Review of Math Wars: A Guide for Parents and Teachers by Carmen Latterell

by William G. Quirk, Ph.D.   (E-Mail:

Carmen Latterell Made Several Correct Observations about the Math Wars
  1. The 1989 NCTM Standards reject most traditional K-12 math content and they also reject the methods of traditional teacher-centered knowledge transmission, 
  2. The NCTM Standards endorse the early use of calculators and claim that standard pencil-and-paper arithmetic is obsolete.
  3. The NCTM Standards endorse the constructivist learning philosophy. According to this philosophy, math teachers can't transmit knowledge.  They are expected to create environments that allow students to discover math facts and skills. Students are expected to learn by carrying out investigations with their peers.
  4. Most holding a Ph.D in mathematics oppose NCTM reform math. Most holding a Ph.D in math education endorse NCTM reform math.
Carmen Latterell Did Not Go Beyond the General Observations Listed Above.  In Particular, She Did Not Provide a Detailed Discussion of the NCTM Standards. 

For a detailed discussion of the 1989 NCTM Standards, click on  Understanding the Original NCTM Standards: They're Not Genuine Math StandardsHere is an excerpt:

In the 1989 NCTM Standards, the NCTM Says Traditional K-12 Math is Obsolete

The "Introduction" to the1989 NCTM Standards claims that their 54 "standards" detail what mathematics students need to know". Mathematicians will be puzzled by this claim. They won't find "focused, specific, basic, teachable, and measurable" math content for the K-12 years, and they won't find traditional K-12 math. They'll find the NCTM has redefined the meaning of "math", frequently emphasizing that traditional K-12 math content should receive "decreased attention". Hard as it is to believe, they want to eliminate traditional K-12 math content and substitute calculator skills, math appreciation, and a whole range of general, content-independent "process skills". The NCTM emphasizes social goals and psychological considerations, not traditional math content.  The NCTM wants you to believe that K-12 math should no longer cover the content that has been traditionally taught under the headings "arithmetic", "algebra", and "geometry".

For a detailed discussion of the 2000 Revised NCTM Standards, click on Understanding the Revised NCTM Standards: Arithmetic is Still Missing
Here is an excerpt:

On April 12, 2000, The National Council of Teachers of Mathematics (NCTM)  released Principles and Standards for School Mathematics (PSSM), a 402 page revision of  the 1989 NCTM Standards. The next day The New York Times reported: "In an important about-face, the nation's most influential group of mathematics teachers announced yesterday that it was recommending, in essence, that arithmetic be put back into mathematics, urging teachers to emphasize the fundamentals of computation rather than focus on concepts and reasoning."  It was further reported that "the council added strong language to its groundbreaking 1989 standards, emphasizing accuracy, efficiency and basic skills like memorizing the multiplication tables."

Compare the preceding New York Times quotes to the following contradictory quote, published at the same time that PSSM was released: 

When calculators can do multidigit long division in a microsecond, graph complicated functions at the push of a button, and instantaneously calculate derivatives and integrals, serious questions arise about what is important in the mathematics curriculum and what it means to learn mathematics. More than ever, mathematics must include the mastery of concepts instead of mere memorization and the following of procedures. More than ever, school mathematics must include an understanding of how to use technology to arrive meaningfully at solutions to problems instead of endless attention to increasingly outdated computational tedium.   -NCTM,  Commonsense Facts to Clear the Air
It's clear that The New York Times was fed misleading NCTM propaganda, perhaps designed to placate "math wars" opponents.  Not surprisingly, in Understanding the Revised NCTM Standards: Arithmetic is Still Missing, we show that the NCTM has not rediscovered arithmetic.  Similar to the original NCTM Standards, PSSM is vague about the major components of arithmetic mastery:
    1. Memorization of of basic number facts
    2. Mastery of the standard algorithms of multidigit computation.
    3. Mastery of fractions
The NCTM has toned down the constructivist language, but they still stress content-independent "process skills" and student-centered "discovery learning".  Similar to the 1989 NCTM Standards, PSSM emphasizes manipulatives, calculator skills, student-invented methods, and simple-case methods.

Carmen Latterell Did Not Discuss the Details of Any Specific Reform math program.  

Here are Major Characteristics of
one K-5 Reform Math Program: TERC's Investigations in Number, Data, and Space
For More About TERC K-5 Math, see:
For Other Examples of how Reform Math Educators think, See: