- The 1989 NCTM Standards reject most traditional K-12 math content and they also reject the methods of traditional teacher-centered knowledge transmission,
- NCTM denotes the National Council of Teachers of Mathematics.
- The term "reform math" is used to identify K-12 math programs that attempt to follow the NCTM Standards.
- The "math wars" are about the NCTM Standards and NCTM reform math.
- The NCTM Standards endorse the early use of calculators and claim that standard pencil-and-paper arithmetic is obsolete.
- 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.
- 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 holds a Ph.D in Math Education.
- The author of this book review, William G Quirk, holds a Ph.D in Mathematics.

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

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 (

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of how to use technology to arrive meaningfully at solutions to problems instead of endless attention to increasingly outdated computational tedium.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,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:Commonsense Facts to Clear the Air

- Memorization of of basic number facts
- Mastery of the standard algorithms of multidigit computation.
- Mastery of fractions

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

Here are Major Characteristics of

- TERC insists on the ongoing use of hands-on tools (manipulatives, "models," and calculators).
- They say concrete tools must always be available and regularly used.
- TERC strongly rejects the idea that children must eventually migrate from hands-on tools to abstract thinking.
- TERC rejects the need for memorization and practice.
- They say that student's familiarity with single-digit number facts must "
**grow out of lots of experience with constructing these facts on their own.**" BA, Page 72 (emphasis added) - There's no additional gain in conceptual understanding associated with the task of trying to "construct" one more basic number fact.
- TERC doesn't think it's possible to understand memorized information. But knowledge must first be loaded into the brain before it can connected to other knowledge and "understood." Explicit memorization is sometimes the most efficient way to get it there.
- TERC fails to understand that it's often desirable to move to automatic use of knowledge. The mind must be free to think at higher levels of complexity, without consciously revisiting underlying details. For example, the key idea of the standard algorithms is that multi-digit calculations are reduced to multiple single-digit calculations. If children don't have instant recall of the single-digit number facts, they aren't equipped with the essential pre-knowledge for easily carrying out multi-digit computations.
- TERC fails to clearly define terms.
- They regularly state: "We don't ask students to learn definitions of new terms."
- They offer some "definitions," typically using multiple undefined terms to "define" a new term.
- They favor "natural language" and "personal language."
- TERC emphasizes "familiar numbers."
- The "
__landmark numbers__" are 5, multiples of 10, and multiples of 25. - Landmark number are also known as
__anchors__. - The "
__familiar fractions__" are limited to proper fractions with denominator equal to 2, 3, 4, 5, 6, 8, 10 or 12. Thus 7 and 11 are not familiar denominators. Perhaps TERC is opposed to gambling. - Note: 12 is included because it's needed for TERC's clock face method for adding fractions.
- TERC doesn't believe in defining terms, so you won't find the preceding definitions in TERC materials. This is what they appear to mean by these phrases. We welcome their clarification.
- Although TERC rejects explicit memorization of basic single-digit number facts, they expect students to remember many non-basic facts about landmark numbers and familiar fractions.
- TERC omits standard formulas.
- TERC emphasizes estimation and many right answers.
- They suppress the concepts of precision and accuracy.
- TERC proudly rejects standard computational methods.
- No standard algorithms for multi-digit computation.
- No standard methods for operations with fractions and decimals.
- No general methods for calculating with numbers.
__TERC emphasizes special case methods involving landmark numbers and familiar fractions.__- TERC attempts to directly teach their shallow and misleading content.
- They claim to offer a "constructivist" approach where students discover math as they play games and carry out investigations. But they provide thousands of pages of teaching instructions and recommended scripts that identify the content they expect kids to "discover."
- Thousands of pages for the teacher, but no text for the student.

- [Please click on References for the meaning of the BA code.]

- The Anti-Content Mindset: The Root Cause of the "Math Wars"
- The Parrot Math Attack on Memorization
- The Bogus Research in Kamii and Dominick's Harmful Effects of Algorithms Papers
- The Reform Math Mindset Behind Phil Mickelson ExxonMobil Math
- Standard Algorithm for Multiplication vs. Reform Math Partial Products