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Constructivism, as practiced by CMP is actually an amalgam of discovery learning, clothed in multiculturalism, with a dash of politically correct, story vignettes to 'connect' the child to real world problems. It's not that these things, in and of themselves are inappropriate, it's just that the program throws so much into a one day lesson, the math gets hijacked.
It's not atypical for one of these vignettes to have a dark skinned blue eyed child, named Ming lee, sitting in a wheel chair, talking in Spanish to her friend Sascha from Russia. Put that in front of a child who is reading at a third grade level as an introduction to a seventh grade lesson on solving proportions, and you have the makings of a nightmare. It's very hard at times to get by the intro.
Then when you get into the lesson's problem sets it is very often the case that the problems serve up a hodge-podge;fill out a table, look for a pattern, find equivalent fractions, make a graph, and on and on. It makes my head explode sometimes and I've been doing math forever.
I understand the need to make connections and provide spaced repetition but it should never get in the way of base understanding in the topic at hand. When it does, and the paradigm is discovery/group learning, the results are not pretty.
The math gets lost in a blizzard of roadblocks around; the weird names, and how come we saw that guy in the wheel chair last year, and are trees really alive, and why is the Chinese guy speaking Spanish to a Russian, do I really have to make a table, and on and on.
You mix this altogether and it's a toxic stew for behavior because each child is hung up on a different facet of the jewel. If you can't put all these fires out fast, really fast, the third of your class that is ADHD gets going with the third of the class that is laughing at the goofy names, while the last third passes notes about the day's scoop.
The math is lost. Instead of providing a structure to hang the practice and spaced reps upon, CMP rips the structure into tiny little pieces in the arcane hope that the kids will put it all together again.
C. and I used to laugh about the many and multi-splendored names of the children populating Saxon's word problems. The one I remember best was: Monifa.
Monifa?
Who in the world is named Monifa? (Apart from a pygmy hippo in Australia, that is.)
Of course today I wonder whether the choice of "Monifa" was John Saxon's little in-joke on multi-culturalism in math books.
16 comments:
We are truly doomed methinks. Many of the names that I see on my roster have to be misspellings in the delivery room. I have kids tell me that I'm spelling their names wrong so I go and look up their intake docs and sure enough, I had it right.
I don't want to put up actual names but some examples are; ett where the intent was eth, cha where the intent was sha, cr where it should have been chr. That's just the beginning.
Then you have what I call the 'theme meme', like a daughter named Chastity with a mom called Virgin (should it be the other way around, perhaps).
I'm not sure if these things are coming from deranged nurses or parents who can't spell. Either way, doomed!
Yes, methinks CMP needs a little clarity. Of course, I haven't seen the second edition--I hope my info is out of date.
And FYI--CMP doesn't teach division of fractions at all. Nowhere. In the whole sequence. So if you were wondering why your child doesn't remember how to divide fractions, now you know.
The second edition is prettier, with more and better color pics (yeehah). Did I ever tell you guys about the consultant conversation I overheard?
It was all about how we, as math teachers, weren't leveraging the pictures enough (to excite the kids about math). I have a student who is struggling with finding equivalent fractions. He's probably above the 90th percentile.
Here's the dilemma. If you have something like 4/20 and you want to change it to a percentage you can; use a benchmark (simply recognize it as 1/5 or 20%), convert it to x/100 (knowing that the numerator is then 5x4, so 20% again), or you can divide and multiply by 100 (.20 x 100 so 20% again). This student can do this kind of stuff at will, along with a few other neat tricks you would never think of. The problem is that if I give him something like 4/9 he's dead in the water. He actually told me that no one ever taught him how to do that.
So even though he's got a nifty bag of tricks for common and friendly numbers, he really doesn't have a deep enough appreciation of what's going on to extend his 'tricks' into a meaningful, extensible, universal, algorithm. With the kind of numbers he'll encounter in the real world he's uneducated.
This is the ugly truth of discovery learning. You only learn what YOU discover. It's like that little blind mouse who describes an elephant by feeling its tail. While the teacher is running around the room deciphering the pictures and teaching 2nd grade skills, the students, the really bright students, discover what they happen upon.
The rest, well, that's left for next year's teacher to deal with.
The district is using proportions here to get around division with decimals, although they did make a 2 day attempt at teaching division as a technique to convert a fraction into a decimal. (successful students will be considered for Accelerated 7th)
What percent of 9 is 4?
%/100=is/of
x/100=4/9
Cross multiply:
x=400/9
divide
x=44.4 (repeating) %
Alternatively for those that weren't taught division in elmentary and didn't get it in this lesson, one simply rote memorizes 1/9 = 0.11(repeating) and multiplies by 4 to get 0.44(rep). Same for 1/2,1/3,1/4,1/5,1/6,1/7,1/8 (bonus pts for recognizing this as 1/2*1/4) and 1/9. This year they had ten days to get their table memorized, up from 4 days two years ago.
Who in the world is named Monifa?
Tch, tch. Monifa is an African girls' name -- and not a rare one, either. It's also used by folks in the Caribbean, esp. Trinidad. A lot of African given names are unusual to American ears -- but with more and more African refugees here, and children with African names attending school, I don't have any concerns about including multi-cultural names in math books, nor in portraying kids in wheelchairs etc. -- but Paul B's example does take it a little to the extreme.
Interestingly, DISTAR did this way back in the '60's. The first versions of DISTAR Reading showed children of varying races and cultures with and without white canes, walkers and wheelchairs (which were never an issue in the stories -- the kids would be engaged in regular stuff, and the pictures would just happen to show different ethnicities or disabilities).
Paul B, there's a trend now towards using very original spellings of otherwise familiar names -- Breeyanna, Meekeighla, Charise (there's your cha example), Abbigayle, etc. You can't chalk it up to poor spellng, people are intentionally spelling the name in an original way.
Point taken on the names. Why then, do the kids insist on telling me that I'm spelling it wrong?
The problem is that if I give him something like 4/9 he's dead in the water. He actually told me that no one ever taught him how to do that.
That's exactly what I found with my 6th grade Math Master's students (top of the class). If the denominator wasn't a factor of 100, they could not get a percentage, period.
When I told them they should consider the fraction line to represent division, and that they could convert every fraction to a decimal via long division (which they knew, amazingly) they were stunned. The "aha" moment was one I'll never forget--they thought this was the coolest thing they'd seen.
They were all stuck on either visual fractions (e.g., 1/8 of a pie) or "friendly numbers"--thank you, Everyday Math....not.
We used to laugh at math textbook word problem names back when I was a kid in the '80's. All the black, Hispanic, and Asian kids in our school had normal names like Larry, Ginny, Angela, Bryant, Laurie, Elena, and so on. So we never understood the exotic names in our textbooks...
Tch, tch. Monifa is an African girls' name -- and not a rare one, either. It's also used by folks in the Caribbean, esp. Trinidad.
You would know that!
That is soooooo John Saxon! All through his books he uses extraordinarily rare vocabulary words; gratuitous vocabulary!
It's just like him to use a real African name as opposed to the multicultural names in the other textbooks.
So if you were wondering why your child doesn't remember how to divide fractions, now you know.
What's bad about this, apart from the obvious, is that you can't just pick this up when you're 17 and headed off to college.
It takes 10 years for memories to "consolidate" in the brain, and I now think consolidation is probably essential to being able to use elementary school math in college math.
Here's a post about Jim Milgram's experience with Stanford students trying to make up for lost time.
Consolidation is key! I've got a post up on something like consolidation. I think learning is largely a process of imprinting pattern on our pattern sensitive brains. What we perceive as factoids might really be just lint on a giant canvas and it's the canvas that we should be 'teaching'. Check out Face It on my blog.
True story! At a school meeting considering Sing. Math:
"We can never adopt these books, there are no pictures of children of different races!"
That was all that mattered to that guy. BTW-Everyone in the meeting disagreed with him, then proceeded to point all of the varying children in the books.
CassyT, that's hilarious! (In a sad way.) When I was growing up, we had no pictures whatsoever in our math books except for diagrams of circles, vectors, conic sections, constructions, etc. Maybe if they took out all the useless photos and drawings of children discovering math, the books would be more useful, smaller and lighter, and as a bonus, the school board couldn't complain about the races of the children in the pictures.
expert memory:
The researchers say this means that experts do not have a larger working memory capacity than non-experts. Instead, their memory is more detailed. If experts really had a larger capacity, then they should be more accurate when the faces shift from upright to cube versus inverted to cube. They're not, even though they could spot a different upright face three times more often than a different inverted face. So experts remember more details, just not more different items.
is expert Memory Better than non-expert memory?
I think this is support for the observation that experts have long-term memories stuffed chock-full of content.
PREVENTING classroom discipline problems should be the number one goal of all programs and policies dealing with behavior --- !
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