Monday, August 15, 2005
!! September 12, 2005 link to the
Taos Discussion [36]
and strategy
for mathematics education renewal !!
Send comments to
psp**@ontologystream.com (remove the “*” to get a valid email address)
bead game thread on educational renewal
This letter is a first
letter to President of New Mexico Highlands University. The second letter is at [9].
President Aragon,
It was a pleasure to receive a
phone call from Dean Mendes. I understand that he has recently been appointed
Dean of Arts and Sciences, and that he has had a long standing interest in
mathematics (and science) educational outcomes. We discussed the
state of mathematics education for freshman students.
As it is Saturday, and his email
address is not as yet posted on the web site, I ask that this message be
forwarded to him.
Objective measurements show the
state of mathematics education to be consistent across the breadth of our
American society. The state of mathematics education reform is stable and
resists efforts at transformation. One consequence is that mathematics is
regarded with distaste by most adult Americans.
The mathematics education “system” seems to be set up incorrectly based on a number of structural constraints. I have observed the natures of freshman mathematics for the past thirty years, while teaching over 80 classes, and developing computer technology related to human knowledge representation.
The errors and problems in
computer science stem from our societies inability to understand elements of
human communication, economic theory and the foundational aspects of
abstraction, and abstract knowledge (such as the design of computer
interfaces). These problems in the foundations of computer science can be
best contemplated when one understands the foundations of mathematics.
Whereas the technology enabled by computers advances continually, the
understanding of mathematics, human communication and economic aspects related
to information technology does not.
The core of my work has to do
with social beliefs and the effect that these have on one’s perception of
self. My theory of Acquired Learning Disability (in mathematics) is based
on cognitive neuroscience and theoretical immunology. I have not really
tried to publish this work, as I know that the concepts – while natural – are
likely to be controversial within the education and mathematics
community. As I approach my 54 th birthday, I want to publish this
work.
I have developed the basis for
two books, one at the graduate level for education majors and one as a freshman
“arithmetic and introduction to the foundations of mathematics” text book.
http://www.ontologystream.com/beads/QuestionOfAccess/AQA.htm
The graduate level text addresses
the cognitive neuroscience and biological response mechanisms, using a well
developed literature to ground my theory. The graduate level text also
deals with university governance issues such as the way the freshman
requirements are structured. I make the case that this structure serves
the departments of mathematics interests well, allowing the hiring of pure
mathematicians and continuing the advance of mathematics and computer
science. But the freshman instruction in mathematics is NOT serving the
broad interests of the university nor of the individual students, except
marginally. Whereas this seems factual and easily observed; the
university governance has not been able to address the structural
problems.
Due to these structural issues,
most universities are placed into a position of neglect. The neglect is
accommodated by assuming that the students are simply not willing and not able
to learn properly.
The outcome from freshman
experiences with mathematics varies. If the expectation on the student is
so low as to not challenge the student, then the university participates in a
type of fraud. The curriculum is watered down to allow the students to
pass. Why require that students take the courses? The answer is, of
course, the university’s accreditation constraints require a freshman
mathematics component. The department’s status and budget is also
elevated because there is a mathematics and computer science requirement.
What I propose is that freshman
instruction be developed to reflect a new curriculum that is seen by the
students are surprising and unexpected. The theory I have developed
suggests that novelty creates an orienting reaction and through this orienting
reaction one might break down the self image of most freshman students.
This self image has set aside the natural capabilities that each of our
students have.
A teaching philosophy is being
developed at several high schools in
One needs some novelty and
unexpected challenge, and then success at overcoming the challenges.
I struck on the concept of
re-teaching arithmetic, but in number bases that were not base 10. One
finds many nice things about this approach.
The challenge at first seems
impossible, but then the challenge is meet when one begins to focus on basic
principles. It should not matter is one uses base 5 or base 17 to compute
the answer to an arithmetic problem.
I have observed that the students
get involved in playing all types of interesting “number theory” games related
to divisors and remainders. My experiences with classes I have taught
this way is that half-way into the semester, most students awaken to a natural
interest in higher mathematics, including the Calculus and topics like topology
and real number analysis.
Even if only as an adjunct
instructor; I am interested in demonstrating this new approach to mathematics
remediation at NMHU. My time would be well spent as I expect to be
completing the two books this Fall. However, it has been my desire to
join the faculty and to interact with the various departments, linguistics,
psychology, cultural studies etc; and faculty in an examination of the
unique potential that exists for NMHU. Seeing that there are no faculty
positions open, perhaps a visiting position might be arranged.
Dr Paul Stephen Prueitt