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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
S
trategies
O
vercoming
L
earning
C
hallenges
The Challenge
Not valuing mathematical knowledge for its utility in
solving problems
The Solution
Step 1
of the LPM (why) is the key to motivation for learning as well as how to pursue understanding
instead of rote (and disinterested) learning. Asking “Why?” allows you to define not only the point of
what you’re learning, but meaningful application of it up front. Your mathematical learning becomes a
problem solving toolkit instead of simply a series of things you’ve learned. When you ask “Why?” as a
learner, you’re actively engaging with the content and building your problem solving skills.
The Challenge
Limited use of prior knowledge / Assuming all the
information or learning is new
The Solution
Step 3
of the LPM (prerequisites) has to do with the knowledge that will be used for the current learning.
The speed and quality of learning will be enhanced by finding all the similarities between prior knowledge
and what is currently being learned. What is left over (what wasn’t similiar to prior knowledge) is the
new knowledge that must be learned, a significantly reduced challenge
!
The Challenge
Trouble transferring knowledge into new contexts
The Solution
There are five different dimensions of mathematical complexity: 1) expanding number systems, 2) level
of abstraction, 3) incorporation of new notations and mathematical objects, 4) expansion of mathematical
statements, and 5) expansion of the mathematical set of properties, axioms, and theorems. As you
learn mathematics, you repeatedly revisit these five dimensions, but at increasingly complex levels.
Step 3
of the LPM (prerequisites) is critical here because it directs you to intentionally recognize what
previous learning you will be needing and using in order to help you not only build upon that previously
learning, but also to transfer it into new contexts.
The Challenge
Lack of precision in the use of mathematical language
The Solution
Step 6
of the LPM (vocabulary) is a critical step when it comes to learning because words in the context
of mathematics almost always have single, stable, and very precise meanings. As you improve your
ability to focus on the terms in question and learn their definitions, your ability to read mathematical
content will improve and become increasingly effective. A good tip is to take a term you think you
understand and rephrase it, in your own words. If you can do this, the chances are good that you
understand the meaning of the word...and that beats memorizing someone else’s words every time!