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Reasoning, Data, Chance
Exploring Discrete Math
Investigating Geometry
Learning from Teaching Cases
Implementing Lesson Study
Applied Probability
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The PCMI 2007 Summer Session has three strands:
 Developing Mathematics: Probability Through Algebra
 (2 hours per day, 5 days per week)
 Focused on learning mathematics by working problems together, this course explores the fundamental mathematics on a topic that has its roots in secondary level, and is related to the mathematical theme of the Institute. Careful work on this topic allows teachers (and students) to understand exactly how elementary and more advanced procedures in the specific content area are derived and generalize. The course is structured so that each participant can work at his/her own level. Those who are more mathematically advanced may be asked to help those with less preparation. The course is conducted by teacher leaders from the PROMYS program at Boston University. The focus of this strand is entirely on mathematics, although opportunity is provided within the course for reflection on the approach used by the instructors and to consider the implications of such an approach for teaching in secondary classrooms. The topic for the summer is described below:
You're at deuce in a tennis game and are 60% likely to win each point. How likely are you to win the game? What is the probability that you roll a sum of 13 when 5 dice are thrown? What is the most likely sum when 5 dice are thrown? Take an expression like x^6+x^5+x^4+x^3+x^2+x and raise it to the fifth power.
What do you get? If you raise it to higher and higher powers, what is the distribution of the coefficients "in the long run?" How does the "random" button on your calculator work? What's the probability that two positive integers, chosen at random, have no common factor? And most importantly, what do all these questions have to do with each other?
In this threeweek course, we'll investigate questions like these (and more). No background in probability or polynomial algebra is assumed, but by the end of three weeks, we promise beautiful mathematical ideas that will make your head spin.
 Reflecting on Practice: Connections to Research
 (1 hour per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)
 After considering research related to teaching and learning mathematics, participants will reflect on the implications of this research for what takes place in classrooms. The discussion will be grounded in the development of lessons, student work, and classroom practice. Participants will work collaboratively to develop teaching and learning resources in order to implement ideas from their discussion. The focus will be on teaching strategies that use problemsolving and openended approaches
 download: Research References for Week 1 [username/password required]

 Working Groups
 (2 hours, 4 days a week)
 As part of their summer activities, each participant selected for the 2007 Secondary School Teacher Summer Program will be assigned to a small subjectspecific working group, which will prepare an activity or resource for the profession (with the associated mathematics) for piloting during the following year. The working groups are:

 Reasoning from Data and Chance
 Exploring Discrete Mathematics
 Investigating Geometry
 Learning from Teaching Cases
 Implementing Lesson Study
 Applied Probability
 Teacher Professional Continuum
