The National Council of Teachers of Mathematics is an educational subject matter group for mathematics teachers in elementary, junior high, and high school.  Unfortunately it has tried to be more than what it is capable of being, in my opinion. 

Several subject matter organizations in the 1980's and  1990's put forth "Standards" using that word to suggest that there was some kind of verifiable, vetted program that would improve the teaching of a subject.

 Nothing could be further from the truth! 

"Standards" were not standards at all!  They were merely a list of cockamamie "education school" concepts that were developed and based on hokum science. That anyone took them seriously is a testament to the gullibility of the people residing in the fields of education.

But believe them they did.  And why shouldn't they?  Most of the people making decisions on such matters are themselves products of non-academic college schools of education!

 Say something enough times, and it becomes real. Say it even more and the public will buy into it too!

 Here are the suggestions put forth by the NCTM in the 1980's:

An Agenda for Action

Recommendations for School Mathematics of the 1980s

The National Council of Teachers of Mathematics recommends that:

  1. Problem solving be the focus of school mathematics in the 1980s;

  2. Basic skills in mathematics be defined to encompass more than computational facility;

  3. Mathematics programs take full advantage of the power of calculators and computers at all grade levels;

  4. Stringent standards of both effectiveness and efficiency be applied to the teaching of mathematics;

  5. The success of mathematics programs and student learning be evaluated by a wider range of measures than conventional testing;

  6. More mathematics study be required for all students and a flexible curriculum with a greater range of options be designed to accommodate the diverse needs of the student population;

  7. Mathematics teachers demand of themselves and their colleagues a high level of professionalism;

  8. Public support for mathematics instruction be raised to a level commensurate with the importance of mathematical understanding to individuals and society.

Agenda For Action: Problem Solving

Recommendation 1
Problem Solving must be the Focus of School Mathematics in the 1980s

The development of problem-solving ability should direct the efforts of mathematics educators through the next decade. Performance in problem solving will measure the effectiveness of our personal and national possession of mathematical competence.

Problem solving encompasses a multitude of routine and commonplace as well as nonroutine functions considered to be essential to the day-to-day living of every citizen. But it must also prepare individuals to deal with the special problems they will face in their individual careers.

Problem solving involves applying mathematics to the real world, serving the theory and practice of current and emerging sciences, and resolving issues that extend the frontiers of the mathematical sciences themselves.

This recommendation should not be interpreted to mean that the mathematics to be taught is solely a function of the particular mathematics needed at a given time to solve a given problem. Structural unity and the interrelationships of the whole should not be sacrificed.

True problem-solving power requires a wide repertoire of knowledge, not only of particular skills and concepts but also of the relationships among them and the fundamental principle that unify them. Each problem cannot be treated as an isolated example. This recommendation looks toward the need to solve problems in an uncertain future as well as here and now. As such, mathematics needs to be taught as mathematics, not as an adjunct to its fields of application. This demands a continuing attention to its internal cohesiveness and organizing principles as well as to its uses.

Recommended Actions  

1.1 The mathematics curriculum should be organized around problem solving. 

1.2  The definition and language of problem solving in mathematics should be developed and expanded to include a broad range of strategies, processes, and modes of presentation that encompass the full potential of mathematical applications. 

1.3  Mathematics teachers should create classroom environments in which problem solving can flourish. 

1.4  Appropriate curricular materials to teach problem solving should be developed for all grade levels. 

1.5  Mathematics programs of the 1980s should involve students in problem solving by presenting applications at all grade levels. 

1.6  Researchers and funding agencies should give priority in the 1980s to investigations into the nature of problem solving and to effective ways to develop problem solvers. 

You can go here to read the rest of their nonsense:

If the reader has waded through this compilation of baloney, he will see the problem.  Anyone with an academic background has to be nonplussed at some of these items! 

These suggestions do not describe an intelligent way to teach mathematics! 

The problem is that teachers of mathematics may never have taken a real, true college level mathematics course--ever! And for some of them, if they took such a course, they may not have even passed it. They have instead, taken "math education."  Trust me--"math education"  has not much to do with real mathematics. And it is easily "passed."

If one has the gumption, he should ask each of his children's mathematics teachers what college courses they had in mathematics. Ask too if they took a real college mathematics course what their grade was or if they even passed it!  You could ask that question, by the way, of any public school administrator you happen to run into, also. You won't be surprised at the answer to that question--it will be just as I've described.

Having pointed out the inherent problem with the teaching of mathematics in our public schools, one must decide what to do about the situation.

After my suggestions elsewhere that parents either teach their children themselves all that they need to know the year before they are supposed to learn material in public schools, or that parents simply homeschool their children, or that they send them to a qualified private school, I would suggest that parents band together and raise Cain about the situation in our schools.  When people run for the school board, ask them what they know about the NCTM Standards.  If they say they don't know anything, educate them.  If they say those Standards are fine, don't vote for them! Just for fun, you might want to ask them if THEY took a real college level math course and how they did!

But whatever you do, make certain that YOUR child knows his tables (addition, subtraction, multiplication and division) through 12's, that he can multiply and divide using fractions, that he can work with a decimal point, that he knows the square roots of the obvious numbers, and that he can long divide--and all without the help of a calculator. That's all he needs to know by the end of the fifth grade. 

If he has to perform 33 steps to add 27 and 92, be sure that he knows there is a more commonsensical way to do it!

When you child gets to Algebra, make certain that he learns Algebra and that he is not being taught "rainforest Algebra." 

(If you don't know what "rainforest Algebra is,"  Google it.)

If you want your child to be a scientist, an engineer, a physician, a physicist, a chemist, or a mathematician (or anything related to those subjects), you might want to think very seriously about hiring a tutor (if you cannot teach him yourself), or enrolling your child in a private school.

Remember that the  thrust of public education these days is to dumb down 85% of the students so they may satisfy the requirements and needs of corporate America, and if you want your child to be in the 15% that are not a part of that thrust, you need to be pro-active and learn what this scheme by our government is all about.  (The NCTM is part of the scheme whether they know about it or like it.)

Visit the topic "Mathematics" under the "Education" heading on this web site for more information about the teaching of mathematics.