*visions*as "standards".

Here, a major critic of fuzzy math describes the difference between real and bogus standards. Real standards are focused, specific and coherent.

Contrast this with what the visionaries consider "standards":

The NCTM Standards claim to describe K-12 math content. What kind of a description has the NCTM given? Note: The links in this section will take you to sections of chapters 3 and 4.

Not focused

The NCTM recommends a "broad curriculum", not focused math topics.

The 54 NCTM "standards" are broad topic headings, such as "Mathematics as Communication".

Not specific

The NCTM conspicuously avoids being specific about math content. Each of their 54 "standards" is a multiple-page document.

The NCTM does appear to believe that kids should learn how to count during the K-4 years, but they never actually state this explicitly. Amazing.

Not basic

The NCTM doesn't recognize math as a structured knowledge domain with a core foundational subset of basic domain-specific math facts and math skills. They invite open-ended discovery learning, driven by student interests, not a lesson-by-lesson buildup of core math knowledge.

Not teachable

The NCTM rejects the dictionary definition of "teach" ("impart knowledge or skills"). But they still want to call them "teachers". Their roles is to "guide" and create rich enabling environments to excite student interests for discovery learning, with no two students necessarily discovering the same thing..

Even if the NCTM wanted teachers to teach, their version of K-12 math content is often too broad and ill-defined to be teachable.

Not measurable

Because of their fundamental belief in "broad content" and "discovery learning", traditional objective testing must be rejected by the NCTM. All they can do is to attempt to "discover" what each kid has discovered. The NCTM recommends "testing to find success".

Not linked to grade

The NCTM standards are not specific about what should happen in each grade. They just discuss general learning goals for grade levels K-4, 5-8, and 9-12.

Not concise

As far as writing is concerned, the NCTM rejects "less is more". They constantly repeat words and phrases, often hundreds of times. Examples includes: "vision", "problem solving", "real world", "calculator", "computer", "explore", "experience", "power", "construct", "concrete", "estimate", "measure", and "pattern".

Redundant

The excessive redundancy of the NCTM Standards allows the key ideas to captured in the extracted quotes found in Chapter 3 and Chapter 4.

Not Genuine Math

This is the topic of Chapter 3.

Not brief

The NCTM has produced 59 documents, totaling 258 pages. The NCTM hopes you will be convinced by the weight of the pages.

Not selective

The NCTM is repelled by the very thought of a narrow selection of content. They preach broad exploration, not carefully selected math topics.

Not pedagogically neutral

The NCTM Standards are not about math, and they are not about standards. They are a vehicle for preaching "progressive" teaching methods.

## 4 comments:

I noticedt that Alfie (sounds like a Muppet character) does not like standard. I suppose real standards. He must like NCTM's pseudo standards.

What Does It Mean to Be Well Educated?: And More Essays on Standards, Grading, and Other Follies

by Alfie Kohn

According to Bill Quirk's definition, you're right. The NCTM's standards aren't standards. But what Quirk is describing is really curriculum, which the NCTM leaves up to states, districts, schools and teachers to design. The NCTM's standards are merely a starting point which states use to design exactly the focused, teachable curricula you are talking about.

It's funny to see you poking fun at names like Kohn's when you who won't sign your own posts with yours.

"According to Bill Quirk's definition, you're right. The NCTM's standards aren't standards."

Then they shouldn't call them standards but visions or longings or somesuch. Why would an organization that purports to be about math education shy away from specifying a curriculum?

"It's funny to see you poking fun at names like Kohn's when you who won't sign your own posts with yours."

Dissenters like me are not looked upon favorably in the cult atmosphere created by the ed establishment. I couldn't speak my mind freely without repercussions if I went public (at this point anyway).

Kohn quotes the secretary of education under President Johnson as saying that good standards should be as 'vague as possible.' I know how you feel about Kohn, but I think this illustrates that saying that the NCTM's standards aren't true standards because they're vague is becomes a matter of semantics.

You ask a very good question about why the NCTM doesn't specify curricula. This is a very thorny issue. I would first suggest that there are many different ways of teaching mathematics well (and, of course, many ways of teaching it poorly). I wrote a rebuttal to a critique of 'integrated' math curricula and argued that the author was way too obsessed with the curricula's integrated nature. That is, that the sequencing of math topics is a relatively arbitrary matter in any math curriculum; so criticize the specific pedagogy but don't waste your breath with romantic notions of there ever having been a 'one true sequence.' I taught in a very traditional high school last year, and some students took Algebra I- Geometry - Algebra II while others took Algebra I- Algebra II- Geometry. If the NCTM wrote more specific standards it would unnecessarily restrict flexibility.

On the political side, curriculum design in the U.S. has long been the domain of a large number of publishers, districts, schools and individual teachers. Several leading industrialized countries, in contrast, have strict nationalized curricula. I think it was the French education minister once bragged that he could walk into any classroom on any given day in France and know what was going to be taught. In the US, this would be considered an enormous intrusion of the federal government into local rights. The NCTM couldn't go any further with curriculum specifics because it would have been politically suicidal.

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