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:
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.