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Institute for Advanced Study/Park City Mathematics Institute Designing and Delivering Professional Development. July 14, 2008 Johnny W. Lott jlott@olemiss.edu. Draft Agenda for Sunday, July 13. 5:30 Introductions Review of Agenda for the week Reflections for professional development
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Institute for Advanced Study/Park City Mathematics InstituteDesigning and Delivering Professional Development July 14, 2008 Johnny W. Lott jlott@olemiss.edu
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, 2003. • Assign working groups. • Reasoning from Data and Chance • Exploring Discrete Mathematics • Investigating Geometry • Learning from Teaching Cases • Visualizing Functions • Algebraic and Analytic Geometry 7:00 Adjourn
Draft Agenda for Monday, July 14 8:20 Developing Mathematics Silver King 2, 3 11:00 Reflecting on Practice Silver King 2, 3 12:00 Lunch 1:00 Working Groups TBD 3:15: Cross Program: George Hart Grand Theater Research Professor, Department of Computer Science at Stony Brook 4:30 DDPD Meeting Coalition 4 • Reflection on day • What is integrated mathematics? 5:30 Adjourn
Draft Agenda for Tuesday, July 15 8:20 Developing Mathematics Silver King 2, 3 11:00 Reflecting on Practice Silver King 2, 3 12:00 Lunch 1:00 Working Groups TBD 4:30 DDPD Meeting Coalition 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, 2008. 5:30 Adjourn
Draft Agenda for Wednesday, July 16 8:20 Developing Mathematics 11:00 DDPD Meeting: Sharing practices Roger Knobel, University of Texas Pan American Susana Salamanca, New Mexico State University 12:00 Lunch 1:00 Afternoon Off
Draft Agenda for Thursday, July 17 8:20 Developing Mathematics Silver King 2, 3 11:00 DDPD Meeting Coalition 4 Discussion of “Geometry Between the Devil and the Deep Blue Sea” by Hans Freudenthal, Educational Studies in Mathematics 3 (April 1971): 413-435. Implications for your work 12:00 Lunch 1:00 Working Groups TBD 3:15 Cross Program: Clay Lecturer Grand Theater 4:30 DDPD Meeting Coalition 4 Reflection on day and implications for professional development 5:30 Adjourn
Draft Agenda for Friday, July 18 8:20 Developing Mathematics Silver King 2, 3 11:00 Conversation with DDPD Coalition 4,Tent Groups: Middle School interest High School interest 12:00 Lunch 1:00 DDPD Meeting Coalition 4 3:15 Great Pi and e Debate Grand Theater 4:30 Next Steps for DDPD if needed Coalition 4 5:30 Adjourn
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;
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): 334-335. 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.