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Science, Technology and Mathematics
In mathematics, science and technology, rule and pattern based
knowledge for better or worse, expands through the trial and
error discovery or invention of methods with repeatable, reproducible and
hence verifiable results. Some of that knowledge is recorded on
paper and delivered clarified and summarized in school. For
mathematics, science and technology, instruction may report
what has been found, and give students a comprehension of key
skills and concepts and a comprehension of how scientific and
technological knowledge has grown along with the benefits, origins and
limitations of that growth. There are stories to be told and
connections to be reported. Yet lab activity in school, to brief to
confirm or duplicate in full the multigenerational history of a
subjects, serves to introduce equipment and how careful setup and
observation in the development and confirmation of methods in science and
technology led to and may lead to results or evidence that is repeatable
and reproducible. The extent and breadth of science and technology
has to be presented in an authoritative with teachers and textbooks
effectively saying look at the patterns which haven been found or
thought and here is some of the evidence or reasoning which justifies and
links them together.
In science and technology, verification or refutation of an new
assertion in science and technology may comes from observation in
and outside of a lab, with controlled circumstances, repeatable and
reproducible, preferred. In mathematics and mathematical
models, rule and pattern based knowledge begins with assumptions, and
then relative to those assumptions, an statement is considered verified
when and only when the statement is implied by a least one direct or
indirect deductive chain of reason, repeatable and reproducible.
The development of science and technology is just too complex and
nonlinear for student alone to reconstruct. Summaries are required to
give students a practical command of the subject and an awareness of the
benefits, origins and limitations of ideas and methods, so that science
and technology are applied with caution. Not all is certain.
Errors may be introduced in the summary or exposition of ideas. So
vigilance is required and teachers should comment on what can be easily
observed or not by students or people in the street, and what requires
dedicated equipment to verify. Vigilance is also required since
lies or half-truths can be put forward in the guise of statistics,
science and/or technology. Finally, education departments in
support or development of national pride may slant the history of skill
and concept development to create local heroes in place of recognizing
the international nature of development.
In contrast, the development of mathematics can be simpler. The
historical development of mathematics is too complex or contorted for
students to follow, and that development did not appear in a deductive
manner. But students may be offered a self-contained, almost a
historical, thought-based command and comprehension of arithmetic,
algebra and geometry in ways sufficient for practical ends and sufficient
too, if wanted, for the further study of pure mathematics .
Further Readings: For more reflections on the benefits,
origins and limitations of rule and pattern based methods or processes
in thought and deed, see Volume 1A, Pattern Based Reason. The latter
provides background information but not a remedy for the above
difficulties.
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