Transcript SQ3R in the Math Classroom

SQ3R in the Math
Classroom
When will we ever use this in
the real world?
Why incorporate reading
techniques into math?
1. The product of three, and a
number decreased by two, is
forty two. Find the number
2. The product of three and a
2. The product
of 3 and
a number,
number,
decreased
by two
is forty
decreased
by
2
is
42.
Find
the
number
two. Find the number.
The Importance of Reading and
Writing in the Math Classroom
NCTM (2000) stated students learn math more
efficiently and more deeply when reading and
writing is directed at learning mathematics
Students who have the opportunity, encouragement,
and support for speaking, writing, reading and
listening in math classes reap dual benefits: they
communicate to learn math and they learn to
communicate mathematically
The Importance of Reading and
Writing in the Math Classroom
Learn to use the language to focus on and work through
problems
Communicate ideas coherently and clearly
Organize ideas and structure arguments
Extend their thinking and knowledge to encompass
other perspectives and experiences
Understand their own problem solving and thinking
process as well as those of others
Develops flexibility in representing and
interpreting ideas
Stamps information into their minds
Ability to put the math concepts into their own
words and understanding
Modify their reading behaviors when faced
with difficulty
Construct meaning as they read by monitoring
comprehension, evaluating new information,
connecting new information with existing
ideas, and organizing information in ways that
make sense
SQ3R Applied to Math
Associated with George Polya’s Four Steps to Problem
Solving (Understand, devise plan, carry out plan, look
back) 1957
In 1965 L. Fay developed the SQRQCQ for Math
(survey, question, read, question, compute, question)
Use this technique every time you are tackling a
problem to not only demonstrate your thought process
out loud but also to give the students an example of
how to approach problems in a logical manner,
determine what strategy to use, and construct a plan
Then have students model and practice this technique
on their own through group work
Survey
First we need to get a general understanding or nature of
the problem (you don’t have to have it solved by the time
you are done reading it!)
Read through the entire problem, pausing at end of each
sentence so they don’t all just run together and become
meaningless
Identify/look up any math vocabulary or terms that you
don’t understand
Question
What is the main goal? What are we trying to find? Assign
variable(s) to these right away
When I think out loud, I try to use natural curiosity to turn
the problem into a puzzle we are trying to solve (change
the wording of the problem into a question)
What information are we going to need to solve it?
What information is actually given to us already?
Read
Go back through problem and break it down into pieces:
what information is given, what do you need (read
actively)
Make sure to use and understand proper vocabulary and
math symbols
How does this problem relate to the math concepts we
have been using? What math will we need to use to solve
it?
Draw pictures, use charts - show given information and
missing information in a different way
Recite/Compute
analyze what we have just read, always keeping in mind
what the main goal is, the variables we are using, use
charts or drawings if needed
Discuss the strategy of actually solving the problem
(show different methods to use)
put the abstract formulas and equations into your own
words (very important to do because this is what the
students will mimic during group work)
notice any patterns to previous problems?
solve the problem
Review
Verbalize, verbalize, verbalize! (put the problem solving
into their own words)
Did we actually answer the problem and find our main
goal?
Does our answer make sense and is it in the correct
context?
Can we go back and describe the steps we took to finding
the answer and how we tackled the problem?
Did it compare to other problems we have done? How did
Problem Solved!
Increases student’s confidence
Put thought process and problem solving into
their own words (sense of ownership)
Leads to increased conceptual understanding,
ability to retain information, and apply and
demonstrate knowledge
Become independent learners and use critical
thinking skills
Example Problem #1
You are flying to Chicago for a trip. The flight
over took three hours and you overheard the
pilot saying that the average plane speed
was 600 mph and there was a tailwind on the
way over. You noticed while you were waiting
at the gate for your return flight back, the
return flight was scheduled to be five hours
due to the fact that you would then be
traveling against the wind. How far is your
one way flight to Chicago and how did the
wind affect the speed of the plane (assuming
the avg plane speed stayed constant in both
directions)?
You are flying to Chicago for a trip. The flight over took three hours and you overheard the pilot
saying that the average plane speed was 600 mph and there was a tailwind on the way over.
You noticed while you were waiting at the gate for your return flight back, that the return flight
was scheduled to be 5 hours due to the fact that you would then be traveling against the wind.
How far is your one way flight to Chicago and how did the wind affect the speed of the plane?
Distance
Over
Back
Rate
Time
Example Problem #2
The flight to New York is 3000 miles and it takes six hours
to fly there when there is no wind speed at all to affect the
speed of the plane (either with the wind or without). Before
you were getting ready to take off for your return flight
home, you overheard the pilot say that there is a tailwind
speed of 100 mph for the flight back and therefore, you
should land early, assuming that the plane speed remains
constant. If your flight is leaving at 11:30 (AZ time), what
time should you tell your ride to expect you at the airport to
pick you up?