Modern Education and Critical Thinking
The demand in modern or post-modern education theory
(constructivism) for problem solving and critical thinking are undermined
by course design changes which do not require drill and practice in
arithmetic, so that arithmetic provides repeatable and reproducible
results, and to the point that students are taught or shown that care,
patience and self-discipline is required to mastery multistep
methods. Allowing students to skip that care, patience and
self-discipline needed to obtain repeatable and reproducible results
leads to wishful and suspect critical thinking and problem solving
abilities. The use and combination of rules and patterns one at a
time and then one after another represents the start of deductive reason
and deductive connection, construction and Euclidean codification of
skills and concepts. For very critical thinking and problem solving
skills demanded, students need the ability and self-discipline to follow
rules and patterns in a repeatable, reproducible and thus verifiable or
objective manner. But they also need the knowledge that rules and
patterns, even those with seemingly repeatable, reproducible and
therefore verifiable results need not be reliable. Again, That is where
critical thinking appears. Further in problem solving, students should
meet or be given solutions to problems previously met, so that there is
not continuing need to re-invent solutions, and so that students can
repeat or develop further what others have done. Students need the
ability to recognize and solve open problems, but that stand on a
knowledge of what has been done before and a deliberate coverage of the
benefits, origins and limits of rule and pattern based processes in
thought and deed. A balance is needed. Past practices should not be
pushed aside. Students should learn about them, their benefits, origins
and limitations, while learning to go beyond when needed.
Critical thinking in science is based on statements that can be tested
and the empirical accumulation of practices that work in some measure if
not completely. There-in lies an behavioral approach to learning
and teaching in science, mathematics included. Modern cognitive
theory which says teachers and schools should not test students because
(i) whatever a student thinks is valid for him or her; (ii) because
rule and pattern based skills and concepts is not real learning;
and because (iii) student success on one test is no guarantee of
success on further tests, do so in opposition to empirical perspective of
mathematics and science.
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