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 low-threshold, high-ceiling, 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.