afford it, there's always Kumon or online courses such as Johns Hopkins' CTY. But what about families who don't have that kind of cash?
The children who will be most hurt by the "fuzzy math" program are those whose parents are less educated and less affluent (who are also disproportionately African-American or Latino). These families also have less ability to simply move to a town with better schools, enroll their kids in a private school, or homeschool.
One of the elementary schools (Marumso Hills) is 61% Hispanic. If english-speakers don't understand it, can you imagine the spanish speaking parents trying to wade through it?
Carol Knight has to use the SAT scores to justify the change to Investigations because as many have pointed out, there was no "math crisis."
BTW, I'm in neighboring Stafford county. We adopted Everyday Math 3 years ago. Thus, my kids are still homeschooled. Some parents I know of 4th graders are seeing the lack of skills their kids possess and the lack of traditional algorithms being introduced. We too have lots of military families - they know it's garbage. I predict an uprising here soon.
Prince William County is in Virginia. Tucked between Fairfax, Loudon, and Stafford counties.
[Prince William officials cite research from the "Investigations" publisher showing that the percentages of students using the curriculum who are passing state exams have increased in school systems in 20 states. Prince William's data showed that 80 percent of second-graders who used "Investigations" in the past school year were proficient in all 10 skill areas of a Stanford Diagnostic Mathematics Test.]
I think voodoo math helps raise scores in a perverse way.
Parents who see voodoo math are horrified and start teaching their kids. The kids then become more proficient and get better scores.
"Researchers" then cite the higher scores as proof that voodoo math is great.
"'Researchers' then cite the higher scores as proof that voodoo math is great."
It's all relative. I know that in our town, things were really, really awful before. I'm not talking about 25-40 years ago. A few years ago, they were using MathLand. Then they started using Everyday Math. They saw improvement on the standardized tests. Duh! They went from really, really awful to really bad. On top of that, they are now trying harder because of NCLB. Parents are paying attention to the scores and they better go up. That's good ... up to a point. So what do we have now? Everyday Math that they can point to and show improvement. Big deal!
Our school just had a big open house about Everyday Math. Apparently, they were getting some flack, so they held a PR event. This was not to get input from parents. It was to "inform" parents. They are the experts. Parents are not.
I'm sure tests get a boost from parent help or tutoring. My son got a 97% raw score on the test. They don't care how he got it. It makes them look good. They could take a very simple survey of the parents of kids who are taking algebra in 8th grade. They don't do that. They send home a stare-required survey that ONLY asks whether we parents feel prepared to support our kids at home.
Go easy on me - I'm not familiar with Investigations of Whatever (I'm a homeschooling mom using everything from Singapore and Math Mammoth to university texts) but does, "Christian tried breaking the problem into easier-to-digest numbers." mean he broke it down as follows:
(600 + 200) + (70 + 40) + (4 + 9)
If so, that seems like a really good exercise and it's how I would do that question in my head. I don't see anything voodoo or fuzzy about that.
Or maybe I'm wrong. Does fuzzy mean the particular methods being taught or that those are taught to the exclusion of traditional methods?
Hi Ken!
I've been experiencing D-Ed Reckoning mortification....one of the comments I wrote on your blog is WRONG, WRONG, WRONG.... (the one reward & putting things on cue...)
GREAT FIND
Boy, if I were Pearson I would not want to eff with the Pentagon.
The school educrats are more concerned about rewards and awards for innovation
One of Mike Schmoker's books says that across the board award-winning schools are worse than non-award-winning schools.
He says that to win an award the school has to marshall all its resources, fill out applications, send in portfolios or god-knows-what -- awards bestowed upon schools are invariably a sign of low quality.
Which is hilarious given that our middle school is the only school in the district that is award winning.
It is a National School of Excellence.
Meanwhile on the Just for Kids site Elizabeth told us about the middle school is far below the average for good NY middle schools.
What about the kids whose parents' math skills aren't as strong as an engineer's?
Hi, Crimson!
You're new around here, I gather.
(That's a joke - this site started back when I first began trying to teach math to my child without having engineer skills...)
We have the same survey.
Tri State Consortium - right?
blech
Parents who see voodoo math are horrified and start teaching their kids. The kids then become more proficient and get better scores.
Remember when, quite awhile back, we were discussing the "fact" that scores initially go up with these programs but then drop significantly when the kids hit middle school??
Was it Anne D. who was saying that?
I've seen that pattern more than once, including in Scarsdale with Math Trailblazers (and I presume we're going to see it here, too).
The Scarsdale scores were very interesting. Before they adoped Trailblazers their K-8 math scores were ahead of Irvington's always.
Then (iirc) Scarsdale adopted Trailblazers and their scores in elementary school went up. (I may have this part wrong - I don't know if their scores went up or if they always had higher scores than Irvington.)
In any case, Scarsdale's strong 4th grade math scores relative to ours were one reason we adopted Trailblazers, I presume.
But as soon as the Scarsdale kids got to middle school their scores plunged and, in 8th grade, were significantly below Irvington's scores.
Same story with the retired Schaumberg teacher I met at the airport. She said their scores had soared with Everyday Math, but their 8th grade scores were a mess.
She didn't make the connection - she thought the middle school needed to adopt fuzzy math, too. Then their scores would also be great.
Of course, from her POV, that was logical.
"Fuzzy" in this case probably means the school has refused to teach him the standard algorithm - not that they've taught him to use the standard algorithm and are also giving him practice in the associative property.
Is associative property right?
The other hallmark of fuzziness here is the confusion and, above all, the struggle. This child can't do the problem. He's drawing lines all over the place, he's stuck, his dad is coming to the rescue --- this is pretty much the standard trajectory.
"Go easy on me - I'm not familiar with Investigations of Whatever (I'm a homeschooling mom using everything from Singapore and Math Mammoth to university texts) but does, "Christian tried breaking the problem into easier-to-digest numbers." mean he broke it down as follows:
(600 + 200) + (70 + 40) + (4 + 9)"
Probably not.
Usually the intent here is to transform, in this example:
674 into '675 - 1', and
249 into '250 - 1'
Notice that we've got much nicer numbers to work with. So ...
675 - 1
250 - 1
-------
925 - 2
And then you count down by two to get 923.
Another version would be:
674 = 700 - 26
249 = 250 - 1
--------------
950 - 27
923
What is *annoying* is that I often do this myself ... but:
*) It requires *very* good number sense, which 7 and 8 year olds usually don't have (and one way to get this number sense is by lots of practice with the standard algorithms)
*) If it breaks down, I can always fall back on the standard algorithm. These kids don't seem to have been taught this algorithm.
I don't see anything wrong with this approach, I just wouldn't teach it to 7 and 8 year olds. I would *never* teach it to 7 and 8 year olds as the primary approach...
Hope this helps.
-Mark Roulo
Dawn,
One reason I call this approach voodoo math is because its proponents rail against practice (drill and kill) and committing knowledge to memory. Kids are supposed to become proficient by magic. Then you have the neurotic aversion to efficient algorithms. Constructivists claim traditional algorithms are harmful to children.
I was looking at 5th grade EM and saw that the lesson on fraction division tries everything to avoid invert and multiply. Apparently, invert and multiply is an impossible task. Instead, they try other approaches. One is quite interesting. For fraction division, they find the LCD and rename the fractions. Then you divide top by top and bottom by bottom.
You might have seen the Inconvenient Truth video that shows different ways to multiply. I find exercises that stress place value and expanded notation to be useful. But see how TERC does it. Working memory overload! And it's with friendly numbers to boot. Imagine what happens when the numbers get unfriendly.
I link to this video at my site:
http://instructivist.blogspot.com/2007/01/fuzzy-math-video.html
Dawn,
My husband had the same initial reaction to seeing a brief demonstration of fuzzy math that you did and he has his degree in math. It all looks good on the surface. However, from what I understand, they do teach this method to the exclusion of other methods.
Singapore does teach algorithms "coneptually" before teaching the algorithm, however, the student is not required to write down the the concepts using algebraic notation. Instead, they briefly work with manipulatives, learn to do a few problems mentally, and then proceed to the algorithm. In Singapore, the student doesn't have to catch on to the concept in order to successfully take tests, he could simply memorize number facts and algorithms and do quite well, although not as well as a student who had recourse to various methods of solving the same problem.
"Then you divide top by top and bottom by bottom. "
Can you give a specific example?
The example EM gives is
6 div by 2/3
Change 6 to 18/3 and divide the numerator and denominator by the numerator and denominator of 2/3.
This gives you 9/1 or 9.
The fly in the ointment is that the problem is designed to yield a whole number as the quotient.
It gets messier when you try this method with, say
3/5 div by 2/3 where the end result is a fraction. It'll confuse the kid since you get 9/10 over one.
So, efficient algorithm avoidance leads to limited applicability but the gains in deep conceptual understanding are enormous.
Thanks guys.
I heard some of the fuss over fuzzy math and I've seen that video Instructivist but I think I wasn't quite understand the whole.
To be truthful, I've sometimes searched for constructivist stuff because it seemed like a great way to stretch the kids and a good compliment to what we're doing at home.
But as Mark pointed out, it's probably a good compliment because the kids are very familiar with the standard algorithm.
What is *annoying* is that I often do this myself ... but
Singapore Math teaches - and practices - these techniques in mental math exercises.
Myrtle
Have you read Liping Ma's book?
If not I think you'd like it. At one point a Chinese teacher explains the divide the numerator by the number to and the denominator by the denominator method to Ma & she says she'd never heard of doing it that way.
Of course, neither had I.
But as Mark pointed out, it's probably a good complement because the kids are very familiar with the standard algorithm.
I think that's probably true (that constructivist math exercises can be a good complement).
But that's where I'd just go with Singapore Math in the first place (or else with Saxon supplemented by by Singapore or Singapore supplemented by Saxon...)
Catherine, One of the very first lessons in Saxon 6/5 to teach division of fractions uses the numerator-divided-by-the-numerator and the denominator-divided-by-the-denominator approach. It later teaches using the reciprocal method.
In between the two methods, it uses a whole number (2)divided by a fraction (1/2) or 3 divided by 1/4 to teach the student to think "How many 1/2's are in 2?"
or "How many 1/4's are in 3?" etc. In talking with the students on how we could solve this problem, we usually start with "How many 1/4's are in 1" and progress to "How many 1'4's are in 2, or in 3?" I had a student who said he knew how to solve it and I let him show us. He changed the 3 to 12/4's and divided numerator by numerator and denominator by denominator.
It should be noted that we had previously worked on other ways to write a 4 or a 3 and we may have used 12/4's to name 3. At least that's what I figured had taught him that!!!
I had never heard of that method but it worked on those types of problems. The method does become more challenging (for 5th graders) initially when you try it on 3/5 divided by 2/3. I've got 2-3 students who would get it, but it's not worth confusing the class yet.
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