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Topic: NCTM Assessment Recommendations not Base on Experience (Part 6
of Open Letter)

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Frank Allen

Posts: 17
Registered: 12/6/04
NCTM Assessment Recommendations not Base on Experience (Part 6
of Open Letter)

Posted: Dec 8, 1995 10:16 AM
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3. The Need for Reform
Reform! Don't we wish that our students could again attain the
higher performance levels they reached in the 40s, 50s and early 60s?
Instead of talking about "reform" we should be talking about regaining lost

Keep in mind that when the Standards writers talk about reform they are
talking about curriculum and teaching reform not about social reform that
would send kids to school ready to learn (Goal 1). Has the council
considered the implications of this situation? (See Enclosure 3 Crisis in
school mathematics due to social conditions for which standards provide no

Enclosure 3 Crisis in school mathematics due to social conditions for which
Standards provide no remedy.

The standards writers have failed to provide an analysis of
existing conditions in order to show a need for these changes. While they
refer briefly to "A Nation at Risk" they do not seem to realize that
conditions deleterious to learning have intensified by at least one order
of magnitude in the last 30 years. Consider that not all pupils are
clear-eyed seekers of truth from Central Casting with unlimited time for
data gathering and individual conferences. A very substantial number of
our "students" come to school in no condition to learn. It is difficult
to teach students who, due to social conditions outside of school, are
bone-tired, terrified, drug sodden or absent. As Clarence Page says,
"The public schools have become a dumping ground for the problems of the
larger society." Maybe--just maybe--this has something to do with lower
test scores.
Plans to reform our schools overlook that about half of our
youngsters grow up in families that are not adequately instilling traits
that are pedagogically essential. Frequent divorces, a bewildering
rotation of significant others, and parents who come home from work
exhausted both physically and mentally have left many homes with a
tremendous parenting deficit. Instead of providing a stable home
environment and the kind of close, loving supervision that character
formation requires, many child-care arrangements simply ensure that
children will stay out of harm's way. As a result, personality traits
essential for the acquisition of math, English and various vocational
skills are often lacking. Children come to school without
self-discipline, and they cannot defer gratification. Nor can they
concentrate on, or mobilize themselves for, the tasks at hand.*

But an influential group of our math educators, who are insulated
from these unpleasant classroom realities, seem to be completely unaware
of the appalling school conditions that are prevalent in many depressed
areas of our country including our inner cities. They have seized upon
the present emergency, that was largely caused by these conditions, to
proclaim a need for far-reaching changes in teaching and curriculum that
have little substantive support in either research or experience and are
not relevant to the problems that beset us. (The Titanic has hit an
iceberg and is sinking. Let's rearrange the deck chairs.)
The suburban schools in affluent areas don't need these changes.
Their math departments are staffed by an elite group of highly trained,
highly skilled professionals. While some suburban schools are beginning
to have their problems (the rise of gangs and the sentiment that only
"geeks" do homework) they are already incredibly good insofar as curriculum
and instruction is concerned. The problems confronting schools in our
depressed areas are, for the most part, not amenable to the changes
proposed in the Standards.
Since the Standard's writers have misapprehended the cause of the
present crisis in school mathematics, how can we trust their solution?

Frank B. Allen


*From an article entitled, "First, educate the reformers" by the nationally
syndicated writer
Amitai Etzioni. (Chicago Tribune 7/9/91)

Comments on the NCTM's Standards on Assessment

The ten assessment procedures recommended by the NCTM
"Standards" (pp 193-237) are so subjective and make such heavy demands
on the teachers' time that they are not practical for a teacher working under
normal teaching conditions. "Normal teaching conditions" implies five math
classes averaging about thirty, plus at least one extra-curricular assignment.
Therefore, let every speaker at the forthcoming ICTM "Leadership
Conference" place the left hand on a copy of Stone-Millis "Plane Geometry",
(Benj. H. Sanborn and Company, 1915) or some other strong geometry text
from the period before they were emasculated , and take the following oath:
"I solemnly swear that I have used the procedures I am about
to advocate under normal teaching conditions for a period of
at least two years. Moreover, I used these procedures in all five
of my mathematics classes."
If this decimates your speaking corps, as it will unless they resort to
wholesale perjury, you can spend your time more profitably constructing
examinations and tests which are valid measures of the students
understanding of school mathematics. A teacher who can neither devise or
select such tests should not be teaching mathematics.

Brief Comments about Certain Criteria

Alignment. We have sense enough to know that our tests should
"measure the content of the curriculum" (p 193).
Standards 4,5,6,7,8,9. We have always tried to ensure that our
evaluation procedures (exams, tests, bids, etc.) measured mathematical
power, ability to communicate (write clear explanations), reasoning, mastery
of mathematical concepts, and proficiency with mathematical procedures.
Standard 10. Mathematical Disposition. We have always sought to
inculcate a positive attitude toward mathematics. However, it never
occurred to us to use our perception of how well we had succeeded in this
regard as a component of the students course grade. We thought that if the
student had a favorable disposition toward mathematics this would cause him
(generic) to study harder and would be reflected indirectly, but
effectively, in his test grades.
It is irresponsible for the NCTM to advocate assessment procedures
which are devoid of any validation under normal teaching conditions in
either research or experience. Moreover, if it were widely adapted it would
so drastically change our procedures and criteria for measuring student
progress that all comparisons with past records would be invalid. It is
something like what would happen to baseball records if each batter were
given four strikes instead of three.
Lord Stockton once said, "The Liberals have once again come forward
with many new and good ideas. Unfortunately, none of the good ideas is
new and none of the new ideas is good". This analysis applies pretty well
to the 9-12 Standards. The NCTM assessment plan is a new idea that is not
good. Drop it.

Frank B. Allen

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