What do potato peels or reflecting mirrors have to do with graduate-level mathematical concepts?
Four National Science Foundation math fellows at Case Western Reserve University will use vegetables and other household objects to help Cleveland high school and middle school teachers discover the amazing world of mathematics by manipulating objects in a new graduate course, "Mathematics and the Imagination."
"It's unheard of to use manipulatives in a graduate-level course," said math fellow Brendan Foreman.
The fellows spend half of their time in mathematical research at CWRU and the other half working at Collinwood and East Technical High Schools, as well as many other sites in the Cleveland Public Schools. The fellows lend their expertise to Cleveland school teachers through the Cleveland Collaborative for Math Education of the Cleveland Education Fund.
The math fellows -- Foreman, Ben Ford, Naomi Klarreich, and Alina Stancu -- along with David Singer, professor of mathematics at CWRU, plan to make the graduate-level math course accessible to teachers.
One of the obstacles the fellows have encountered is that many elementary teachers certified to teach kindergarten through grade eight have not had math classes in college, while those teachers with math certification have not had much exposure to the new methods of exploring mathematics through manipulatives.
Continuing education credits for teacher certification are given for graduate-level classes, but Ford notes, "The only people truly qualified to take traditional graduate mathematics courses in college are mathematics majors." By this rule, any non-mathematics majors will never get any further mathematics courses, he adds.
"We will have to work hard to make it accessible for those without a solid math background," says Stancu.
From July 6-27, the fellows will team-teach the three-credit course that teachers can use toward their continuing education requirements.
"Our goal is two-fold," says Klarreich. "For middle school teachers, it is primarily to increase their math content knowledge. For high school teachers, we're hoping to give them new ways of looking at math content and to introduce them to a program they can hopefully offer their students."
Fifteen Cleveland school teachers will prepare for the free course this spring by participating in the Cleveland school district's offering of the Gelfand Program, a university-based correspondence study course in mathematics started at Rutgers University and being adopted by other universities.
Participants are from John F. Kennedy High School, East Technical High School, Central Middle School, John Hay High School, Garfield Heights Middle School, Max Hayes Vocational High School, Garrett Morgan Middle School, Thomas Jefferson Middle School, and the math department at the Cleveland district headquarters.
The fellows have modeled the course after a program created by the Geometry Center at the University of Minnesota. After completing the spring and summer work, the teachers will begin using this discovery method with their students in the fall, with assistance from the fellows.
Singer received a $655,000 grant from NSF in 1996 to pilot the Educational Postdoctoral Fellowships in Mathematics. The program will help Cleveland teachers retool for the classroom with new teaching strategies to boost student achievement and raise the number of students passing the state proficiency test in math -- one of Cleveland students' stumbling blocks towards earning a high school diploma. Each fellow receives a $35,000 stipend and works with a faculty mentor.
NSF funding came after Singer testified before Congress in 1994 about the state of mathematics education and the need to expose university personnel, who will teach future math teachers, to what occurs in the classroom.
This is the second year of the program. In the first year, the fellows helped teach courses on integrated mathematics of algebra and geometry at Collinwood, helped design and teach a statistical course using graphing calculators at East Tech, tutored for the proficiency test at Glenville High School, and assisted a kindergarten teacher with computer-based mathematics programs at Kenneth Clement Elementary School.
Last year the fellows also designed a workbook for parents and students to use at home in preparation for the fourth grade proficiency test in math. They have finished a sequel workbook for sixth graders.
The fellows also established a Web site (http://www-math.cwru.edu/~bjf6/C2ME/Milestone.html) so teachers can access math resources through the Internet.
"It has been clear from the start that at the elementary level, the focus should be working with teachers and helping their mathematics competence," said Ford. He assists elementary teachers through the math collaborative's Project TEEM (a group of elementary school math leaders) and also at Kenneth Clement School.
Since the math curriculum has undergone a tremendous change in the past five years, teachers need to know vastly different kinds of mathematics than they did before, he adds. This has motivated teachers t, learn more about math.
The variety of ways of teaching math can be bewildering for teachers without experience, says Ford.
With pressure on teachers to raise achievement levels, some teachers worry about taking risks. "If you are going to experiment with new ways of teaching," Klarreich adds, "teachers need some experience with those ways of learning."