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Reasoning from Data and Chance
Exploring Discrete Math
Investigating Geometry
Implementing Lesson Study
Visualizing Functions
Learning about Topology
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Ning: PCMI 2011
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The PCMI 2011 Summer Session has three strands:
 Developing Mathematics: Some Applications of Geometric Thinking
 (2 hours per day, 5 days per week)
 This course explores the fundamental mathematics on a topic that has its roots in secondary school mathematics and is related to PCMI's mathematical research topic. Working together, participants will understand how elementary and more advanced procedures in the specific content area are derived and generalized and will exercise mathematical habits of mind in the process. The course is structured so that each participant can work at her/his own level. The focus of this strand is entirely on mathematics, although participants may wish to reflect on the approach used by the instructors and to consider the implications of such an approach for teaching in secondary classrooms.
This year's course will focus on geometry as a useful tool for studying and understanding all kinds of phenomena inside and outside mathematics. Participants in this course will exercise some geometric habits of mind like creating functions that can give insight on a geometric problem, or looking for things that don't change when the inputs of a function change. We'll apply these habits to a wide variety of situations, including geometric optimization and the Fundamental Theorem of Algebra. We will explore some of these topics using dynamic geometry environments (such as the Geometer's Sketchpad®, GeoGebra or Cabri). No prior background with these mathematical topics or software will be assumed.

 Reflecting on Practice: Connections to Research
 (75 minutes per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)
 Using Formative Assessment to Inform Instruction and Uncover Misconceptions
 Does what students say matter? How can you figure out what they are thinking about math? And then, what do you do with what you hear?
Participants will consider research related to teaching and learning mathematics with a particular focus on student thinking and how it can be used to shape instruction. The discussion will be grounded in the study of lessons and classroom practice in both the United States and other countries as participants will work collaboratively to better understand how they can design and use formative assessment in their own classrooms.

 Working Groups
 (2 hours, 4 days a week)
 As part of their summer activities, each participant selected for the 2011 Secondary School Teacher Summer Program will be assigned to a small subjectspecific working group, which prepares a first draft of an activity, lesson, reflection on a piece of mathematics or another product useful for the secondary classroom that can be shared with other teachers. The working groups are:

 Reasoning from Data and Chance
 Exploring Discrete Mathematics
 Investigating Geometry
 Implementing Lesson Study
 Visualizing Functions
 Learning about Topology
