Using Web-Based Resources to Promote Critical Thinking

Evan Glazer

University of Georgia

eglazer@coe.uga.edu

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

NCTM 2001

Overview

Background Critical Thinking Web-Resources Problem Posing Classroom

Environment Progress?

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

Background

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

– Doctoral Candidate in IT at UGA

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

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

– Doctoral Candidate in IT at UGA

– InterMath - problem solving with TEMIs.

Under the direction of Jim Wilson and others http://www.intermath-uga.gatech.edu/

Background

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

– Doctoral Candidate in IT at UGA

– InterMath - problem solving with TEMIs.

– Six years of teaching high school mathematics in Illinois

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.

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

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.

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.

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

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

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

Background

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

– 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.

Background

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

– 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

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

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

– 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.

Available September 1, 2001

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

Greenwood Publishing

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 ofyour administrators off of your island...

Critical Thinking in Mathematics

Critical thinking in mathematics is the ability and disposition to incorporate prior knowledge, mathematical reasoning, andcognitive strategies to generalize, prove, or evaluate unfamiliar mathematical situations in a reflective manner.

Is it subject specific?

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

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

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Critical Thinking Concept Map

Where should you place the flag?

devise and justify a strategy that will determine a fair position for the flag at the beginning of the game.

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,

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

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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 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."

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

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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 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?

I now ask...

Analyze the data set and predict the interval(s) of timeduring 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 Ill-structured that

doesn’t 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.

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

The Teacher

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

Promote student ownership -

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

act as a consultant and learner without influencing judgment

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

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

Progress?

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

NCTM Standards 1989-2000

Opportunity to Realize a Vision

Ill-structured that doesn’t guide students

Try to design meaningful situations

Promote experimentation and making conjectures

Analysis leads to generalization, proof, or evaluation

Methods Data sets and

Data bases Predictions Simulations Dynamic

Environments

Web Sources

Using Web-Based Resources to Promote Critical Thinking

Evan Glazer

University of Georgia

eglazer@coe.uga.edu

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

NCTM 2001