The PCMI 2014 Summer Session has three strands:

Math Course: Fractions, tilings, and geometry

(2 hours per day, 5 days per week)

Are there any rectangles whose perimeter and area have the same numerical value? Are there any rectangular boxes whose surface area and volume have the same numerical value? Can the plane be tiled with kites and chevrons? In how many ways can 1/2 be written as a sum of unit fractions? How are all of these questions related? We'll investigate these and other delights over the course of three weeks. No prior knowledge is assumed---the only prerequisite is a love of working on interesting problems.

 

Reflecting on Practice: Productive Discussions

(75 minutes per day, 5 days per week, plus opportunities for informal sessions in late afternoon and evenings)

Classroom conversations are central in developing student understanding of mathematical concepts. What should discussions look and sound like to make reasoning and making sense of mathematics the norm? What are some strategies for managing discussions to enable students to be partners in the learning process? Participants will consider research related to teaching and learning mathematics with a particular focus on facilitating discussions. The work will be grounded in the study of discourse in lessons and classroom practice in the United States and in other countries.

 

Working Groups

(2 hours, 4 days a week)

As part of the summer activities, each participant selected for the Summer School Teacher Summer 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 or to one of two special working groups. The assignments will be made based on participant interest and experience as well as the needs identified by schools and districts. The teams will be formed by grade level (elementary, middle school, high school) with respect to content related to the following strands: number, measurement, algebra, geometry, functions, or statistics. The two special working groups are Lesson Study and Modeling Materials Discretely (this group will attend the Undergraduate Summer School course with this name).

• Lesson Study
• Modeling Materials Discretely
• Elementary
• Structure and Patterns
• K-2 Situational Word Problems
• Fractions 3-6
• Number Line
• Middle School
• Ratio & Proportional Relationships
• Fractions
• Differentiation
• Technology
• Multiple Representations
• Path to Functions
• Socio-Mathematical Norms
• High School
  • Algebra II
  • Differentiation
  • Functions
  • Perseverance
  • Modeling
  • Reasoning
  • Inference
  • Reflection
  • Writing and Thinking

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.