Welcome to PMI, everyone!  We will be doing these blog recaps at the end of every day,  both to list the handouts you received, the homework for the next day, and to keep track of how far we’ve come.  Please add your comments to this post and keep the discussion going!

We started with the welcomes from Math Department Chair Yuxi Zheng, along with the director of PMI George Andrews.   Then we moved into the first problem-session: “Kayaking on Lake Champlain,” and saw how the same problem can be solved in a variety of ways (e.g., charts, graphs, and algebra), and even how the same problem can be interpreted in multiple ways (e.g., round up or not?).  Next was a discussion of productive versus unproductive attitudes about mathematics, which lead into a debate about what it means to be fluent versus being efficient.  Be sure to keep an eye out for your own habits of mind and what attitudes you hold.

Following a break we had the Pre-Assessment, and then lunch.

In the afternoon we started up with a discussion of equality and the equals sign, along with chains of equalities and what it means for two algebraic expressions to be equal.  After the break we moved into Unit 2, introducing the adjective-noun theme and the Fundamental Principle of Addition (add the adjectives and keep the nouns).  We then explored the consequences of the Fundamental Principle of Addition as it applies to place-value and fractions.

Handouts from today:

• Front Matter: Cover page, Course Overview, Course Expectations
• Unit 1: Fundamentals (21 pages)
  • We will be skipping pages 1.4, 1.5, 1.10, 1.15, 1.16, 1.18, 1.19, 1.20, 1.21.
• Unit 2: Perspectives on Addition (14 pages)
  • We will be skipping page 2.14.  As of today we’ve discussed pages 2.1–2.7.

Homework:

• Read the Course Overview and Learning Objectives.
• The Film Developing Problem (Page 1.2)
  • Find multiple solutions to the Film Developing Problem
  • How is this problem similar to the Kayaking problem?  How is it different?
• Read Principles to Action: Section titled “Implement Tasks that Promote Reasoning and Problem Solving” (pages 17-24).
  • Reflect on a typical in-class math lesson (use your textbook to refresh your memory). Using the descriptions of Levels of Cognitive Demand in Figure 3 (p. 18), be able to describe the types of mathematical thinking your students are required to engage in during a typical lesson.
  • Reflect on a typical homework assignment that your students complete (use your textbook to refresh your memory). What level of cognitive demand do most of the tasks on a typical homework require of your students?
• Guess my noun (Page 2.7), first 5 problems (or more if you like)