Using WebBased Resources to Promote Critical Thinking

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Using Web-Based Resources to Promote Critical
Thinking
NCTM 2001

• Evan Glazer
• University of Georgia
• eglazer_at_coe.uga.edu

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Overview

• Background
• Critical Thinking
• Web-Resources
• Problem Posing
• Classroom Environment
• Progress?

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Background

• Doctoral Candidate in IT at UGA

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Whats Instructional Technology?
My definition The analytical and systematic
processes in the design, development, and
implementation of instruction and learning
environments.
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Baptism Bulldawg Style
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Background

• Doctoral Candidate in IT at UGA
• InterMath - problem solving with TEMIs.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Under the direction of Jim Wilson and others
http//www.intermath-uga.gatech.edu/
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Background

• Doctoral Candidate in IT at UGA
• InterMath - problem solving with TEMIs.
• Six years of teaching high school mathematics in
  Illinois

http//www.arches.uga.edu/eglazer/NCTM2001.html
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You might be a real teacher if...

• You grade papers in the car, during commercials,
  in faculty meetings, in the bathroom, and (at the
  end of the six weeks) have been seen grading in
  church.

• You have a disjointed neck from writing on boards
  without turning your back on the class.

• You are written up in medical journals for the
  size and elasticity of your kidneys and bladder.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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You might be a real teacher if...

• You have been timed gulping down a full lunch in
  2 minutes, 18 seconds. Master teachers can eat
  faster than that.

• You know it is better to seek forgiveness than to
  ask permission.

• You buy Excedrin and Advil at Sam's.

• You know secretaries and custodians run the school

http//www.arches.uga.edu/eglazer/NCTM2001.html
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You might be a real teacher if...

• You hear the heartbeats of crisis always have
  time to listen know you teach students, not just
  a subject and you are absolutely
  non-expendable.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Background

• Doctoral Candidate in IT at UGA
• InterMath - problem solving with TEMIs.
• Six years of teaching high school mathematics in
  Illinois
• Web-based development since 1993.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Background

• Doctoral Candidate in IT at UGA
• InterMath - problem solving with TEMIs.
• Six years of teaching high school mathematics in
  Illinois
• Web-based development since 1993
• I have a passion for working with kids, teaching,
  learning, mathematics, and running

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Mathematicians have the unique talent of
determining howfast they are running, and how
much faster they need to runby the end of the
race in order to set a personal record.
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Background

• Doctoral Candidate in IT at UGA
• InterMath - problem solving with TEMIs.
• Six years of teaching high school mathematics in
  Illinois
• Web-based development since 1993
• I have a passion for working with kids, learning,
  mathematics, and running
• Research and writing interests include
  communities of practice and technology
  integration.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Available September 1, 2001
Greenwood Publishing
Links to over 200 web-sources including some
activities from prealgebra to calculus are
available online at
http//www.arches.uga.edu/eglazer/NCTM2001.html
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What is Critical Thinking?

• Define it in your own words

Critical thinking is reasonable reflective
thinking that is focused on deciding what to
believe or do. Ennis (1987)
http//www.arches.uga.edu/eglazer/NCTM2001.html
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The result of a non-thinking curriculum

• There are 26 sheep and 10 goats on a ship. How
  old is the captain?

Over 75 of the students claimed they had solved
this problem using some form of arithmetic
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Suggested Theme Song...
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Imagine if you had the opportunity to vote one
ofyour administrators off of your island...
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Critical Thinking in Mathematics
Is it subject specific?
Critical thinking in mathematics is the ability
and disposition to incorporate prior knowledge,
mathematical reasoning, and cognitive strategies
to generalize, prove, or evaluate unfamiliar
mathematical situations in a reflective manner.
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Critical Thinking Concept Map
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Where should you place the flag?
Three teams are to play a game of capture the
flag. The goal of the game is to be the first
team to move a flag from its starting position
on the field to another teams home base without
getting tagged. If the home bases are located
anywhere on the perimeter of the field,
devise and justify a strategy that will determine
a fair position for the flag at the beginning of
the game.
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Is Learning Easier with the Internet?

• Information at our fingertips in a timely manner.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Is Learning Easier with the Internet?

• Information at our fingertips in a timely manner.

• False sense that the Internet makes our life
  easier.

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Quotes from Recent Advertisements

• Now setting up your online course is so easy you
  can do it in under 15 minutes.
• Life just got easier. Join the Webolution
  Excite students Enthuse staff.

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What are you doing to save time?
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Is Learning Easier with the Internet?

• Information at our fingertips in a timely manner.

• False sense that the Internet makes our life
  easier.
• Is understanding mathematics about finding
  information, or applying it?

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Interesting Web-based Sources

• Data sets and Data bases
• Predictions
• Simulations
• Dynamic Environments

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Data Sets and Data Bases
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Additional Data Sources

• Astronomy
• Travel Times
• Maps
• Salaries
• Banking
• Sports
• Consumer Indexes

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Predictions
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Numeracy in Baseball

• "Babe Ruth made a great mistake when he gave up
  pitching. Working once a week, he might have
  lasted a long time and become a great star."
  Tris Speaker (Manager of the Cleveland Indians),
  commenting on Babe Ruth's plans to change from a
  pitcher to an outfielder, spring 1921

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Numeracy in Baseball

• "Half this game is ninety percent mental." Danny
  Ozark, Phillies manager
• "The only reason we're 7-0 is because we've won
  all seven of our games." David Garcia, baseball
  team manager
• "We have only one person to blame, and that's
  each other." Barry Beck, New York Ranger, on who
  started a brawl

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Movie Trivia
In 1939, the Hollywood Production Code dictated
what could and could not be shown or said on
screen, and Rhett Butler's memorable last line
raised redflags. A few of the suggested
alternatives were "Frankly my dear... I just
don't care," "...it makes my gorge rise," "...my
indifference is boundless," "...I don't give a
hoot," and "...nothing could interest me less.
Fortunately, producer Selznick electedto pay a
5,000 fine and keep the original, "Frankly my
dear, I don't give a damn."
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Movie Trivia (cont.)

• In 1929, producer Michael Selznick paid Gone with
  the Wind novelist Margaret Mitchell 50,000 for
  rights to the film. At the time, this was the
  highest sum that had ever been paid for an
  author's first novel.
• Lucas had trouble getting funding for Star Wars,
  most studios thinking that people wouldn't go to
  see it. In fact, 20th Century Fox was so sure
  Star Wars was going to be a disaster that they
  came within a matter of days of selling off their
  stake in the film as a tax shelter.

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Additional Prediction Sources

• Internet Access
• Download Speeds
• Demographics
• Tricks related to composite numbers

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http//www.smalltime.com/dictator.html
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Simulations
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Additional Simulation Sources

• Homer Simpsons test of fate
• Stopping a forest fire
• Air traffic control system
• Bath time with Archimedes
• Billiards on different shaped tables
• Monty Hall problem
• Birthday problem

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Dynamic Environments
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Lets try 1000 Wurfe
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Click on red
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Click on blue
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Click on green
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Click on blue
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Click on green
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Additional Dynamic Environments

• Adjustable function graphers
• Dynamic geometry constructions
• Statistics activities
• Science experiments
• Rotating three-dimensional objects
• Graphing limits

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Problem Posing Techniques

• Ill-structured that doesnt guide students

http//www.arches.uga.edu/eglazer/NCTM2001.html
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I used to ask...
The goal of this problem is to find a cosine
function thatmodels temperature data over a
year. We will use this function to predict the
interval(s) of time of the year when the
temperature is at least 65 degrees F.
Question 1 - List the Xmin, Xmax, Ymin, and Ymax
values.
Question 2 - What is the amplitude?
Question 3 - What is the phase shift?
Question 4 - What is the vertical shift?
Question 5 - yadda yadda yadda

can you predict the next
question? Can your students predict the next
question?
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I now ask...
Analyze the data set and predict the interval(s)
of time during the year when the temperature is
suitable for wearing shorts. Explain your
reasoning and show all of your work.
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Problem Posing Techniques

• Ill-structured that doesnt guide students
• Try to design meaningful situations

http//www.arches.uga.edu/eglazer/NCTM2001.html
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A Consequence of Bad Problems
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Problem Posing Techniques

• Ill-structured that doesnt guide students
• Try to design meaningful situations
• Promote experimentation and making conjectures

http//www.arches.uga.edu/eglazer/NCTM2001.html
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Problem Posing Techniques

• Ill-structured that doesnt guide students
• Try to design meaningful situations
• Promote experimentation and making conjectures
• Analysis leads to generalization, proof, or
  evaluation

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Sample Investigation

• Ill-structured that doesnt guide students
• Try to design meaningful situations
• Promote experimentation and making conjectures
• Analysis leads to generalization, proof, or
  evaluation

Your long lost uncle has willed your family an
undisclosed amount of money to use as a down
payment on a house. Your parents express two
concerns in search of this property 1. They do
not want to pay mortgage insurance and 2.
Ideally, they would like as much space
possible. Based on the patterns in the
neighborhood housing sale prices, recommend two
homes that your family should consider
purchasing.
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The Classroom Environment

• Learner
• Teacher

http//www.arches.uga.edu/eglazer/NCTM2001.html
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The Learner

• Exploration and discovery are methods used to
  help construct solutions

• Communication primarily takes place in small
  groups

http//www.arches.uga.edu/eglazer/NCTM2001.html
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The Teacher

• Encourage an open atmosphere to raise questions,
  challenge ideas, and take risks.

• Promote student ownership -

act as a consultant and learner without
influencing judgment
http//www.arches.uga.edu/eglazer/NCTM2001.html
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Do we avoid critical thinking?

• Pressures of standardized tests
• Directed instruction is easier to manage and
  assess
• Takes more time to grade student responses
• Only honors students can do this
• Not understanding right away is uncomfortable -
  we dont want to see students fail

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Progress?
If an unfriendly foreign power had attempted to
impose on America the mediocre educational
performance that exists today, we might well have
viewed it as an act of war. We have, in effect,
been committing an act of unthinking, unilateral
educational disarmament. A Nation at Risk,
1983
http//www.arches.uga.edu/eglazer/NCTM2001.html
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NCTM Standards 1989-2000
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Opportunity to Realize a Vision
Methods
Web Sources

• Ill-structured that doesnt guide students
• Try to design meaningful situations
• Promote experimentation and making conjectures
• Analysis leads to generalization, proof, or
  evaluation

• Data sets and Data bases
• Predictions
• Simulations
• Dynamic Environments

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Using Web-Based Resources to Promote Critical
Thinking
NCTM 2001

• Evan Glazer
• University of Georgia
• eglazer_at_coe.uga.edu

http//www.arches.uga.edu/eglazer/NCTM2001.html