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This is not to say that skill mastery is not expected in Everyday Math. Fact automaticity is expected and nurtured through various games and practice routines.Hmm. That appears to be the extent of the expectations for mastery. I don't disagree, except I think we need mastery on much more than the basic facts.
The final document with the word "mastery" in it from EM comes from the 2001 Algorithms in Everyday Mathematics. The paper states as a justification for the non-standard algorithm the fact that in one study (not identified), only 60% of US 10-year-olds achieved mastery of the traditional subtraction "borrowing" algorithm. Unfortunately, EM doesn't tell us how many US 10-year-olds achieve mastery of the alternative algorithms EM has used to teach subtraction for the past 15 years.
Anybody have any data on whether US 10 year olds are faring any better these days?
Based on the EM website, it seems that calling EM anti-mastery is probably a fair characterization. Discussion?
14 comments:
I picked up on this same quote about the 60% of students fail, and asked someone at McGraw Hill some questions about that quote. This has been documented in my article which appeared in Ed Next, along with the name of the person who never supplied me an answer but asked me if I was a reporter and who I was writing the story for. Her name was April Hattori. She has since left McGraw Hill.
I decided to inquire further, however, and after the article was published, contacted Andy Isaacs. He said they couldn't find a cite for it but were trying to find it. I bugged him again some time later but they couldn't find it. First I heard from Andy's colleague, Jim Flanders who said:
"Sorry, it fell off the radar. I'll try to resurrect my line of
investigation through Max. It's a long story, but I think the fellow
who wrote the paper did it during a course as a graduate student of
Max's but who since has abandoned academia. It wasn't published, so
I'm hoping that Max still has it. If not, we would have to track it
down independently and I'm not happy about that prospect. So let me try Max one more time."
Some time passed, and then I heard from Andy Isaacs:
"I'm sorry to say we have not been able to track the cite down -- it appears to be somewhere buried in the memory of one or more of the first edition authors and we haven't had the time to comb the literature closely enough to identify the study. At this point, the best we can do is assure you that the pseudo-citation will be deleted in the next revision of the materials. Sorry not to be more helpful. If we manage to locate the study, we'll let you know."
I was not happy with his answer so replied as follows:
"What upsets me is that the 'pseudo citation' as you term it appears prominently and has thus been considered by many schoolboards in their decision making process. Who knows how reliable the rest of your "research" is? I do note that a large portion of EM's research base was conducted by personnel connected with EM (William Carroll figures prominently)."
He replied:
"OK. You say that you don't like EM and are not reassured by this pseudo-citation. While we don't want to encourage you to go over the rest of our stuff with a fine tooth comb, (I WONDER WHY NOT; BG) we do think you should get some perspective. First, we discuss lots of research results, almost all of which are properly cited -- we don't, in fact, know of any other such lapse on our part. It seems as though you are throwing out the baby with the bath water. We suspect, in fact, that this is precisely your aim. Second, if you look at the research bases for other curricula, you will find that ours is far more explicit and well articulated than what exists for any other curriculum (or at least any other curriculum we know of). Compared with perfection, EM certainly falls short; compared with other curricula, we do much, much better. Third, the research that forms part of the basis of our materials is only one form of research related to EM. There is also the vast body of research about student achievement with EM, which is again imperfect but is far more extensive and higher-quality than exists for any other curriculum. See, for example, the number and quality of the EM studies in the research the recent National Research Council panel looked at: At least two thirds of the higher-quality comparative studies identified by the panel were of EM, far more than any other the other four elementary curricula had."
It gets a bit ugly after that, but my concluding statement was:
"If you do choose to withdraw the 'psuedo-citation', I believe it would be proper for a statement to be made to the effect that the citation was removed because there is no evidence to support it, and apologize for any false impressions it may have caused."
Andy's reply:
"Thanks for the advice."
Your tax dollars at work.
I'm assuming this exchange came before the WWC showed that much of the EM research was in fact a sham.
Yes. The exchange took place in 2005.
My favorite quote:
Algorithms and Everyday Mathematics by Andrew C. Isaacs
"Reducing the emphasis on complicated paper-and-pencil computations does not mean that paperand-pencil arithmetic should be eliminated from the school curriculum. Paper-and-pencil skills are practical in certain situations, are not necessarily hard to acquire, and are widely expected as an outcome of elementary education. If taught properly, with understanding but without demands for “mastery” by all students by some fixed time, paper-and-pencil algorithms can reinforce students’ understanding of our number system and of the operations themselves. Exploring algorithms can also build estimation and mental arithmetic skills and help students see mathematics as a meaningful and creative subject."
I had an exchange with Mr. Isaacs over this (and other) quotes in this article, with the same sort of non-response as Barry. I was basically told to look at the big picture. After all of the criticism they have gotten, I'm surprised they haven't pulled the article.
"... not necessarily hard to acquire ..."
So do it.
"... widely expected as an outcome of elementary education..."
But they wouldn't do it if they could get away with it. They see no linkage between mastery and understanding.
"... but without demands for “mastery” by all students by some fixed time..."
Mastery is just not that important in EM. Look at the homework sheets; barely enough for any kind of superficial understanding.
This whole paper is filled with this stuff.
So, yes. EM is anti-mastery by definition. That's why so many schools supplement it. But I have found schools using that term and not really doing anything about it. It's no guarantee that the kids will ever learn invert and multiply. Supplement is a great way to get parents off your back.
I talked with our school board representative, Janie Strauss (Dranesville District, Fairfax Co. VA)about my concerns with Everyday Math. I've relayed this elsewhere but the only assurance she could give me was that Fairfax County School Board advises schools that EM should be supplemented. They don't say with what materials or how. As a result, each teacher does it differently.
My daughter's fifth grade math teacher, (who is from China), essentially supplanted EM by using copies from the older textbook, and gave the students lots of problems to work out. The only thing that he used from EM were the pre- and post-tests.
Her third grade teacher didn't use EM at all, and relied totally on the previous textbook (Harcourt Brace's "Math Plus" ).
The problem with supplementation vs supplantation, is that EM jumps around so much, that you can't supplement it. In the midst of teaching fraction multiplication suddenly they jump to measurement of angles. So the best way to supplement it is to ignore it and use a better textbook. Easy to say; hard to do.
My view is that EM was designed for the full-inclusion market. This requires no filters (high expectations of mastery) that would separate the kids by ability, and spiraling of the material so that kids get to see the same things each year. Move the kids along "without demands for 'mastery' by all students by some fixed time". "Exploring algorithms can ... help students see mathematics as a meaningful and creative subject." Add in a bunch of modern ed-school hype of no one right method, and you've got a hot product.
Lower expectations. Little or no mastery. Math appreciation.
The education world is so bad that this sort of curriculum was not laughed out of existence before it even got started.
" EM jumps around so much, that you can't supplement it."
Exactly. It's hard to supplement an anti-mastery program with mastery. You can add more problems to the HomeLink each night, but that doesn't stop EM from hopping off to another topic the next day.
To the deleter of the comment:
Andy? Is that you, Andy?
Nope. Just me deleting a duplicate post, but it does look suspicious.
This is an interesting thread.
EM is Anti-Mastery!
Then there is my old thread:
EM's Smoking Gun!
News flashes from the Daily Math Enquirer!
Yawn.
Somebody's laughing at us.
Perhaps they are a little concerned, but not much, unless we can get a lot more parents to pay attention. They already get away with ignoring mathemeticians.
Who wrote Algorithms in Everyday Mathematics? Was that Andy Isaacs? THere is no name attached to the paper on the EM website.
So it sounds like it was Max's fault, huh? I notice that since 2005, the paper, with the bad quote, is still easily available on the EM website.
Still, assume for a minute that the quote is true -- only 60% of US kids mastered the traditional, "borrowing" algorithm for subtraction. If we accept it as true for the sake of the argument, do we have any evidence at all that more than 60% of US 10-year-olds can subtract double digit numbers using reform algorithms?
do we have any evidence at all that more than 60% of US 10-year-olds can subtract double digit numbers using reform algorithms?
Exactly so. In fact, here is the direct quote from the "Algorithms in EM":
“In one study, only 60 percent of U.S. ten-year-olds achieved mastery of the algorithm using the standard regrouping (borrowing) algorithm. A Japanese study
found that only 56 percent of 3rd
graders and 74 percent of 5th graders achieved mastery of this algorithm.”
The questions I originally sent to McGraw Hill inquired: What test
was used? Were all schools tested?
How was “failure” defined? Were any
follow-up studies conducted? And similar questions about Japan. I remarked that a generation of adults appears to have mastered the traditional algorithms
just fine.
LynnG, related to mastery... I found the following comments solicited from teachers and included in a 1996 review of EM written by a Palo Alto parent. The review is still posted at MathematicallyCorrect.
Spiraling
"Every concept is taught 5 times in 5 different ways over two years before mastery is expected. It works well." FH
"Every concept is taught 5 times in 2 years, so teachers have to learn to let go." BW
"The jumping around threw teachers off at first; now they realize it is a solid approach." HS
"Like spiraling aspect." WM
"Love the spiral and connection to other areas of the curriculum. No longer reviewing a lot and not challenging students." KA
"Spiraling threw people off. After training, some are very comfortable; others are still learning not to require mastery initially." MW
I was amused at that last one.
Wow! People knew spiraling was bad... before my children were born!
In our school district, spiraling is considered an essential element of "best practices". Spiraling is holy. You must spiral on before mastery occurs.
We do Investigations. We spiral on.
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