Institute for Advanced Study/Park City Mathematics Institute Designing and Delivering Professional Development July 14, 2008 Johnny W. Lott

Draft Agenda for Sunday, July 13 5:30 Introductions Review of Agenda for the week Reflections for professional development Discussion of reading: “The Integration of the School Mathematics Curriculum in the United States: History and Meaning” by Zalman Usiskin, In Integrated Mathematics Choices and Challenges, (Sue Ann McGraw, Ed.). Reston, VA: NCTM, Assign working groups. –Reasoning from Data and Chance –Exploring Discrete Mathematics –Investigating Geometry –Learning from Teaching Cases –Visualizing Functions –Algebraic and Analytic Geometry 7:00Adjourn

Draft Agenda for Monday, July 14 8:20Developing MathematicsSilver King 2, 3 11:00Reflecting on PracticeSilver King 2, 3 12:00Lunch 1:00Working GroupsTBD 3:15: Cross Program: George HartGrand Theater Research Professor, Department of Computer Science at Stony Brook 4:30DDPD MeetingCoalition 4 –Reflection on day –What is integrated mathematics? 5:30Adjourn

Draft Agenda for Tuesday, July 15 8:20Developing MathematicsSilver King 2, 3 11:00Reflecting on PracticeSilver King 2, 3 12:00Lunch 1:00Working GroupsTBD 4:30DDPD MeetingCoalition 4 –Reflection on day –Math resulting from curriculum decisions and designing professional development around the decisions; an example will be taken from The Classification of Quadrilaterals: A Study of Definition by Usiskin and Griffin, Information Age Publishing, Inc. Charlotte, NC, :30Adjourn

Draft Agenda for Wednesday, July 16 8:20 Developing Mathematics 11:00DDPD Meeting: Sharing practices Roger Knobel, University of Texas Pan American Susana Salamanca, New Mexico State University 12:00Lunch 1:00 Afternoon Off

8:20Developing MathematicsSilver King 2, 3 11:00DDPD MeetingCoalition 4 Discussion of “Geometry Between the Devil and the Deep Blue Sea” by Hans Freudenthal, Educational Studies in Mathematics 3 (April 1971): Implications for your work 12:00Lunch 1:00Working GroupsTBD 3:15Cross Program: Clay LecturerGrand Theater 4:30DDPD MeetingCoalition 4 Reflection on day and implications for professional development 5:30Adjourn Draft Agenda for Thursday, July 17

Draft Agenda for Friday, July 18 8:20Developing MathematicsSilver King 2, 3 11:00Conversation with DDPDCoalition 4,Tent Groups: Middle School interest High School interest 12:00Lunch 1:00DDPD MeetingCoalition 4 3:15Great Pi and e DebateGrand Theater 4:30Next Steps for DDPD if neededCoalition 4 5:30Adjourn

Definition of Integrated Mathematics An integrated mathematics program is a holistic mathematics curriculum that— –Consists of topics from a wide variety of mathematical fields and blends those topics to emphasize the connections and unity among those fields; –Emphasizes the relationships among topics within mathematics as well as between mathematics and other disciplines;

Definition of Integrated Mathematics An integrated mathematics program is a holistic mathematics curriculum that— –each year, includes those topics at levels appropriate to students’ abilities; –is problem centered and application based; –emphasizes problem solving and mathematical reasoning; –provides multiple contexts for students to learn mathematics concepts;

Definition of Integrated Mathematics

Reading for Sunday “The Integration of the School Mathematics Curriculum in the United States: History and Meaning” by Zalman Usiskin, In Integrated Mathematics Choices and Challenges, (Sue Ann McGraw, Ed.). Reston, VA: NCTM, 2003.

Integration by Usiskin Using unifying concepts –SMSG used sets, functions, logic, etc. Using merged areas of mathematics –UCSMP did it with same titles for courses but merged topics; Functions, Statistics, and Trigonometry Using removal of distinctions between areas –COMAP; the ARISE Project Using strands—separate but equal –Unified Mathematics in New York Using interdisciplinary integration –SIMMS Project in Montana

References for “Sunday” Beal, J., D. Dolan, J. Lott, and J. Smith. Integrated Mathematics: Definitions, Issues, and Implications: Report and Executive Summary. ERIC Clearinghouse for Science, Mathematics and Environmental Education. The Ohio State University, Columbus, OH: 1992, 115 pp. Lott, J. W., and C. A. Reeves. “The Integrated Mathematics Project.” Mathematics Teacher 84 (April 1991): Usiskin, Z. “The Integration of the School Mathematics Curriculum in the United States: History and Meaning.” In Integrated Mathematics Choices and Challenges, (Sue Ann McGraw, Ed.). Reston, VA: NCTM, 2003.

Gail’s Problem Solve 2x + 3y = 15 5x + 2y = 21 A student wrote 8x + y = 27 11x = 33 x = 3 Was the student correct? What did the student do?

Assigned problem 1 Using only tape and a pencil, construct an angle bisector.

Assigned Problem 2 Find the point P so that the sum of the lengths AP and BP is a minimum.