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 ----------------------------------------------------------------- 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 -------------------------------------------------- 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. ----------------------------------------------------------------- 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. ----------------------------------------------------------------- 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. ----------------------------------------------------------------- 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