Aren't we suffering from a generation of teaching with the philosophy of
Dr.
William Glasser and his "Schools Without Failure"? Shouldn't a high
school graduate be prepared to pass a "College Algebra" class which is
probably similar to what most of us on this list probably took as Algebra I
in high school? I know they aren't prepared, and, hence, our problem.
Reply:
Glasser was the first psychologist who challenged traditional
psychotherapy in the mass media with his book " Reality Therapy". He
refocussed patient concern from blaming parents, environment, society,
etc. to taking responsibility for one's own actions, forgetting past
"excuses" and concentrating on changing one's behavior (he felt that
changes in behavior would cause changes in the attitudes which led to
the "sick" behavior - not the other way around).
He applied his idea in a Ventura California school for juvenile delinquent
girls with success. Later, he expanded on his ideas in an attempt to have
high school students take more responsibility for their learning by using
guided discovery techniques in the context of cooperative learning, with
the teacher intervening only to provide guiding hints or questions or a
summary after students had struggled with concepts. In no way are
standards to be compromised, according to my reading of Dr. Glasser.
The title of the book "Schools Without Failure" might give the impression
that standards are lowered to accomodate everyone - to those who
have not read the book.
On the matter of a College Algebra similar to what we all took in high
school, I hope the subject has made some improvements over (1) word
problems taught in a separate section, or, if sprinkled throughout the text,
presented in categories, each having its own recipe (2) algebraic
manipulations of rational and radical expressions more complicated than
one can find in any applications found in calculus or differential
equations texts (3) the definition, theorem, example, format followed by
a plethora of similar simple answer problems to which the example
template (recipe) is be applied (4) littlle or no use of computing
technology such as graphing calculators (5) lack of any emphasis on
communicating mathematics orally or in writing (6) artificial, short-and
single-answer "applications" requiring no estimation, checking or
sustained effort.
The NCTM and the AMATYC Standards embody attempts to improve
courses "we probably took ... in high school". I would hope that college
algebra would be affected by these reforms.
Unfortunately, you cannot implement most of these reforms with
traditional texts and materials.
I'm currently teaching a guided discovery-, cooperative learning-,
graphing calculator-based course in intermediate algebra (class test
edition of 'Intermediate Algebra: Models, Functions and Graphs',
Addison-Wesley 2-year college version of a course taught in some 700
high schools). It is not perfect, but it is the only text I have seen which
allows a discovery approach which is not undermined by template
examples which students can use as a substitute for thought.
I think Glasser provides a nice alternative to traditional psychotherapeutic
techniques and to tradtional education.
Mike Mallen
Santa Barbara City College.