Transcript Using Web-Based Resources to Promote Critical Thinking

NCTM 2001
Using Web-Based Resources to
Promote Critical Thinking
Evan Glazer
University of Georgia
[email protected]
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Overview
 Background
 Critical Thinking
 Web-Resources
 Problem Posing
 Classroom
Environment
 Progress?
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Background
– Doctoral Candidate in IT at UGA
http://www.arches.uga.edu/~eglazer/NCTM2001.html
What’s Instructional Technology?
My definition:
The analytical and
systematic
processes in the
design,
development, and
implementation of
instruction and
learning
environments.
Primary Areas of the Field
- Training
- Technology integration
- Performance support
- Evaluation
- Instructional Models
- Learning Theories
- Distance/Web-based learning
- Virtual reality
- Learning with/from technology
- Computer-based interactive learning
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Baptism Bulldawg Style
Background
– Doctoral Candidate in IT at UGA
– InterMath - problem solving with
TEMIs.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Under the direction of Jim Wilson and others
http://www.intermath-uga.gatech.edu/
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
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
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
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 nonexpendable.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
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
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
Mathematicians
have the unique
talent of
determining how
fast they are
running, and how
much faster they
need to run
by the end of the
race in order to set
a personal record.
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
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
Available
September 1, 2001
Greenwood Publishing
Links to over 200 websources including
some activities from
prealgebra to calculus
are available online at
http://www.arches.uga.edu/
~eglazer/NCTM2001.html
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
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
Suggested Theme Song...
Imagine if you had the opportunity to vote one of
your administrators off of your island...
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
Critical Thinking Concept Map
QuickTime™ and a
GIF decompressor
are needed to see this picture.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
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 team’s 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
Is Learning Easier with the
Internet?
 Information at our
fingertips in a timely
manner.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
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
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.”
What are you doing to save time?
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?
“Interesting” Web-based Sources
 Data sets and Data bases
 Predictions
 Simulations
 Dynamic Environments
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Data Sets and Data Bases
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
Additional Data Sources
 Astronomy
 Travel Times
 Maps
 Salaries
 Banking
 Sports
 Consumer Indexes
Predictions
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
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
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 red
flags. 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 elected
to pay a $5,000 fine and keep the original,
"Frankly my dear, I don't give a damn."
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.
Additional Prediction Sources
 Internet Access
 Download Speeds
 Demographics
 “Tricks” related to composite numbers
QuickTime™ and a
GIF decompressor
are needed to see this picture.
http://www.smalltime.com/dictator.html
Simulations
Additional Simulation Sources
 Homer Simpson’s 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
Dynamic Environments
Let’s try 1000 Wurfe
Click on red…
Click on blue…
Click on green…
Click on blue…
Click on green…
Additional Dynamic Environments
 Adjustable function graphers
 Dynamic geometry constructions
 Statistics activities
 “Science” experiments
 Rotating three-dimensional objects
 Graphing limits
Problem Posing Techniques
 Ill-structured that
doesn’t guide students
http://www.arches.uga.edu/~eglazer/NCTM2001.html
I used to ask...
The goal of this problem is to find a cosine function that
models 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?
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
Problem Posing Techniques
 Ill-structured that
doesn’t guide students
 Try to design
meaningful situations
http://www.arches.uga.edu/~eglazer/NCTM2001.html
A Consequence of Bad Problems
Problem Posing Techniques
 Ill-structured that
doesn’t guide students
 Try to design
meaningful situations
 Promote
experimentation and
making conjectures
http://www.arches.uga.edu/~eglazer/NCTM2001.html
Problem Posing Techniques
 Ill-structured that doesn’t
guide students
 Try to design meaningful
situations
 Promote experimentation
and making conjectures
 Analysis leads to
generalization, proof, or
evaluation
Sample Investigation
Your long lost uncle has willed your family  Ill-structured that
an undisclosed amount of money to use as a
doesn’t guide
down payment on a house. Your parents
students
express two concerns in search of this
 Try to design
property:
meaningful
situations
1. They do not want to pay mortgage
 Promote
insurance; and
experimentation and
2. Ideally, they would like as much space
making conjectures
possible.
 Analysis leads to
generalization,
Based on the patterns in the neighborhood
proof, or evaluation
housing sale prices, recommend two homes
that your family should consider
purchasing.
The Classroom
Environment
 Learner
 Teacher
Qui ckT ime™ and a
GIF decompres sor
are needed to s ee this picture.
http://www.arches.uga.edu/~eglazer/NCTM2001.html
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
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
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 don’t want to see
students fail
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
NCTM Standards 1989-2000
Opportunity to Realize a Vision
Web Sources
Methods
 Data sets and
 Ill-structured that doesn’t
Data bases
 Predictions
 Simulations
 Dynamic
Environments
guide students
 Try to design meaningful
situations
 Promote experimentation
and making conjectures
 Analysis leads to
generalization, proof, or
evaluation
NCTM 2001
Using Web-Based Resources to
Promote Critical Thinking
Evan Glazer
University of Georgia
[email protected]
http://www.arches.uga.edu/~eglazer/NCTM2001.html