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Designing and Delivering Professional Development for Integrated Mathematics

This draft agenda outlines a professional development program focused on integrated mathematics. Topics include reasoning from data and chance, exploring discrete mathematics, investigating geometry, and more. The agenda also includes discussions on curriculum decisions and designing effective professional development.

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Designing and Delivering Professional Development for Integrated Mathematics

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  1. Institute for Advanced Study/Park City Mathematics InstituteDesigning and Delivering Professional Development July 14, 2008 Johnny W. Lott jlott@olemiss.edu

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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;

  9. 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;

  10. Definition of Integrated Mathematics

  11. 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.

  12. 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

  13. 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.

  14. 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?

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

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

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