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.
The NCTM recommends a "broad curriculum", not focused math topics.
The 54 NCTM "standards" are broad topic headings, such as "Mathematics as Communication".
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.
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.
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.
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.
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".
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.
The NCTM has produced 59 documents, totaling 258 pages. The NCTM hopes you will be convinced by the weight of the pages.
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.