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The PCMI 2013 Summer Session has three strands:
 Math Course: Probability, Randomization, and Polynomials
 (2 hours per day, 5 days per week)
 Pick two positive integers at random. What is the probability that the two numbers don't have a common factor? What happens to the probability if the numbers are picked from 1 to 100. 1 to 1000? 1 to infinity? Roll 5 dice. What is the probability of rolling a sum of 13? What sum is most likely? What does the distribution of sums look like? These questions can be answered with the help of algebra. The course will also explore the meaning and definition of standard deviation and variance, the effects of repeating an experiment many times, and ways to generate or test random data. The contexts and methods developed in the course will be lowthreshold, highceiling, with plenty of interesting mathematics for any grade level.

 Reflecting on Practice: Making Tasks Count
 (75 minutes per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)
 The focus is on the nature of tasks teachers assign students and how the tasks are implemented in classrooms. Participants will identify characteristics of tasks that make them mathematically worthwhile and modify tasks to make them a better learning experience for students as well as explore strategies for how to organize and manage students as they are working. They will consider what they as teachers can do to maintain the cognitive demand of tasks, yet provide scaffolding for students if they struggle. The discussion will be grounded in research related to teaching and learning mathematics including typical tasks and their implementation in other countries.

 Readings prior to Week 1:
Discourse That Promotes Conceptual Understanding by Elham Kazemi
Teachers: Will We Ever Learn? by Jal Mehta

 Working Groups
 (2 hours, 4 days a week)
 As part of the summer activities, each participant selected for the Summer School Teachers Program will be assigned to a small team that will focus on an activity related to the Common Core State Standards in Mathematics or to related state standards, either for use with students or for professional development with teachers. The assignments will be made based on participant interest and experience as well as the needs identified by schools and districts.

 Lesson Study
 Curvature Group
 Elementary
 Whole number addition
 Whole number multiplication
 Fractions
 Middle School
 Functions
 Geometry
 Modeling
 Ratio & Proportional Relationships
 Statistics & Probability
 High School
 CalcReady
 Geometry
 Mathematical Practices
 Parental Communication
 Statistics
 Algebra
 Tasks Design
 Modeling
 Accepted participants will be notified of their assignment prior to the summer session and specific topics within each content area will be decided upon at that time. The teams will be responsible for producing lesson plans or activities for teachers to use in their classes or workshops and for preparing implementation strategies for dissemination of the materials.
