STEVENSON DOWN ON NCTM STANDARDS
NCTM are fuzzy standards that aren't helpful to most students or
teachers, and aren't what the Chinese and Japanese do.
Date sent: Sat, 20 Dec 1997 11:13:01 -0600 (CST)
From: firstname.lastname@example.org (Marilyn Keller Rittmeyer)
Subject: Please Forward: From Harold Stevenson, author of THE LEARNING GAP
Dr. Harold Stevenson, author of THE LEARNING GAP and University of Michigan
researcher who has for 15 years analyzed math education in Eastern Asia and
the United States, wrote the following as a response to the previous
posting about the NCTM standards:
Pardon our delay in responding to your question about the NCTM
standards. In our view the NCTM standards present a very vague,
somewhat grandiose, readily misinterpreted view of what American
children should learn in mathematics. Moreover, the view fails
to meet what we would consider to be the meaning of "standards."
Standards should involve a progression of accomplishments or
competencies that are to be demonstrated at defined times in the
child's schooling. The NCTM standards give no indication (beyond
four-year intervals) of the sequence with which the content is to
be presented and are not helpful to the classroom teacher in
designing lessons that meet the standards.
The NCTM standards list goals with which no one would be likely
to disagree. Of course, we want children to value mathematics,
to be mathematics problem solvers, to be confident of their
ability, to be able to reason and communicate mathematically.
Certainly, students must develop a number sense, have concepts of
whole number operations, and the other kinds of skills and
knowledge indicated under NCTM's curriculum standards. But the
published standards do not integrate these two important
components, the general attitudes and mathematical
skills. Another important aspect is how realistic it is for
teachers to implement these vague ideas in their everyday
teaching. In many cases, schools elect to emphasize students'
general attitudes and fail to provide them with opportunities to
learn fundamental mathematics skills. As a result, the new NCTM
approach of teaching math is often criticized as being fuzzy and
susceptible to multiple interpretations.
The goal in establishing standards is to set up something that
can be implemented. How is the regular classroom teacher
expected to be able to implement these standards? It is
interesting that, although a high percentage of American teachers
indicate that they are aware of the standards, many are unable to
provide explicit examples of how they have done this. In
many cases, the demonstration of their teaching to the
standards is very confusing to the students. The problem is in
the manner in which the standards are organized and written as
well as their lack of sufficient clarity that would enable their
The NCTM standards include the following types of goals and
problems. "In grades 5-8," for example, "the mathematics
curriculum should include numerous and varied experiences with
problem solving as a method of inquiry and application so that
students can use problem-solving approaches to investigate and
understand mathematical content....etc." Problems at
different grade levels include examples such as the following:
"I have some pennies, nickels, and dimes in my pocket. I put
three of the coins in my hand. How much money do you think I
have in my hand?" or "Students are given a carefully drawn
picture of a roller-coaster track. The challenge is to sketch a
graph (with no numbers) to represent the speed of the roller
coaster versus its position on the track." How are these to
influence the everyday conduct of mathematics classes? How does
one integrate mathematical computation with such problems? Where
does one go after presenting these examples? They may have some
use for a very well prepared teachers and a very bright group
of students, but they are of little help to the majority of
teachers, teaching the majority of our
In short, "fuzzy" is a kind word when it comes to describing
the NCTM standards.
A graduate student just came by and we read him some examples
from the NCTM volume. "Why those
aren'tstandards," he said with some
indignation. We agree.
Compare the NCTM standards with the Japanese curriculum
guidelines where provision of developmental and systematic cues
for instruction are one of the main focuses. Here are examples
from the second grade:
Objectives: To help pupils deepen their understanding of the
concept of number and notation. Furthermore, to help them
understand the cases in which such calculations as addition,
subtraction, and multiplication are applied, and to enable them
to perform basic calculations.
To help pupils understand gradually the meaning of quantities
such as length and volume, and their measurement, and to enable
them to measure length and volume.
To help pupils to understand gradually the concepts of
fundamental geometrical figures and space.
And then the contents offer very specific guidelines for the
mathematics skills expected of children at that grade level. For
For Numbers and Calculation.
To help pupils understand the concept of number and how numbers
are represented, and to help them develop their abilities to use
To count objects by re--arranging them into groups of the same
size or by classifying them. To classify and arrange simple
matters and express them by using numbers. to know the way to
represent number by the decimal numeration system, and the size
and order of numbers up to 4-digit numbers. To help pupils deepen
their understanding of addition and subtraction, and develop
their abilities to use them. etc. etc.
Japanese and Chinese teachers do not use calculators or
computers in mathematics classes because they want the students
to understand the concepts and operations necessary for the
solution of problems. Early reliance on these aids does not
provide the necessary experience in manipulating concrete
objects, an experience which helps children learn the basics of
The Japanese and Chinese teaching also provides opportunities
for group discussion, an activity that is considered to be
essential for efficient learning..
Only at the high school level, after students have had a clear
understanding of mathematical concepts are East Asian students
given the opportunity to use a calculator as a tools in solving