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 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 148:20 Developing Mathematics Silver King 2, 311:00 Reflecting on Practice Silver King 2, 312:00 Lunch1:00 Working Groups TBD3:15: 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, 311:00 Reflecting on Practice Silver King 2, 312:00 Lunch1:00 Working Groups TBD4:30 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 AmericanSusana Salamanca, New Mexico State

University12:00 Lunch

1:00 Afternoon Off

8:20 Developing Mathematics Silver King 2, 311:00 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 Lunch1:00 Working Groups TBD3:15 Cross Program: Clay Lecturer Grand Theater4:30 DDPD Meeting Coalition 4

Reflection on day and implications for professional development

5:30 Adjourn

Draft Agenda for Thursday, July 17

Draft Agenda for Friday, July 18

8:20 Developing Mathematics Silver King 2, 3

11:00 Conversation with DDPD Coalition 4,TentGroups: Middle School interestHigh School interest

12:00 Lunch1:00 DDPD Meeting Coalition 43:15 Great Pi and e Debate Grand

Theater4:30 Next Steps for DDPD if needed Coalition 45:30 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 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

• Solve2x + 3y = 155x + 2y = 21

A student wrote8x + y = 2711x = 33x = 3Was 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.

B

P

A