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Multi-step methods in many arts and disciplines at school and work
require the knowledge or awareness that errors in a step of a method
or calculation lead to incorrect results and that care is needed to avoid
such errors. This kind of care and intelligence follows say from
practice in (i) Column methods for arithmetic (addition,
subtraction, multiplication and division), in (ii) logic, that is
the direct and indirect use of implication rules one at a time and one
after another, to arrive at conclusion, and in (iii) recipes, plans,
instructions for cooking or construction.
Next, critical thinking and problem solving skills in general may begin
with development and emphasis of the ability to follow multi-step methods
with care, starting with chains of calculations or reason in arithmetic
and logic, and continuing with systematic or trail and error approaches
to solving jigsaw puzzles. The jigsaw puzzle questions
- are all the piece present?
- Is there a plan or picture to follow?
may develop the ability to think within the box or close to it. Thinking
out of the box in combinatorial and opportunistically is fine but the the
benefits and limits of the ability to work in the box with the available
pieces should be practice first - thinking out of the box has a place
when thinking in the box does not work.
Emphasizing critical thinking and problem solving in mathematics course
design out of the box is nonsense if in the box skills and concepts are
not developed first.
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