Chairman of Mathematics Robert Fefferman instructs a session in his department’s project to train Chicago public school mathematics teachers.

Professors train high school teachers to express mathematical concepts

A classic mathematics book by a Russian mathematician and mathematics texts from Singapore are providing the foundation for weekly training sessions intended to help nearly 40 Chicago public high school teachers enhance their math instruction skills.

The yearlong program, taught in separate seminars by Robert Fefferman, the Louis Block Professor and Chairman of Mathematics, and Robert Zimmer, Senior Associate Provost and the Max Mason Distinguished Service Professor in Mathematics, began in October 1998 and is part of a three-year project to provide additional training in mathematics for Chicago public school teachers.

Each seminar also has an experienced instructor: Lydia Polonsky, teacher at the University Laboratory School, and Susan Eddins, a founding teacher of the Illinois Mathematics and Science Academy. The schools and participants in the seminars were selected by two officials of the Chicago Public School Administration, Telkia Rutherford and Clifton Burgess, in cooperation with Paul Vallas, chief executive officer of Chicago Public Schools.

The program is supported by a $408,000 grant from the Gabriella and Paul Rosenbaum Foundation of Chicago. The foundation’s president, Madge Goldman, has been a longtime advocate of improving the teaching of mathematics.

Fefferman, who is Co-principal Investigator for the program, said it is important for teachers to be comfortable talking about mathematics and especially to emphasize the excitement and beauty of the subject. “Most people have the impression that mathematics consists of formal manipulation of symbols, completely without intuition. This is absolutely wrong, and if teachers can strengthen their ability to express mathematical ideas to their class rather than emphasizing the recording of formulas on the blackboard, then this will be very beneficial. We are combining outstanding curricular materials with this emphasis on communication of important ideas to help the teachers to achieve their desired goals,” said Fefferman.

Fefferman also pointed out the importance of improving mathematics education for school children, “Today, mathematics is so fundamentally important in everyday life and in such a wide variety of industrial and scientific applications that children must have high-quality training in this area. Without it, their future is at risk.”

The Singapore materials, like many texts from East Asia, are small volumes of problems that students attempt to solve in class and at home. Asian teachers often encourage students to work together on a limited number of problems during the class sessions to develop skills for solving mathematical problems through discussion and teamwork.

Mary Willmore, a mathematics teacher at Jones Academic Magnet School who has applied her seminar experience in the classroom, said that this approach has helped her freshman algebra students. “I think this method makes them more comfortable with mathematics. It’s also given me another way to teach mathematics,” she said.

Judith Knauss, a mathematics teacher at Curie High School, said, “What I like about the seminars is the sharing that goes on. We learn lots of good ideas listening to other teachers.”

The teachers study the book Algebra by famed Russian mathematician Israel M. Gelfand, currently at Rutgers University. The book exemplifies a Russian tradition of research mathematicians writing material to assist teachers of mathematics at the precollegiate level. “The book has some fundamental ideas presented in an ingenious way. It enhances the teachers’ appreciation of mathematics,” Fefferman said.

Izaak Wirszup, Professor Emeritus in Mathematics, is an expert on international mathematics education and the other Co-principal Investigator of the Amoco-sponsored University of Chicago School Mathematics Project.

“One of the criticisms of American mathematics curricula and texts is that they are a mile wide and an inch deep,” said Wirszup.

“A characteristic of the Asian and Russian materials is their brevity. Although the books themselves are compact, the ideas they convey are quite profound. With skillful teaching, their content can be adapted quite easily to an urban school system. Through seminar discussions, the materials help teachers develop deeper mathematical understanding among students. A major advantage of the seminars as well is that they provide a new chance for teachers to become learners again, to feel encouraged and stimulated. This could help spark a renaissance in mathematics teaching in our public schools,” Wirszup added.