Welcome to the 2015 PMI Workshops!

# Today we…

We begin with a welcome from the group: Andrew Baxter, Fran Arbaugh, Andrea McCloskey, Charles Helou, and Beth Lindsey. We also had a welcome from Math Department Chair Yuxi Zheng. We then dove into the *Kayaking on the Susquehanna River* problem, and discussed (1) the issue of ambiguity in a written problem, (2) the multiple modes of solution, (3) how those solutions can relate to each other, and (4) how different methods have different advantages and disadvantages. For example, the algebraic method was fast but without extra work it did not answer the more practical question of how to decide between venues for other lengths of time. After the break, we spent the rest of the morning on the pre-assessment.

After lunch we discussed the “Smarter Than We Think” article. Then we read the beliefs chart on page 11 of *Principles to Action* and had small group discussions about our own beliefs about teaching and learning mathematics. We will continue to discuss the ideas of a “growth mindset” and “fixed mindset” as the weeks go on.

We finished Unit 1, discussing what equality should mean, and how students misunderstand it. We also began Unit 2 by discussing the adjective-noun theme and how it applies to addition. We then applied the adjective-noun theme to see how it makes sense of the place-value system in addition and adding fractions with a common denominator.

Here are the definitions of the Strands of Mathematical Proficiency that were in the PowerPoint today:

Conceptual Understanding – comprehension of mathematical concepts, operations, and relations.

Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification.

Strategic Competence – ability to formulate, represent, and solve mathematical problems.

Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

*Adding it Up: Helping Children Learn Mathematics*, National Research Council (2001, p. 116).

This book can be downloaded for free at:

http://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics

### Handouts

- Paperwork to be completed.
- Front matter for Math as a Second Language (e.g., title page, table of contents, expectations)
- Unit 1: Fundamentals
- Unit 2: Perspectives on Addition

### Homework

For Tuesday:

- Solve the Film Developing Problem(s)
- Focus on problems 1 and 2.
- Attempt at least two of the three variations in problems 3, 4, and 5, as time permits.
- (Leave space in your notebook for discussion notes.)

- Optional: The riddles from Unit 1, and Guess My Noun from Unit 2.
- Read in
*Principles to Actions*:- Sections titled “Progress and Change” and “Effective Teaching & Learning” (pages 1-12 – stop reading at the middle of page 12)
- Section titled “Implement Tasks that Promote Reasoning and Problem Solving” (pages 17-24).

- Respond (in your notebook) to the following prompts:
- Reflect on a typical in-class math lesson (use your textbook to refresh your memory) that you have taught. Using the descriptions of Levels of Cognitive Demand in Figure 3 (p. 18), 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?

- Bring your math textbooks to PMI on Tuesday.

Fran ArbaughHere are the definitions of the Strands of Mathematical Proficiency that were in the PowerPoint today:

Conceptual Understanding – comprehension of mathematical concepts, operations, and relations.

Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification.

Strategic Competence – ability to formulate, represent, and solve mathematical problems.

Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

Adding it Up: Helping Children Learn Mathematics, National Research Council (2001, p. 116).This book can be downloaded for free at:

http://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics