Science Education

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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.