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Q
uantitative
R
easoning &
P
roblem
S
olving
2
© 2014 Pacific Crest
W
hat Do You Already Know?
Tapping into your existing knowledge
1. What are three concepts you can teach others in mathematics, including explaining the “
why’s”
of
the concepts (i.e., “Why can you do that?” or “Why does it work?”)?
2. In the process of learning mathematics, how often do you ask
why
you can do a certain thing (e.g.,
subtract a number from both sides of an equation)?
3. What are the three most important mathematical ideas you use when you’re solving problems?
4. What do the practices of
prediction
,
estimation
,
validation
,
finding similarities
,
finding
differences
,
using
examples
,
modeling what if
, and
generalizing
play in the learning of mathematics?
5. Think about someone you know who seems to learn math quickly. What are three things that person
does that helps them do that?
6. Think about someone you know who is “math smart.” What does this mean and what is it that makes
him or her “math smart”?
7. What is the relationship between mathematical learning skills and being “smart”?
M
athematical Language
Terms and notation
Levels of Learning in Mathematics (Bloom’s Taxonomy)
— the five levels of measurable
knowledge (from lowest to highest): information, conceptual understanding, application,
problem solving, and research
mathematical learning skills
— learning skills that are embedded in everyday behavior and operate
in conjunction with specialized knowledge. (e.g. analyzing differences)
I
nformation
What you need to know
R
eadings
R
esources
Methodology
T
he
L
earning
P
rocess
Scenario:
You received a Smartwatch for your birthday. It’s a great piece of technology,
with all kinds of advanced functions and apps, but it’s currently showing the
date as December 12, 2012, and the time as 12:12 p.m. Obviously, you’re going
to need to set the watch to the correct date and time.
Step
Explanation
Watch it Work!
1. Why
Identify and explain your reasons for
learning.
You want to start wearing and using
your new Smartwatch.
2.
Orientat
i
on
Develop a systematic overview of what
is to be learned.
Look over the contents of the package,
the watch, and printed materials.
3.
Prerequisites
Identify necessary skills and background
knowledge needed for the learning task.
Include reading skills, ability to follow
instructions, and fine motor skills.