Though problem processing really begins in the messy but interesting world
around us, the first Look stage of problem identification and posing
has been routinely left out of the mathematical curriculum of my three
sons over the last 13 plus years of their education. Tests, worksheets
and classroom experiences in math have exclusively started with a page
of problems to be solved. The emphasis has not been on the relevance of
mathematics, but on learning to work the systems of solutions discovered
by those with mathematical sense. Though much discussion is given to the
step of observation in science class, in reality, little authentic work
with real unsolved problem areas is provided. Math and science too often provide
students with almost no sense that there is a place for them to make their
mark with their own contributions until well into coursework that comes
years after they have had to make important career directing decisions.
It is little wonder over the last twenty years that there has been a steady
and significant decline in the number of college graduates seeking careers
in math, science, business and information technology, areas which generally
require at least one higher level mathematics course in calculus. This
decline continues in spite of the strong need for and consequently higher
salaries for such graduates in order to support and expand our high technology
culture. Note below the different terminology for the same stages of problem
solving.
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. | Math | Science | Local Actions
(e.g., calculators, spreadsheets, databases, word processing, outlining, draw, paint, video, audio, animation, virtual reality, ) |
Global Tools
(networks of computers) |
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Look |
|
Problem Posing
|
find, read, cut, copy, paste, renumber, outline
(humans, not computers, choose problems and purposes) |
Search online databases ; know online contact & reference systems; data space transport protocols |
Evoke |
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Problem Solving
|
type, record
(humans, not tools, generate and elaborate) |
computer conferencing (Netnews, LISTSERVs), collaborative screen use of any program, collaborative writing, talk, chat, email, GIS (Graphic Information Systems) |
Assess |
|
Persuasion | check, lookup, read, listen
(tools have nothing to say about the substance of the teacher and learner's work) |
email, groupware, netphone, video conferencing (CU-SeeMe, private networks) |
Publish/ Perform |
|
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table of contents, index, format, print
(humans, not tools, have value systems thru which to appreciate or take comparative measurement of the works of others) |
Net tools: FTP; audio and video streaming; World Wide Web; virtual
reality; wireless palmtops & PDAs.
Legacy systems: TV, radio stations, publishing houses. |
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The language invoked by science and math deserves to be more strongly
integrated across their content areas. Note in particular the terminology
at the Evoke stage, expressions that each support the goals of the other.