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.
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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
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–
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
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
Developing Mathematics
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;
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
• 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.
A
B
P