Review of Math Wars: A Guide for Parents and Teachers by Carmen Latterell
Carmen Latterell Made Several Correct Observations about the Math Wars
- The 1989 NCTM Standards reject most traditional K-12
math content and they also reject the methods of traditional
teacher-centered knowledge transmission,
The NCTM Standards endorse the early use of calculators and claim that standard pencil-and-paper arithmetic is obsolete.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
Most holding a Ph.D in mathematics oppose NCTM reform math. Most holding a Ph.D in math education
endorse NCTM reform math.
- 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.
Carmen Latterell Did Not Go
Beyond the General Observations Listed Above. In Particular, She
Did Not Provide a Detailed Discussion of the NCTM Standards.
- 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
Original NCTM Standards: They're Not Genuine Math Standards. Here is an excerpt:
In the 1989 NCTM Standards, the NCTM Says Traditional
The "Introduction" to the1989 NCTM Standards claims that their 54
detail what mathematics students need to know". Mathematicians will
puzzled by this claim. They won't find "focused, specific, basic,
and measurable" math content for the K-12 years, and they won't find
K-12 math. They'll find the NCTM has redefined the meaning of "math",
emphasizing that traditional K-12 math content should receive
attention". Hard as it is to believe, they want to eliminate
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
math content. The NCTM wants you to believe that K-12 math
should no longer cover the content that has been traditionally taught
the headings "arithmetic", "algebra", and "geometry".
For a detailed discussion of the 2000 Revised NCTM Standards, click on Understanding
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
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
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:
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.
- 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 one K-5 Reform Math Program: TERC's Investigations in Number, Data, and Space
For More About TERC K-5 Math, see:
- 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)
[Please click on References for the meaning of the BA code.]
no additional gain in conceptual understanding associated with the task
of trying to "construct" one more basic number fact.
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.
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.
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.
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.
For Other Examples of how Reform Math Educators think, See: