# Learning Math: Data Analysis, Statistics, and Probability

## Practical examples highlight the basic concepts of data analysis and statistics in this video- and web-based course for K-8 math teachers.

A video- and web-based course on basic concepts of statistics for K-8 teachers; 11 half-hour video programs, course guide, and website.

Learning Math: Data Analysis, Statistics, and Probability is one of five video- and Web-based mathematics courses for elementary and middle school teachers. These courses, organized around the content standards of the National Council of Teachers of Mathematics (NCTM), will help you better understand the mathematics concepts underlying the content that you teach.

Data Analysis, Statistics, and Probability introduces statistics as a problem-solving process. In this course, you can build your skills through investigations of different ways to collect and represent data, and describe and analyze variation in data. Through practical examples, you will come to understand some statistical concepts, such as data representation, variation, the mean and median, bivariate data, probability, designing statistical experiments, and population estimations. The concluding case studies, divided into grade bands for K-2, 3-5, and 6-8 teachers, show you how to apply what you have learned in your own classroom. The course consists of 10 two-and-a-half hour sessions — nine topic sessions and a classroom case study targeted to the three different grade bands. Each has a half-hour of video programming, problem-solving activities available in print and on the Web, interactive activities and demonstrations on the Web, and questions for class discussion or individual reflection.

### Video Index

Session 1: Statistics As Problem Solving
When Measurements Are Inconsistent
Real World: Measurement Error
Bias in Surveys

Session 2: Data Organization and Representation
Counting Raisins, Describing Results
Predicting the Weather

Session 3: Describing Distributions
The Benefits of Grouping Data
Predicting Common Hat Sizes
Displaying Results

Session 4: The Five-Number Summary
Defining Typical
The Median of an Even Set
Building a Box Plot
Box Plot as Summary

Session 5: Variation About the Mean
The Mean and Fair Allocation
From Stacks to a Line Plot
Real World: Boston Harbor

Session 6: Designing Experiments
Comparing Designs
Real World: Physicians Health Study
Comparative Box Plots

Session 7: Bivariate Data and Analysis
Points on a Scatter Plot
When X Equals Y
Evaluating Trend Lines

Session 8: Probability
Defining Probability
Constructing a Tree Diagram
Generating Pascal’s Triangle
Pascal’s Triangle as a Shortcut

Session 9: Random Sampling and Estimation
Collecting a Random Sample
Connecting Probability and Statistics

Session 10: Classroom Case Studies

### Who's Who

Content Developer/Facilitator
Appalachian State University, NC

Gary Kader is a professor of mathematical sciences at Appalachian State University. He has been active in the development of educational materials for teaching and learning statistics through his involvement with six statistics education projects funded by the National Science Foundation. These projects developed innovative approaches to teaching and learning statistics and provided professional development opportunities for college faculty. His work in statistics education has focused on activity-based approaches to learning statistical concepts and problem-solving. His interest in activity-based learning led him to direct the NSF project “A Laboratory Course in Mathematics for Liberal Arts Majors.” He received a Ph.D. in Statistics from the University of Georgia in 1980 and B.S. and M.S. degrees in Mathematics from Georgia Southern University. He is a member of the American Statistical Association and the National Council of Teachers of Mathematics, and he serves as a reviewer for the NCTM journal The Mathematics Teacher. He received the Distinguished Alumnus Award from the Department of Mathematics and Computer Science from Georgia Southern University in 1996.

Content Developer
L. Mike Perry
Mike Perry retired in 2002 from Appalachian State University, where he was a professor of mathematical sciences and now works as a consultant in statistics education. His interest in the teaching of statistics led him to direct six projects funded by the National Science Foundation; these efforts developed new approaches to learning statistical ideas, provided teacher education in statistics, and offered professional development to college faculty. His writing focuses on activity-based approaches for learning statistical concepts and problem-solving. He was a lecturer at the Institute of Statistics at Texas A&M University (1978-79) and a visiting scholar at the Royal Statistical Society’s Centre for Statistical Education at the University of Sheffield (1991) and the University of Nottingham (1997). He currently serves as a consultant for the Advanced Placement Program in statistics and frequently reviews articles for The Mathematics Teacher. He received a Ph.D. in mathematics from North Carolina State University and holds Master’s degrees from North Carolina State and Texas A&M universities.

Onscreen Participants

Krus, David and Webb, James (Autumn, 1997). Demonstrating Variance Using the Muller-Lyer Illusion. Teaching Statistics, 19 (3), 72-76. (Session 1)

Demonstrating Variance Using the Muller-Lyer Illusion
Continued

Principles and Standards for School Mathematics. (Reston, VA: National Council of Teachers of Mathematics, 2000) Standards on Data Analysis and Probability by grade level: K-2, 108-115; 3-5, 176-181; and 6-8, 248-255.

Friel, Susan, Bright, George, and Curcio, Frances (November-December, 1997). Understanding Students’ Understanding of Graphs. Mathematics Teaching in the Middle School, 3 (3), 224-227. (Session 2)

Understanding Students’ Understanding of Graphs
Continued

Kader, Gary, and Perry, Mike (November-December, 1997). Pennies from Heaven — Nickels from Where? Mathematics Teaching in the Middle School, 3(3), 240-248. (Session 2)

Pennies from Heaven — Nickels from Where?
Continued
Continued
Continued

Kader, Gary and Perry, Mike (September-October, 1994). Learning Statistics with Technology. Mathematics Teaching in the Middle School, 1 (2), 130-136. (Session 3)

Learning Statistics with Technology
Continued
Continued

Pereira-Mendoza, Lionel and Dunkels, Andrejs (Summer, 1989). Stem-and-Leaf Plots in the Primary Grades. Teaching Statistics, 11 (2), 34-37. (Session 3)

Stem-and-Leaf Plots in the Primary Grades
Continued

Friel, Susan and O’Connor, William (March, 1999). Sticks to the Roof of Your Mouth? Mathematics Teaching in the Middle School, 4 (6), 404-411. (Session 4)

Sticks to the Roof of Your Mouth?
Continued

Kader, Gary (March, 1999). Means and MADS. Mathematics Teaching in the Middle School, 4 (6), 398-403. (Session 5)

Continued

Uccellini, John C. (November-December, 1996). Teaching the Mean Meaningfully. Mathematics Teaching in the Middle School, 2 (3), 112-115. (Session 5)

Teaching the Mean Meaningfully

Noether, Gottfried (1994). Mental Random Numbers: Perceived Randomness and Real Randomness. Teaching Statistics at Its Best, 40-41. University of Sheffield, England: Teaching Statistics Trust. (Session 6)

Mental Random Numbers: Perceived Randomness and Real Randomness

Kader, Gary and Perry, Mike (February, 1998). Push Penny–What Is Your Expected Score? Mathematics Teaching in the Middle School, 3 (5), 370-377. (Session 9)

Push Penny — What Is Your Expected Score?
Continued
Continued
Continued

Perry, Mike (Spring, 1999). Push-Penny: Are You a Random Player? Teaching Statistics, 21 (1), 17-19. (Session 8)

Push-Penny: Are You a Random Player?

Perry, Mike and Kader, Gary (February, 1998). Counting Penguins. Mathematics Teacher, 91 (2), 110-116. (Session 9)

Counting Penguins
Continued

Woolley, Thomas (Autumn, 1998). A Note on Illustrating the Central Limit Theorem. Teaching Statistics, 20 (3), 89-90. (Session 9)

A Note on Illustrating the Central Limit Theorem

Russell, Susan Jo and Mokros, Jan (February, 1996). What Do Children Understand About Average? Edited by Donald L. Chambers. Teaching Children Mathematics, 360-364. (Session 10)

What Do Children Understand About Average?
Continued

### Website Production Credits

Learning Math: Data Analysis, Statistics, and Probability is a production of WGBH Interactive and WGBH Educational Programming and Outreach for Annenberg Media.

The contents of this module were developed in part under a grant to PBS from the Department of Education, Award Number R286A950001-99. However, the contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.

Senior Producer
Ted Sicker

Curriculum Director
Denise Blumenthal

Content Developers
Gary D. Kader, Appalachian State University, NC
L. Mike Perry, Appalachian State University, NC

Classroom Case Studies Developer
DeAnn Huinker, University of Wisconsin, Milwaukee

Curriculum Developer
Anna Brooks

Curriculum Project Coordinators
Laura O’Neill
Sanda Zdjelar

Bowen Kerins
Faye Nisonoff Ruopp

Suzanne Chapin
Susan Friel

Designers
Plum Crane
Lisa Rosenthal
Christian Wise

Web Developers
Joe Brandt
Kirsten Connelly

Online Video Segment Coordinator
Mary Susan Blout

Joe Karaman

Unit Managers
Maria Constantinides

With the assistance of
Tim Barney
Jennifer Davis-Kay
Nina Farouk
Jessica Rueter
Kate Smyres
Julie Wolf

### Video Series Production Credits

Learning Math: Data Analysis, Statistics, and Probability is a production of WGBH Educational Foundation for Annenberg Media.

Executive Producer
Michele Korf

Senior Project Director
Amy Tonkonogy

Content Developers
Gary D. Kader, Appalachian State University, NC
L. Mike Perry, Appalachian State University, NC

Facilitator

Producer
Christine Dietlin

Editor
Glenn Hunsberger

Nicholas Branca, San Diego State University, CA
Suzanne Chapin, Boston University, MA
Mary Eich, Newton Public Schools, MA
Hollee Freeman, TERC, Mass.
Susan Friel, University of North Carolina, Chapel Hill
DeAnn Huinker, University of Wisconsin, Milwaukee
Susan Lamon, Marquette University, WI
Miriam Leiva, University of North Carolina, Charlotte
Joan Lukas, University of Massachusetts, Boston
Carol Malloy, University of North Carolina, Chapel Hill
Michelle Manes, Mathematics Teacher and Educational Consultant, MA
Bill Masalski, University of Massachusetts, Amherst
Arthur Powell, Rutgers-Newark College of Arts and Sciences, NJ
Sid Rachlin, East Carolina University, NC
Faye Nisonoff Ruopp, Educational Consultant, MA
Marty Simon, Pennsylvania State University
Myriam Steinback, TERC, MA

Content Editor
Srdjan Divac, Harvard University, MA

Associate Producers
Irena Fayngold
Jessica Rueter

Project Coordinator
Sanda Zdjelar

Production Manager
Mary Ellen Gardiner

Post Production Associate Producer
Peter Villa

Production Coordinator
Lisa Eure

Location Coordinator
Nathan Gunner

Director
Fred Barzyk

Camera
Sam Ameen
Bill Charette
Bart Childs
Lance Douglas
Larry LeCain
Steve McCarthy

Audio
Steve Bores
Chris Bresnahan
Mario Cardenas
Charlie Collias
David King
Keith McManus
Giles Morin
Andy Turrett

Grip
Brian Snider

Intern
David Siegel

Design
Gaye Korbet
Daryl Myers
Alisa Placas

On-line Editors
David Eells
John O’Brien

Sound Mix
John Jenkins
Dan Lesiw

Original Music
Tom Martin

Narrator
Judy Richardson

Joe Karaman

Unit Manager
Maria Constantinides

Office Coordinators
Justin Brown
Ivy Moylan
Laurie Wolf

### Special Thanks

Session 1: Measurement Error: This Old Tape Measure
Norm Abram, Tom Silva, This Old House

Session 2: Data Organization and Representation: Weather Forecasting
Kim Martucci, Fox Studio 25, WFXT Boston

Session 3: Describing Distributions: New Balance
New Balance Inc.:
Jim Tompkins, President and C.O.O.
Stan Mescon, Sales and Product Planning Manager
Dave Elder, Manager of Production Planning

Session 4: The Median: Salary.com
Bill Coleman, Vice President of Compensation, Salary.com

Session 5: Variation About the Mean: The Boston Harbor Project
Massachusetts Water Resources Authority:
Dr. Andrea Rex, Lisa Wong, Nicole O’Neill

Session 6: Designing Experiments: Physicians’ Health Study
Brigham and Women’s Hospital:
Howard Sesso, Division of Preventive Medicine
Dr. Michelle Holmes, The Channing Laboratory

Session 7: Bivariate Data and Analysis: Anthropological Studies
Mark E. Mack, Professor, Biological Anthropology, Howard University
Archival photographs courtesy of The Library of Congress

Session 8: Probability: Risk Analysis
Doug McCrum, President, Global Specialty Risk
Archival footage courtesy of Sekani, Inc., and KD&E, Inc.

Session 9: Random Sampling and Estimation: Lake Victoria
New England Aquarium
William Oweke Ojwang, Les Kaufman, Biology Dept., Boston University
Archival footage courtesy of Nile Ziemba, North River Media, and New England Aquarium

Session 10: Classroom Case Studies
Suzanne L’Esperance, Northwest Elementary School, NH
Ellen Sabanosh, Gerald M. Parmenter School, MA
Paul Sowden, Eleanor Johnson Middle School, MA

Site Location
Oak Hill School, Newton, MA

### Credits

Produced by WGBH Educational Foundation. 2001.
• Closed Captioning
• ISBN: 1-57680-481-X