dzd@cosivax.UUCP (Dean Douthat) (04/10/84)
Here in Ann Arbor, there is an ad hoc committee composed of area
middle and high school teachers, coordinators and university
educators [teachers] plus people working in technology-based
organizations on R & D, service, production etc. [practitioners]
Its purpose is to organize a one-day long conference for teachers
in mid-May:
Industry/Education Conference
on
MATHEMATICS & TECHNOLOGY: Tools and Disciplines for Living
One major goal is to contrast the practitioner's technological
and dynamic view of mathematics with the teacher's traditional
and static school view. A hoped for result is that teachers will
gain a better understanding of the changing role of mathematics
in society as a whole and in the workplace. This might lead to
better student motivation and curriculum improvements.
Having been suckered into giving the keynote address for this
shindig, I have included below some preliminary thoughts and
ideas. By posting these, I hope to stimulate comments and/or
criticisms. Please reply directly; I will post results to the
net.
Thanks in advance,
Dean Douthat
UUCP: ...!sb1!mb2c!uofm-cv!cosivax!dzd | Mail: Zahntron, Inc.
Ma: (313) 995-9762 | 330 E. Liberty
MCI Mail: DDOUTHAT 187-3270 | Suite 3B
TWX/TELEX: 6501873270 | Ann Arbor, MI
Answerback: 6501873270 MCI | 48104
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SCIENTIFIC AND SOCIAL BACKGROUND
Definition of Mathematics (19th Century Style -- Industrial
Revolution Environment)
The science of numbers and quantity.
A self-contained discipline whose end product is quantification,
calculation and memorization. It was a universal requirement on
the same reasoning used to justify school athletics -- "good
discipline (mental)".
Focus = product and answer
Relationship to Students -- only a few specialists can exel in
and enjoy mathematics
Relationship to Jobs and Careers -- only a few jobs demanding
thorough foundation and on-going learning in math. Most people
will train for and have only one or a few different jobs during
career, these will not demand high skill levels and require
little on-going learning.
Relationship to Everyday Living -- little if any application
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Definition of Mathematics (20th Century Style (Informational
Revolution Environment)
The science of symbols and modeling.
Interdisciplinary and flexible whose aim is developing facilities
for estimation, intuition, hunches and testing, discovery of
relations/trends, problem definition and strategies for solution.
Numerical, calulation and memory aspects are so unimportant they
can be left to machines; marginally mental at all.
Focus = process and method.
Relationship to Students -- all living in this information age
need symbolic models to understand what the new technologies are,
how to use them, how to adapt them as they evolve.
Relationship to Jobs & Careers -- Technology changes jobs. Most
can expect to have many jobs throughout careers requiring widely
varying skills and so making on-going learning the expected norm.
To adapt to dynamic work setting requires facility in handling
symbols, models and functional relationships.
Relationships to Everyday Living -- Humans need symbolic models
of their world to deal with it. As their world becomes more
technical, the needed models become more complex. Then math, as
science of symbols and models becomes more important in using,
evaluating, testing, procuring, and regulating technology-driven
social, political and economic issues.
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TECHNOLOGY
RELATIONSHIPS BETWEEN TECHNOLOGY & MATHEMATICS
1. Technology "pulls" Math:
Conceiving, designing, building and operating larger and more
complex systems demands more subtle and powerful Math, especially
for simulation and related symbolic models. Human interface
demands improved mathematics to support better understanding of
natural intelligence. (Marr on visual perception, Grossberg on
non-linear neural models, others?) Increasing capabilities on
machine side demand new mathematical insights. (AI, complexity,
analysis of algorithms, parallelism, networking, others?)
2. Technology "pushes" Math:
New technologies, particularly the key information technologies
(computers and communications) give new tools which push math in
new directions and at faster rates. These have been used in
proof (four-color problem), in conjecture testing (number
theory), in large scale models and simulations (aerodynamics,
atmospherics), in equation/expression simplification and symbolic
solutions (quantum and relativity physics), in real-time adative
control models (plant process control).
3. Mathematics Mirrors Human Central Nervous System:
As a product of the human mind, it should be no surprise that
mathematics mirrors the human brain. The retina, optical ganglia
and visual cortex are "Euclid's axioms in vivo". The major
survival value of the neo-cortex is ability to build, adapt and
use elegant and powerful symbolic models for predicting behavior.
4. Social and Political Issues Reflect Symbolic Models:
Safety of technology, environmental effects of technology, health
hazards and what policies/plans to adopt for these all are far
too subtle to be understood by looking at raw data. They must be
mediated by complex mathematical models. Without an appreciation
of their plausibility, credibility, limitations, sensitivity to
assumptions, sensitivity to data errors, etc., sound political
judgement is impossible.
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WHY SHOULD BUSINESS INVEST IN STUDENTS?
Students need to be adaptive, familiar with business, solid
thinkers and users of technology to succeed as workers.
Long-term productivity and quality of business depends on workers
who are also on-going learners from a sound basis.
Students will become consumers of products with high technology
content. The need to appreciate the advantages of these
products, not fear them, want to own and use them.
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HOW CAN BUSINESS COOPERATE WITH EDUCATION?
Show how technologies are useful and helpful for work, play,
health, safety and even freedom of individuals and groups.
Explain and show how math is applied for developing technology.
Explain and show how math is needed to use and assess technology
wisely and to set policy, plans and priorities for it.
Provide role-models for careers & jobs related to math