# Blog Recap: Week 1 Monday (7/16/18)

A great first day!

We started with introductions, along with welcome messages from Mark Levi and George Andrews.

We then jumped into our first problem, the Star Spangled Banner Problem.  Participants shared a variety of solution methods.  These led to the following formulas:

Formulas for the number of stars after n days

We briefly touched on connections between these, and will return to that later.

We spent the rest of the morning on the pre-test and then participants got a chance to share their backgrounds and start networking before lunch.

After lunch, we discussed “Smarter than We Think” (by Cathy Seeley). We developed posters that listed “inspirations” and “challenges.”

Fran presented three frameworks that guide PMI’s design and implementation:

• Strands of Mathematical Proficiency: What does it mean to know mathematics? Here are the definitions of the Strands of Mathematical Proficiency that were in the PowerPoint today:Adding it Up: Helping Children Learn Mathematics, National Research Council (2001, p. 116).
• 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.

• Standards for Mathematical Practices: What kinds of activities should students engage in while learning mathematics? These are listed in Principles to Actions and defined on in your notebook in the front matter section on page 5.
• Eight Teaching Practices: How should teachers teach so that students engage in learning mathematics so that they become mathematical proficient? This is the main content of Principles to Actions: Ensuring Mathematical Success for All. We will unpack several of these teaching practices over the two weeks!

We ended the day with a discussion of the “Adjective Noun Theme,” which is based on the notion that numbers are most useful when they are considered with context.  Numbers are adjectives describe the amount of some noun.  We then tried to apply this viewpoint to compare similar fractions, treating the denominator as a noun and the numerator as an adjective.

Math HW:

Refer to “Rules that Expire” (Block 1, p. 15 of notebook). For your assigned rules, follow the instructions on the sheet.

Pedagogy HW:

Read Principles to Actions (the blue book): Sections titled “Progress and Change” and “Effective Teaching & Learning”(Pages 1-12)

• What did you learn from reading the “Progress and Change” section about the state of mathematics education in the U.S.? Write a couple of thoughts in your notebook.
• Think about: How did you react to the chart of beliefs on page 11? In your notebook, write a reflective response (a few sentences) to the beliefs chart.