Site Origins
As a secondary school student 1965-9, I suspected difficulties in
algebra were due to its incomplete introduction. That is, the algebraic
shorthand roles of letters and symbols were used, required, but not
clearly nor fully explained. So I watched for a remedy. In fall
1983 as a novice instructor, I gave three lessons, namely
three skills for
algebra, why slopes and
two logic puzzles to make
algebra & calculus simpler to understand and explain; to improve
reading, writing & reasoning skills; and to hint at the role of logic
in mathematics. Since then, I have been trying to tell to fellow
instructors how difficulties in mathematics might be addressed but my
ideas not wanted, were dismissed before being heard.. Today, I am still
trying. Parallel to views that difficulties in mathematics can be
eased by use of indirect instruction to engage or interest
students, my 1965-9 suspicion has slowly become a proposition for a clearer, fuller, wordier
development of algebraic skills, concepts and themes. Site material
shows how in ways motivated by inductive principles for
instruction met in 1981 outside of mathematics. Site material also spring
from examples of guest speakers 1975-82 at McGill University of
different ways to understand and develop skills and concepts in
mathematics and physics.
Writing only began in the last days of 1990 as I saw no hint in
mathematics education literature and practice of the remedies I saw
or sensed for common difficulties. Prior to that my writings aimed
at advancing mathematics itself and not mathematics education. The
mathematic education literature with its focus on delivery matters
obscures the question of what should be taught. It appears that cognitive
theories of learning dismissive of the rule-based fashion in which
mathematicians see their discipline lead course design and delivery in
North America. Sequences of skills and concepts which could be
leaner, which mathematicians see as preparation for calculus
are being obscured or diluted by cognitive theories, dominant or
authoritative in their own way, which say students should find and
construct their own knowledge instead of following authoritative
(textbook) accounts.. This opposition to authority in name of developing
critical thinking undermines them instead as the ability to follow rules
and patterns in a repeatable and reproducible manner is needed before and
besides the question of whether or not particular rules and patterns are
valid.
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