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© 2014 Pacific Crest
27
O
ops
! A
voiding
C
ommon
E
rrors
●
Not knowing the precise meaning of a word or what a symbol represents
Example
: Set A = {3, 5, 7} and B = { 2,3,4,5} What is A
∪
B?
Why?
Understanding the precise meaning of
∪
is necessary in order to understand what is
being asked.
●
Missing an important concept, table or highlighted section
Example
: Division by 0 is undefined, thus a denominator with a variable can’t be equivalent in
value to 0.
Why?
The confusion that can occur by missing an important idea can lead to escalating
misconceptions, such as presenting a solution that doesn’t exist.
●
Not understanding clearly a specific step in a methodology
Example
: Performing the “Quick Read” step ineffectually in the Reading Methodology (the
quick read usually doesn’t allow for creation of the needed set of inquiry questions
for producing effective learning during the comprehensive read).
Why?
A step in a methodology is more than just the step itself — it has a relationship to
prior steps, a function critical for that step, and many implications for future steps.
Understanding both the how and why of each step is critical for performance of the
overall process.
●
Knowing how to do something, but not
why
you can do it
Example
: Knowing that you can flip the denominator to turn a fraction division problem into
multiplication, but not knowing why
Why?
The ability to generalize knowledge comes from comprehension and understanding so
that you can transfer knowledge to new situations such as when you find a fractional
expression in the denominator.
A
re You Ready?
Before continuing, you should be able to ...
I can...
OR
Here’s my question...
fill out a complete reading log
explain each component of a learning
experience
complete a preparatory reading prior
to a comprehensive reading in order to
produce higher levels of learning
work on elevating my inquiry questions
during the reading process
1.3 Learning to Read Mathematics