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Sunday, December 26, 2004



"No honest or even logical person could ever claim to know what is best."

Perhaps I'm misreading you, but does not this comment (about "best practices") contradict what you say elsewhere, for example, when you say that Ed schools do not teach their students "exactly" how to teach?


Good point, Michael!!

But watch how I weasel out of the logical trap...

No BEST way to teach because that implies you've tried then all--which is impossible.

BUT, you can have an EXACT way to teach (do x, then y, then z) even if it is not best. In fact, if you DO try many different but exactly specified ways, you're more likely to be able to say with confidence which was the better.

[Actually, that's wasn't too bad.]


"No BEST way to teach because that implies you've tried then all--which is impossible."

I don't find the professor's weaseling out effort convincing. There aren't infinite ways to teach. If the objective is well defined then it should be possible to ascertain the best teaching method empirically.

Spelling alert: The word in the heading should be SIEGE


Professor Plum's description of the growing strength of the anti-establishment is reassuring and encouraging. It is also encouraging that (at this point) the government plays a positive role in the form of the Ed Department. However, there is a huge fly in the ointment in the form of the tax-supported National Science Foundation. An arm of NSF, called EHR, is under the complete control of progressive/constructivist ed cultists. EHR (NSF) has spent billions to promote constructivist (a/k/a fuzzy math, rainforest math, voodoo math, etc.) on many fronts.

This, and related issues, are discussed in a superb account of math education by David Klein. Long piece, but well worth the effort.

A brief excerpt:

Within a few years, the NCTM produced two additional documents as part of its standards. One published in 1991 was narrowly focused on pedagogy and the other, published in 1995, was focused on testing.58 By 1997 most state governments had adopted mathematics standards in close alignment with the NCTM standards.59

The National Science Foundation

The National Science Foundation (NSF) was the key to the implementation of the NCTM Standards across the nation. Without the massive support it received from the NSF, the sole effect of the NCTM Standards would have been to collect dust on bookshelves. Spurred by the 1989 Education Summit attended by President Bush and all of the nation's governors, the Education and Human Resources Division (EHR) of the NSF set about to make systemic changes in the way math and science were taught in U.S. schools. The blueprint for change in mathematics would be the NCTM Standards.

The NSF proceeded purposefully. The EHR developed a series of Systemic Initiative grants to promote fundamental changes in science and mathematics education in the nation's schools. The Statewide Systemic Initiatives were launched in 1991. These grants were designed in part to encourage state education agencies to align their state mathematics standards to the NCTM Standards. The result was a remarkable uniformity and adherence to the NCTM Standards at the state level.60

Recognizing that education is largely a matter of local control, the NSF also launched its Urban Systemic Initiative (USI) program in 1994. These USI grants were designed to implement the NCTM agenda at the school district level in large cities. The USI grants were followed by a program for Rural Systemic Initiatives. By 1999, the USI had evolved into the Urban Systemic Program. This program allowed renewals of awards made under the USI program.

At first, the Systemic Initiative grants were awarded to proposals generally aligned to the educational views of the NSF, but awardees were allowed substantial freedom to develop their own strategies for reform. As the program evolved, so did the guidelines. By 1996, the NSF clarified its assumptions about what constitutes effective, standards-based education and asserted that61:

All children can learn by using and manipulating scientific and mathematical ideas that are meaningful and relate to real-world situations and to real problems.
Mathematics and science are learned by doing rather than by passive methods of learning such as watching a teacher work at the chalkboard. Inquiry-based learning and hands-on learning more effectively engage students than lectures.
The use and manipulation of scientific and mathematical ideas benefits from a variety of contributing perspectives and is, therefore, enhanced by cooperative problem solving.
Technology can make learning easier, more comprehensive, and more lasting.
This view of learning is reflected in the professional standards of the National Council of Teachers of Mathematics, the American Association for the Advancement of Science, and the National Research Council of the National Academy of Sciences.
The NSF was clear in its support of the NCTM Standards and of progressive education. Children should learn through group-based discovery with the help of manipulatives and calculators. Earlier research funded by the NSF, such as "Project Follow Through," which reached very different conclusions about what works best in the classroom, would not be considered.62 Regardless of what cognitive psychology might say about teaching methodologies, only constructivist programs would be supported.
Along with the Systemic Initiative awards, the NSF supported the creation and development of commercial mathematics curricula aligned to the NCTM Standards. In the decade of the 1990s, the National Science Foundation sponsored the creation of the following mathematics programs for K-12:

elementary school

Everyday Mathematics (K-6)

TERC's Investigations in Number, Data, and Space (K-5)

Math Trailblazers (TIMS) (K-5)

middle school

Connected Mathematics (6-8)

Mathematics in Context (5-8)

MathScape: Seeing and Thinking Mathematically (6-8)

MATHThematics (STEM) (6-8)

Pathways to Algebra and Geometry (MMAP) (6-7, or 7-8)

high school

Contemporary Mathematics in Context (Core-Plus Mathematics Project) (9-12)

Interactive Mathematics Program (9-12)

MATH Connections: A Secondary Mathematics Core Curriculum (9-11)

Mathematics: Modeling Our World (ARISE) (9-12)

SIMMS Integrated Mathematics: A Modeling Approach Using Technology (9-12)

The development of NCTM aligned mathematics programs for K-12 was of obvious importance to the NSF (for a list of math programs explicitly endorsed by the NCTM, see the Appendix). How could the NCTM agenda be carried out without classroom materials that were specifically aligned to the NCTMStandards? An important component of the Systemic Initiatives was the aggressive distribution of NCTM aligned curricula for classroom use. The NCTM Standards were vague as to mathematical content, but specific in its support of constructivist pedagogy, the criterion that mattered most to the NSF. It should be noted that the Systemic Initiatives sometimes promoted curricula not on the list above, such as College Preparatory Mathematics, a high school program, and MathLand, a K-6 curriculum. MathLand was one of the most controversial of the widely used programs aligned to the NCTM Standards.63

In addition to aligning state math standards to the NCTM standards and creating and distributing math books and programs aligned to those standards, the NSF attempted with considerable success to push these approaches up to the university level. Most notable in this regard was the NSF's funding of a "reform calculus" book, often referred to as "Harvard Calculus," that relied heavily on calculators and discovery work by the students, and minimized the level of high school algebra required for the program.64

The NSF also funded distribution centers to promote the curricular programs it had helped to create. For example, an NSF sponsored organization created in 1997 called, "The K-12 Mathematics Curriculum Center," had a mission statement "to support school districts as they build an effective mathematics education program using curriculum materials developed in response to the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics."

The Education and Human Resources Division of the NSF faced a serious hurdle in carrying out its Systemic Initiatives. U.S. K-12 education collectively was a multi-billion dollar operation and the huge budgets alone gave public education an inertia that would be hard to overcome. Even though the millions of dollars at its disposal made the EHR budget large in absolute terms, it was miniscule relative to the combined budgets of the school systems that the NSF sought to reform. It would not be easy to effect major changes in K-12 mathematics and science education without access to greater resources.

To some extent private foundations contributed to the goal of implementing the NCTM Standards through teacher training programs for the curricula supported the by the NSF, and in other ways. The Noyce Foundation was especially active in promoting NCTM aligned math curricula in Massachusetts and parts of California. Others such as the W. M. Keck Foundation and Bank of America contributed as well. However, the NSF itself found ingenious ways to increase its influence. The strategy was to use small grants to leverage major changes in states and school districts. NSF Assistant Director Luther Williams, who was in charge of the Education and Human Resources Division, explained the strategy in a July 1998 Urban Systemic Initiative Summary Update:


Terrific info, Pedant! Thanks.

Do you have any idea WHY so many groups pushed for constructivist math--esp groups that (I would have thought) care about data?

siege not seige? You mean they weren't kidding about i before e except after c? I thought it was a clever ruse.


Plum, you inspire me and totally rock my world. Now, I really hate to be picky, but would you please explain your use of "disingenuous" here? (I am studying for the GRE and working on vocab. I am planning major insurgency in the ed school in which I will enroll.)

"...and mount disingenuous arguments against the preponderance of scientific research that challenges what they teach."


By "disingenuous," I mean they are lying low crawling maggot pies--but "disingenuous" was a quicker way to say it. Are you SURE you want to go to an ed school?

There will be many of THEM... and, correspondingly, few of YOU.


Garbo - if you're serious about going to ed school, go with plenty of mental arms and armor. Don't let the bastards intimidate you, numbers don't equal truth. And keep reading Plum, some of his stuff will reduce them all to jelly-kneed babblers.

Plum - I think you've got the making of the "95 Theses" for Ed Schools. (Except there are only 10 this time.) Now go forth with hammer and nail and pin a copy on every ed school bulletin board you can find! Yeah, there are plenty. And they're nicely decorated too. Gives the pions a nice break from navel-gaz... er... uh... I mean reflection.


Plummy, old sock, I'm afraid your "logic" won't wash. "Best practices" does not refer to "a" best anything: you'll note the plural "practices." We can argue about which practices are indeed best, but there's general agreement on some things: use the board (or overhead, or PowerPoint) when lecturing, state learning goals at the beginning of class, move around the room and engage more students, ask questions at various levels (didactic all the way to "higher order") and so on. Good teachers know this stuff, and new teachers do need to be taught it.


Garbo, I have gone to ed school fully armed. It is indeed a dangerous place. But I have discovered that there is a growing insurgency. Some professors actually believe that it's important to focus on "teaching." Like, how to teach teachers. What's the best way to teach kids. What's the best way to use standardized tests. What kind of research should scholars do to figure out better ways of teaching? (Particularly disadvantged kids.)

I'm lucky. I'm in a place with hope. Be careful out there.

Col. Mustard

A fun exercise on a rainy day (when you don't want to get your new Barrett 50 cal wet practicing)consists of googling the 'code of ethics' for various groups - lawyers, accountants, engineers, teachers, butchers, bakers, etc.

Now score each of them.

Award points by how close to the top a code lists items such as "I will do no harm to my client" and "I will use only field-proven methods in the service of my client."

Subtract points for not mentioning the above items.

Subtract points by how close to the top a code lists items such as "I will take no action that could reflect adversly on a fellow practioner" or "I will never bring discredit to our cozy little band."

Add points for not requiring members to lie or remain silent about miscreanant fellow members.

Add more points for requiring the exposure of unethical behavior.

After the above exercise, you may not care if your Barrett gets wet or not!


Plum, Adrian and JennyD: Thanks for your kind words of caution. Despite my penchant for solitude, I'm not as fragile as one might expect. What doesn't kill you makes you stronger, and parenting two rebellious teenagers is turning me into one tough old b****. I'm in my 40s, which I suppose will make me--ironically--a "nontraditional" student. I have already had one career in aerospace engineering and another teaching math.

I'm applying for Ph.D. candidacy in math education, and plan to do research along these lines: What is it that these schools are doing in which virtually 100% of the students--especially the disadvantaged--demonstrate at least grade-level proficiency in math? Why does it work? Why aren't more schools doing it? How can we in this great country spread these practices to the greatest number of children with the greatest possible speed?

Though I know, through experience and reading, some version of the answers to the first three, I think there's a need for exhaustive empirical research by someone who has studied the history, theories and politics of education, and who also knows math. Though I know I'll reject much of the nauseating mash doled out in the education courses, I'll be in a position to at least generate some insurrectionist thoughts in the next generation of teachers. I have a reputation for "stirring the pot" in a quiet and rational way.

I finally figured out who I want to be when I grow up: Diane Ravitch. I can't expect to achieve her level of eminence, but I like to aim high.

I'm sending in my application this week. I'm considering blogging the whole ed-school experience. (Can blog be used as a transitive verb?)


Col. Mustard's idea about the ethical code lists is terrif. 'Twould make a great post. Anyone wanna do it? I'd be happy to slap it up here. It would also make a fine op-ed piece, or article in one of the anti-establishment mags, such as Education Next or the Fordham Foundation.

The Barrett .50 caliber.... It makes one moan and growl like (or as) a feral cat tucking into its noonday ration of mouse.

[Professor Plum would have to wear some REALLY baggy pants to sneak one of those into the house. But if caught...]

"Just what the heck is that in your pants?"

"Oh, nothing, really. The usual assortment."

"Nothing? Nothing! You ALWAYS say 'nothing.' And it's always SOMEthing."

"It would HAVE to be. That's how reality works."

"It's yet aNUTHER gun. And I emphasize YET."

"Not a gun. Don't call it a gun else you'll be sleeping with it."

"Yes. Yes. But you promised! [whining now. NEVER works.] You said, 'All done. No more.'"

"I realized the arsenal was incomplete. There was a distinct absence of .50 caliber. Left us quite vulnerable, it did."

"Get that THING out of this house." [back to anger.]

"Thing? Would you call it a thing?"

"Cut the quiz! Either IT goes or I goes." [Oooo. Ultimatum. What to do? What to DO?]

"We shall miss you... Come, Barrett. Let me introduce you to some friends. You're going to just love Ms Mossberg. What a barrel!"

Michael and Pedant are right. I was wrong. That makes twice. The first time I THOUGHT I was wrong about something but was, in fact, right; in which case, wrong.

And this time, wrong again. "Best practices," does not (as Michael suggests) imply "the best possible" (which HAD been my interp) but rather "the best we have." Therefore, logically, we CAN advocate certain communication formats and other aspects of instruction without fear of being accused of hyperbole.

I wonder if Jenny D. would honor us with some thoughts on WHY she thinks the ed professoriate is different up her (frozen) way. External forces? Internal combat and routing of the progressives?


Prof. Plum asks:

"Do you have any idea WHY so many groups pushed for constructivist math--esp groups that (I would have thought) care about data?"

It would be important to specify who these "groups" are. NCTM list oodles of supporting groups, but I believe they fall into the category of math "educators" not mathematicians. Indeed, constructivists distinguish sharphly between math "educators" and mathematicians and claim no attention should be paid to the latter.

Ralph Raimi (a fierce critic of fuzzy math

cites the pronouncement of a leader of fuzzy math to this effect:


Usiskin early in the article draws the analogy, that
mathematicians are to mathematics educators ("teachers and those who
train them") as biological research scientists are to practicing physicians.
The analogy is not bad, but fails to imply what Usiskin thinks it does,
which is that mathematicians are not fitted to prescribe for mathematics
education. Most biological research scientists have little interest in
clinical medicine, to be sure, nor do they pretend clinical competence,
and so most of them do not oversee or criticize the work of clinical
physicians; but there are those among them who do study and direct the
creation of new drugs and procedures, and their clinical trials, and who
understand their chemistry and practical problems well enough to write
the detailed accounts physicians rely on every day in their prescriptions.
In the same way there are mathematicians whose oversight of school
mathematics education, were it more prevalent than it is now, could be
of analogous benefit to school mathematics teaching. That is, Usiskin's
analogy itself does not support his condemnation of mathematicians'
interference in school mathematics policy at the content prescription
level. It should, indeed, gladden the mathematicas educators that the
creators of the science they would have correctly broadcast are, some of
them, taking a hand in seeing that its more subtle points are correctly
understood at the retail level.

Mrs. Peacock

Re: Is blogging a transitive verb?

"Of course. Else that most useful adverb 'bloggingly' could not exist," Mrs. Peacock posted bloggingly.


Garbo, All I can say to that is GO KICK A**!



You have a background in Aerospace Engineering and Math and still know about transitive verbs (and presumably intransitive ones as well)? I'm impressed!

I say good luck and give 'em hell up in Edland!


Garbo: Do it, and blog it all. I'm kind of doing the same thing, although I'm in the REALLY messy area of reading comprehension (Plum's favorite thing to rant about).

Come see me

Chris Correa,, blogs about math ed a lot. So does a blog called Teach and Learn.

I'm one of the world's older grad students--no teenagers yet but close. It's a big asset. I had a career as a journalist, which prepared me well for the BS in ed school, and for asking impertinent questions in class.

Stick to your guns, Garbo. You'll be great.

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