PMI@UP Summer 2017 Day 1

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).

  1. Conceptual Understanding – comprehension of mathematical concepts, operations, and relations.
  2. Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.
  3. Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification.
  4. Strategic Competence –  ability to formulate, represent, and solve mathematical problems.
  5. Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

This book can be downloaded for free at this link.


Read Principles to Actions (the blue book):

  1. Sections titled Progress and Change; Effective Teaching & Learning (Pages 1-12)
  2. Section titled “Implement Tasks that Promote Reasoning and Problem Solving” (pages 17-24).

Write answers to the following prompts in your journal:

  • 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), 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?
  • Consider the chart about beliefs on page 11. What is your reaction to this description of unproductive and productive beliefs?

Read through and reflect on the 8 Rules that Expire.

  • When does the rule work?
    • Bonus: What grade level does that scenario occur?
  • Give a mathematical scenario where the rule does not work (at least, not in the way it’s phrased)
    • Bonus: What grade level does that scenario occur?

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