(Bead 8. .) Send note to Paul Prueitt . (Bead 10. .)

Part 2: Chapter 9

A true liberal arts education “about” the nature of
mathematics

August 16, 2002

Chapter 9 and 10 open up the debate about the role that mathematics has in a civil society. This debate has deep ramifications to civil society governance, something that is only initially surprising. What are some of the consequences of ubiquitous discomfort with mathematics?

A story can be told of a
presentation to National Science Foundation management on the teaching of
physics. The position was that there
are “naïve“ notions of how physics process work that must be corrected in
freshman physics courses.

The positive aspects of the Newtonian
curriculum are clear and the author will make this point. Some use of
mathematics will be “taught” as part of the chapter’s material. The relationship between Hilbert mathematics
and classical physics will be explained in a way that will be comfortable to
any reader. However, at the heart of
the Newtonian paradigm lies an assumption that is misleading. It is misleading culturally in specify ways,
as might be discussed in the context of Native American cultural wisdom. It is misleading also in that these
corrected notions do not account for physical phenomenon such as life itself,
nor in many ways of either the string theory or the quantum theories. It should be clear that the challenge of
physics and mathematics is not merely intellectual, but has complex aspects of
apparent conflict with some cultural viewpoints.

Clearly physics works in a
specific fashion and a physics curriculum that reflects Newtonian physics
should present the formal theory. But
biological systems work in ways that are NOT reflected perfectly in Newtonian physics
(citation to the work of Kugler, Rosen and Penrose). Bioinformatics, for example may be far too reductionist in nature
as computer science seems to take an upper hand in the definition of that
scientific communities vocabularies and assumptions. So, perhaps, part of a liberal understanding of mathematics should
allow students to explore the confluence between computer science and Newtonian
physics, and the disconnect between this confluence and quantum theory or biological
sciences.

The most important question to
each human, living anywhere on the planet, is the question, “Who am I’. Some individuals find sufficient answer in a
religious authority, and some individuals find sufficient answer in a
scientific authority. However, the
author holds that a deeper answer lies outside of these authoritarian
regimes. The deeper answer lies in self
knowledge, and in the case of the learned disability in mathematics, the self
knowledge can be transformed from a negative feeling to a positive
feeling.

The issue that is spelled out in
this Chapter is about the native insight that each of us have, perhaps from
birth, and how this insight is violated by the absence of a corresponding
cultural knowledge of self. I is in
this context that the education of the whole self seems violated by the
imposition of freshman college algebra.

The case is made that knowledge of
the nature of mathematics is a different than the skills associated with the
professional mathematician. There is a
skill related to knowing stochastic models of meaning found necessary to the
computer technology of knowledge science.
However, this is not what the average college student needs. The skill is not required.

But an appreciation of what abstraction
is, and perhaps what metaphor is, is a different question. This question goes to the heart of what it
is to be human. What is
abstraction? What is induction? Does the concept of artificial intelligence
make “sense”?

We
have two types of proposals for curriculum refinement:

http://www.bcngroup.org/beadgames/LiberalArtsCore/home.htm

and

http://www.ontologystream.com/beads/QuestionOfAccess/Syllabus.htm

Our
sense it that main stream educators would find this interesting but that the now
standard core curriculum will be seen to be not emphasized. I agree that there is incompleteness to our proposed
materials.

We
have just recently become aware of. The
new draft has the title:

"Mathematics and Science for the
Whole Person"

This
title seems to frame an issue related to whether or not mathematics and science
is socially acceptable to people who think about wholeness.

This
framing (G Lakoff's term) seems to shift the focus from what professional
scientists and mathematicians can do to help K-12 outcome metrics. The framing shifts to the need for a
liberally educated population required to support the democracy. This liberal education needs to produce far
fewer individuals who declare a hate for and discomfort with "math".

The
new work that I am developing is intended to directly more the developmental
student into elements of abstract algebra, and real analysis; with the
assumption that too much attention is spent on algebra skills and "work
problems". It is an interesting
conjecture.

These notes are
formative towards Prueitt’s new book on learning theory.

We expect that the
book will be developed over the next four months.

(Bead 8. .) (Other Beads) (Bead 10. .)