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IAS/Park City Mathematics Institute Program
The IAS/Park City Mathematics Institute (PCMI) is a mathematics education program that integrates the research and education components of the mathematics community in a unique way, allowing members of each to attain a deeper understanding of the mathematical enterprise. The PCMI program brings together high school mathematics teachers, undergraduate and graduate students, college and university faculty, and researchers working at the most advanced levels of mathematical inquiry to participate in distinct but overlapping programs. Educators and researchers come together in a supportive setting where education at all levels is the explicit concern.
The PCMI is sponsored by the Institute for Advanced Study in Princeton, New Jersey and receives major support from the National Science Foundation. The Exxon Education Foundation, the Geraldine R. Dodge Foundation, and Xerox Corporation provide additional corporate funding.
Committed to attracting a diverse community of participants, the PCMI seeks to include individuals from traditionally underrepresented groups in mathematics and provides financial support at all levels of the program. At its core are two three-week summer sessions for researchers, graduate and undergraduate students, and high school teachers of mathematics, which usually are held in Park City, Utah. Each summer session is followed by a year-long program in six geographic sites for the participating high school teachers. Teachers at each of the regional sites work in collaboration with faculty at one of six academic institutions.
Professor Guershon Harel was awarded a grant to serve as a site director for the first cycle (1995-97) of the program. Two of the six sites, Purdue and the University of Louisville, were chosen to continue the program for the second cycle (1997-98).
The program for high school teachers is designed to deepen teachers¹ knowledge of mathematics and to explore new methods of teaching. To this, the Purdue site has added the following goals: (a) to strengthen the cooperation between the Mathematics Department at Purdue and the local schools, and (b) to expose high school students to the usefulness of mathematics in the real world.
In each cycle, 5-7 teachers per site are selected to participate in the program. The selected teachers are individuals who are interested in the dual role of initiating reform within their own classrooms and assuming a leadership role in local and national mathematics reform. Hence, although the number of participants in each site is small, the effect that the program has on other teachers and students is believed to be significant.
During the school year, teachers translate what they have learned during the summer program into more effective pedagogy in their own classrooms and work in collaboration with university level site directors to become leaders of reform in their schools, school districts, and communities.
The activities held this past year at Purdue included:
High school field trip days
Three teachers and their classes visited Purdue: Nancy Cruse, Center Grove High School (Indianapolis); Elaine Ellison, West Lafayette High School; and Faye Barnes, Roosevelt High School, Gary, Indiana. A total of about 70 students attended these activities, which were a great success, thanks to the enthusiastic talks and participation of Purdue faculty members:
- Prof. Carl Cowen (Mathematics)--"What is Mathematics? What Do Mathematicians Do?"
- Prof. Steve Bell (Mathematics)--"Music, Math, and Maple"
- Prof. Steve Samuels (Statistics, Mathematics)--"Two Players, One Winner: Using Probability to Play Games Better"
- Prof. David Goldberg (Mathematics)--"Symmetry"
- Prof. Brad Lucier (Mathematics, CS)--"Geometry of the Real World and Scheduling Difficulties"
- Prof. David Drasin (Mathematics)--"Different Ways to Think of Angle Sums in a Triangle"
- Prof. Dan Phillips (Mathematics)--"Matrices and Cryptography"
- Prof. Jerry Peters (Curriculum and Instruction)--"Being a Student at Purdue"
- Prof. Richard Penney (Mathematics)--"Fractals in Mathematics"
- Prof. Johnny Brown (Mathematics)--"How to Succeed as a Mathematician and as an African American Mathematician"
Joint meeting with other sites
Our site visited the Louisville site for a one-day conference. The teachers shared their experiences on topics such as the teaching of geometry, the use of technology, classroom interactions, etc.
Guest speakers
Professor Fennema from the University of Wisconsin visited Purdue. The teacher participants attended her talk and participated in a gathering with faculty from the Mathematics Department, the School of Education, and Indiana University.
Regular monthly meetings
Each 4-6 weeks the site met to discuss school, curriculum, and classroom issues.
Report on the ICTM Math Contest
by Guershon Harel
Each year the Indiana Council of Teachers of Mathematics (ICTM) sponsors a mathematics contest for middle school and high school students. Fourteen sites participate in the contest state-wide; Purdue is the site that coordinates the contest for the Lafayette area.
The contest consists of five mathematics problem solving tests: Pre-Algebra, Algebra (First Course), Geometry, Algebra (Second Course), and Comprehensive. Each includes about 40 multiple-choice questions and runs 90 minutes. Questions for the first four categories may be related to any of the content identified in the Indiana mathematics proficiency guides or included in state-approved textbooks. The content of the comprehensive category is drawn from pre-calculus mathematics including trigonometry, finite mathematics, simple linear algebra, probability, statistics, and analytic geometry.
This is the third year that I have coordinated the ICTM mathematics contest at Purdue. The contest was held the morning of Saturday, April 18. A math video was presented to interested parents and teachers while students took their exams.
The ICTM Mathematics Contest holds the potential for becoming an effective recruitment event. Usually between 200 and 250 students participate, but with greater effort and additional resources, this number could easily be doubled. The contest day could be expanded to a full day of activities for the students, their teachers, and parents. For example, various faculty members could give presentations while the scores of the tests were being computed, and we could conduct the awards ceremony on-site at the end of the day.
Organizing and coordinating the contest requires an enormous amount of time and effort. Additional resources will be needed in order to expand this event and transform it into an effective mechanism for recruiting talented students to our undergraduate mathematics program.
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