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Five Decades make a difference: Site material
parallels and re-invents a small subset of the following texts and
several more. With some zeal, these texts gave or reflected set
oriented course design and delivery in the late 1950s and
early1960's.
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Report of the Commission on Mathematics,
Appendices,College Entrance Examination Board, New York
1959. Here is a technical base for the senior high school
presentation of many concept. VG
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Secondary Mathematics, A Functional Approach for
Teachers, H. F. Fehr, Teachers College, Columbia
University. 1951 D. C Heath and Company. A wealth of
technical know-how for course design - senior level. VG
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The Growth of Mathematical Ideas, Grades K-12,
Twenty-Fourth Yearbook, The National Council of Teachers of
Mathematics, Washington, D. C. USA 1959. Not my cup of tea.
The site introduction
via examples of a variable as a number or quantity which may vary
may be easily woven into the placeholder view of what is a variable,
but that introduction appears to be clearer for
students.
Five decades ago, there was much discussion of what should
be in primary and secondary mathematics to train engineers, scientist,
mathematicians and math teachers - university oriented types; and to help
the remaining "terminal students". In the great
discussion of what should be done and how, the algebraic way of writing
and reasoning was employed with a partial rather than a full progressive
development of its skills and concepts. The development of trig
with the aid of complex numbers was seen as advantageous, but it was not
implemented may be due to the question of how to introduce complex
numbers in a simple manner.
Cold War Motivation in the 1950s: Sputnik went up
and around the globe. Western societies responded with a thrust to form
or train scientists, engineers and mathematicians with great
zeal. The space (and arms) race was on. Until Gorbachev,
there was an imminent threat of global nuclear
annihilation.. The sputnik motivated,
pre-university secondary mathematics omitted skills and concepts that
might have been useful to "terminal" students - those not
heading for university. Motivation in the pre-university
stream was given in part by the maths in chemistry and physics.
In the last decades, students in the pre-university stream was
widened to include more students -parents wanted their kids to
have chance to go and not be excluded. But in the pre-university
stream, the study of polynomials and radian measure have
not immediate value, save for preparation for calculus. Besides
old and continuing gaps in the progressive or inductive development of
skills and concepts, there has been a motivation gap, a lack of purpose
in and communication of ends & values of instruction, save
for the annual bureaucratic goal of preparing for final
examinations.
Site
methods for the progressive development of algebraic skills
(comprehension of the shorthand role of letters and symbols) upto and
including calculus, continuing with site ideas for basing trig and trig
formulas on a development of complex numbers from Euclidean geometry,
continuing with site introduction of analytic geometry, and site calculus
previews offer a quicker, more accessible and stronger base for students
taking or aiming for calculus. The development of algebra skills, those
related to money matters, will help students aiming for calculus or
not. Course design may be based on the dynamic
programming optimization question of how to maximize the value of each
year of school for students who might not continue while
progressively developing skills and concepts in an observable and
verifiable manner. The terminal rather than the pre-university
stream should be widened to give students as much as possible, a thorough
empirical grounding not in the mathematics needed for academic
studies, but in skills that could be needed or useful in
life, daily or yearly, sooner or later. Even students who are
pre-university need that know-how sooner or later.
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