Institute for Advanced StudyPark City Mathematics Institute Designing

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 • 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 Mc. Graw, Ed. ). Reston, VA: NCTM, 2003. • Assign working groups. – – – 7: 00 Reasoning from Data and Chance Exploring Discrete Mathematics Investigating Geometry Learning from Teaching Cases Visualizing Functions Algebraic and Analytic Geometry 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 11: 00 12: 00 1: 00 4: 30 Developing Mathematics Reflecting on Practice Lunch Working Groups DDPD Meeting Silver King 2, 3 TBD 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 11: 00 12: 00 Lunch Developing Mathematics DDPD Meeting: Sharing practices Roger Knobel, University of Texas Pan American Susana Salamanca, New Mexico State University 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;

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 Mc. Graw, 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 Mc. Graw, Ed. ). Reston, VA: NCTM, 2003.

Gail’s Problem • Solve 2 x + 3 y = 15 5 x + 2 y = 21 A student wrote 8 x + y = 27 11 x = 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.