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Q
uantitative
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easoning &
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roblem
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olving
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© 2014 Pacific Crest
O
ops
! A
voiding
C
ommon
E
rrors
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Believing that practice makes perfect
Example
: Solving all the odd problems from 1 to 43 and checking the answers in the back of
the book or the equivalent on the computer homework problem system to see if you
got the right answers
Why?
A couple of poor habits tend to develop quickly if this is your mindset. First is the
tendency to work backwards from the answer key to try and figure out how to solve the
problems. The second habit is just waiting and bringing problem you couldn’t solve to
class.An exploration of what you don’t know, why you don’t know it, and how to clarify
your understanding never gets addressed in the review and grading of homework.
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Willingness to memorize instead of understanding
Example
: Taking note, step by step, of how your instructor solves a specific problem without
understanding why you can perform specific steps
Why?
Memorized knowledge is fragile (with a short half-life of retention) and can rarely be
transferred to new situations. Knowledge that you can teach others and that you have
generalized is knowledge that you own for a life-time.
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Limited use of prior knowledge
Example
: Learning to solve a linear inequality without using what you know about solving a
linear equation
Why?
As in the previous example, the complexity of solving linear inequalities can be
reduced by about 80% if we apply all we know about solving linear equations to this
new context. The processes used to solve the two types of problems are very similar
and if we apply our prior knowledge, we can learn to solve linear inequalities much
more quickly and easily.
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Errors produced by not validating
Example:
Getting a 75%on an examwhen you understand and have generalized your knowledge
Why?
Everyone makes mistakes that they don’t catch. In math, we have a validation step
that allows you to find your own mistakes, and mathematical mistakes, when found,
can be corrected. In addition to scoring higher on your exams, you will strengthen
your learning process by recognizing how many errors are simple mistakes rather
than actual lack of understanding. This quickly increases your confidence in your
ability to learn mathematics.
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Not using the practice for its intended purpose
Example:
When you fail to understand, always asking others to clarify, explain, or re-teach you
Why?
Learner ownership starts with you doing the critical thinking. Information that you are
given (such as in response to a question) is like knowledge that is memorized —it is
fragile, easily forgotten, and rarely understood. Contrast this with information that you
find and discover on your own: Not only is it something you understand because you
thought your way to it, it is also information you learned and earned yourself. It will
forever be meaningful to you, for that reason. Asking questions is not bad, but before
you ask for knowledge to be handed to you, do what you can to figure it out on your
own, first.