Gail Kaplan uses exactly the same math games to teach second-gradersthat she uses with college students. The only difference is the second-graders do better.
"Often the younger the audience, the more receptive and creative they can be. They haven't been trained not to becreative," says Kaplan, a college professor and Annapolis resident. "The only thing I change is how I describe the directions."
Kaplan, recently appointed to the Committee on the Teaching of Undergraduate Mathematics of the Mathematical Association of America (MAA), invents ways to make math fun.
Kaplan spoke at MAA's annual meeting in Baltimore last Friday about "Learning to Enjoy Mathematics:Techniques for Teaching Mathematical Investigations."
In one course for liberal arts majors, Kaplan, a professor at Washington Collegeon the Eastern Shore, uses games and puzzles that teach significant mathematical concepts. "Basically I don't follow any textbook," she says. "The students develop confidence they can do the math because they already know how to play games. Then we go beyond the game stage into deep math discussions."
Kaplan also uses a series of games called Wff-N' Proof, developed by a Yale law professor. Like chess, speed isn't important, but thinking well is.
The amazing part, says Kaplan, is that people who go through the game series will have completed 60 percent of what they would learn in a college-level symbolic logic course.
Kaplan has used Wff-N'Proof with second- and third-graders. "Research done with these games is incredible," she says. "IQ scores of junior high students in Connecticut who used the Wff-N'Proofgames went up 20 percent."
At the Montessori International Children's House in Annapolis, children reacted well to the math games and puzzles, says teacher Judy Wacker.
"The games were very challenging and a great deal of fun, and (Kaplan said) the children seemed to have less difficulty than some of her college students," Wacker recalls. Kaplan also taught the children math using dominoes, which they had to position on a paper to create addition problems that involved carrying numbers.
In another problem, the children created a one-sided, three-dimensional figure. To make the Mobius Strip, as the figureis called, each child took a two-edged piece of paper and twisted and taped it to create a single edge.
In addition to teaching children herself, Kaplan, during the past four years, has led workshops forteachers at elementary through college level, offering faculty members ideas for math activities.
"The reaction of students often is that they can't really be doing math because they're having a good time," says Kaplan.
After earning her doctorate at SUNY at Stonybrook, Kaplan took her first teaching job at Goucher, her undergraduate alma mater. She then became one of the first women faculty members at the Naval Academy and taught there for eight years before taking a jobat Washington College.
Kaplan had three children in four years, took a year off and began a book for McGraw-Hill originally titled Math for Poets. The book, which Kaplan is revising, outlines a college course for liberal arts majors who must take math.
"It has a smattering of lots of different areas of math but done at an elementary level," she explains. "The basic theme of the book is the discovery process -- you take complicated problems and pose them as questions wherethe answer requires not a leap, but a baby step. With enough baby steps, the student can figure out the answer, and they have the sense of discovering ideas."
The sense of being able to do the work is critical for less-than-enthusiastic students, says Kaplan, who started tutoring professionally at age 16. As a tutor, she found that 45 minutes of an hour's tutoring needed to be spent convincing the students they could do the work, with just 15 minutes on the material. "Psychologically, until you believe you can do it, you can't do it," she says.
She determined then to help students learn math. She's still doing that, now at age 40, teaching differential equations, statistics and mathematical investigations at Washington College.
Asked abouther goals, Kaplan talks about her next book, which she hopes to finish within a few months. The book would include activities for making math fun for elementary-age students through the university level.
Unlike mathematicians who have earned doctorates with the aim of research, Kaplan's interest has always been teaching, she says. "I looked at my Ph.D. as a ticket to teach at the college level at a good school, not a ticket to sit and do ivory tower mathematics," she says. "I'll continue to try and implement innovative techniques for teachingin the classroom."
More specifically, she will continue to focus attention on non-mathematically inclined students, as well as the good math students.
"When you're teaching, the level doesn't matter,"she says. "It's almost more rewarding if it's a student who has low ability or low esteem in their ability, when a student figures something out and has that 'Ahh!' look, you know you've accomplished something meaningful."