ATMNYS New York Math Journal September 2010
How I Used Classification Skills To Jump-Start My Students into the Critical Thinking Process
Catheryne Draper, The Math Studio, Inc.

Is critical thinking a desirable component in mathematics classes? Absolutely. Does classification and sorting help to develop critical thinking strategies? While my intuition has always said “yes,” my recent review of some of the critical thinking literature did not provide an obvious corroborating “yes.” Of the dozen articles I reviewed defining the critical thinking process, only two specifically cited classification in their definitions. My informal interviews with K-12 colleagues on this topic yielded mixed opinions regarding a direct connection although no one considered classification as a non-essential activity.

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Title I Exchange Article 2008
Teachers: How to Help Students “See” Mathematics

Comments from students like “Oh, I see” are like music to many math teachers. Besides using models such as algebra tiles and place value blocks, patty paper and counting sticks, what else can help students to see the math relationships and patterns? This is a good question with a not-so-simple answer.
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Connect magazine 2007
Tracing Geometry

Good math is memorable math, the kind that stays with students so that they can remember it and apply it to new situations. Many students have a significantly better chance of remembering if they can “see” the math and then recognize the connections among topics. It isn’t only about mastering the pieces or the skills; it’s about seeing how the pieces and skills fit together. Our job as teachers is to help students see and hopefully remember valuable mathematical relationships from one grade level to the next. 
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My teaching life changed when I entered a Masters degree program that included elementary teachers, centered on math education development. I was a high school teacher by training and was only slightly aware of elementary and middle school pedagogy and the instructional models used in the early grades. As a result of my new experiences, I decided that I wanted to identify and make more classroom-relevant connections at all levels within the instructional program—elementary through high school. I wanted to illustrate the continuum, not just provide occasional examples.
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October 12, 1997

Math and History Are Teamed Up

Counting the seven peaks of the seven gables is not part of the innovative program, which is called "Spectacular Seven Search: An Interdisciplinary Navigation Adventure," but there are plenty of other math activities built into it.

For example, as part of the program, students visit the historic counting house, which was once used by merchants to keep track of imports and exports. Youngsters will be assigned a problem they can solve only through calculations made from an accounting book. They are also asked to examine the diamond-paned windows at the back of the Hooper-Hathaway House to determine how many panes the builders began with.

The program is a collaborative effort of Cathy Draper, founder of the Math Studio in Salem, and Ann McCamy, school programs manager of the House of Seven Gables. Draper, a former textbook writer, mathematician, and independent educational consultant, has long been introducing innovative ways to learn and visualize math concepts. She volunteered her time to develop the program.

McCamy is responsible for the educational programs and activities hosted by the site, which comprises the House of Seven Gables, the Nathaniel Hawthorne birthplace, the counting house, Hooper Hathaway House, and the Retire Becket House. The two met at a professional conference and say they were amazed at how naturally the subjects of history and math mesh.

For more information, call The House of Seven Gables Education Department at (978) 744-0991. For more information about The Math Studio, call (978) 741-4305.

Go see a sample activity from the Spectacular Seven Search.

North Shore Sunday

Daily Item

Salem Evening News

She fights math anxiety with vision

A News staff report

SALEM - Catheryne Draper once had students measure football field lines to understand angels. She has used blue yarn to teach the mathematical concept of pi. And she believes a five-gallon jug of buttons can help explain statistics more clearly than words.

Draper, the director of the Math Studio who sometimes doubles as Tudo the Clown, shows her students how math works, rather than talking to them about abstract concepts or numbers."

I truly believe a higher percentage of people can understand math. It's not an esoteric subject," Draper said the other day from her studio in the Colonial Office Park. "Especially if they saw it like I see it. But they can't see if there is nothing to see.

Many people have trouble understanding mathematics, according to Draper, because of the traditional teaching methods used. Most teachers talk about math. Yet many students are what Draper calls "visual learners" and must see before they can understand. "Einstein didn't do well in algebra. He flunked algebra. He couldn't do anything until he saw it in his head," she said.

Over 40 percent of students are visual learners, according to a study done by educational authors Dunn and Dunn. Draper said over 60 percent of her students at the Math Studio fall into this same category and must translate verbal instruction to their own visual mind.

The number of people who are illiterate in math, according to Draper, is startling. She finds even more disturbing the wide-spread acceptance of this failure to understand math. She points out there wasn't even a word for math illiteracy until last year when author John Allen Paulos defined it as "innumeracy ... .. tone says out loud, 'I can't read. But people will admit they can't add fractions," Draper said.

"Why is this innumeracy accepted? I don't know," Draper said. "Maybe because a lot of people can't do math. "If we, as teachers don't hit their learning style, then a person doesn't get it. Traditional math is not taught in a myriad of styles."

Draper has developed more than 200 activities to give her math students something to see and touch. Wooden yard sticks screwed together allow students to see parallels and feel angles. Folded cards help a student visualize inverse function. "I want to give them the ability to take a difficult problem and turn it into an easily understood concept," she said"No one has ever asked an opinion in math. 'It's three plus two equals five. Shut up and do it.' I'm asking for students to participate.

"I'm more of a coach," said Draper. "I want the student to have some control over their own learning. When a student learns to control their own learning, their self esteem goes up. When you feel like you have control, you can do anything."

Letters on her wall are a testimony to the method's effectiveness. "Since I have been with you, I have been doing great in math, in fact math is my favorite subject. Thanks a bunch," wrote one student.

"I did awesome in math this year," wrote another.

Draper, who earned both her bachelor's and master's degrees in mathematics from the University of Georgia, began her career as a high school math teacher in Georgia, where she once took students to a football field to measure angles. She has also been an editor and consultant for a publisher of math books.

In 1983, Draper began tutoring from her Salem home, helping students overcome "math anxiety." Her practice grew until she opened her office at the Colonial Office Park in 1985.

Draper, who teaches on a one-on-one basis, has students who range in age from a second grader to a 68-year-old man. Her students are all bright and creative, but have trouble with math. Business professionals, including plumbers and lawyers, go to the Math Studio for help. And she recently tutored a retired man who picked up math as a hobby.

Draper, who sometimes dresses as Tudo the Clown to teach math workshops to youngsters, has had her techniques used in classrooms in Massachusetts, New Hampshire and Washington, D.C. She plans to publish many of the activities next year, which will allow more widespread use of the techniques.

Press Release Alabama AMSTI buys Algebra Game

Attn: Business and Education Editors
Contact: Catheryne Draper, The Math Studio, Inc., 978-741-4305; cdraper@mathstudio.com

Alabama’s AMSTI Education Reform Program Purchases The Math Studio’s “Algebra Game” Innovative math teaching tool from Salem, MA-based company engages students with game format

(SALEM, MA, February 18, 2010) The Math Studio, Inc., the Salem, MA-based publisher of The Algebra Game math instruction decks, is pleased to announce that the Alabama Mathematics Science and Technology Initiative (AMSTI) has purchased The Algebra Game Topic Sets (Linear Graphs, Quadratic Equations, Conic Sections, and Trig Functions) as part of the state’s effort to “identify high-quality programs that support the AMSTI philosophy of instruction.” Since The Math Studio, Inc., launched these instructional decks of cards nationally in 2000, The Algebra Game has been distributed internationally to middle school, high school, technical school, and college classrooms.

The Alabama Department of Education initiated AMSTI in 1999 to improve math and science teaching statewide. In January 2000, a Blue Ribbon committee comprised of some of the state’s best teachers, administrators, and leaders from business and industry formed to design the most effective statewide initiative for improving math and science instruction. That done, subcommittees identified instructional materials that supported the committee’s recommendations. In 2008, AMSTI was honored by being highlighted as the only state-level initiative at the Science Generation: A National Imperative summit. In 10 years, AMSTI’s state funding has grown from zero to $41 million in fiscal 2009 (see www.amsti.org).

About The Algebra Game: Catheryne Draper opened the doors of The Math Studio, Inc., in the early 1980’s to provide user-friendly mathematics instruction for all grade levels. Her underlying purpose was -- and still is – to change the face of math education. Draper’s own teaching experiences directly influenced the development of The Algebra Game, which has proven to be an effective classroom tool. “I knew that getting students involved in their own learning progress was essential to their understanding and remembering,” says Draper. “In my first year of teaching, I was assigned the repeater Algebra I class. Although I didn’t realize it at the time, this was a life-changing event for me because those kids taught me how to really teach them.” What she learned then is that game play engages students, and engaged students succeed.

Draper initially developed The Algebra Game materials as a formative assessment tool in the 1980’s, expanding them into a more comprehensive instructional program in the 1990’s. The Algebra Game has been listed on the Eisenhower National Clearinghouse (www.goENC.com) roster of math and science resources for educators since April 1998. Visit www.mathstudio.com to learn more about The Algebra Game program and how students and teachers respond to using the decks in classrooms.

As president of The Math Studio, Inc., Draper has welcomed the opportunity to teach all grade levels from kindergarten through college, and has served as a math coach, professional development trainer, materials development consultant and editor, and assessment item writer. Before starting her own business, Draper was a high school teacher, a district supervisor, a state advisor, and a consultant and editor for textbook and supplementary math material publishers.

For more information, contact: Catheryne Draper, The Math Studio, Inc., Tel: 978-741-4305; cdraper@mathstudio.com