Wednesday, April 19, 2017

NCTM 2017: Day 1

Where We Disagree on the SMPsRaymond Johnson

  • Group of Algebra I teachers met over the course of  two years where they individually identified which math practice(s) were encouraged by different IM tasks, and then talked about where they disagreed
  • Over time their agreement increased—this process a potentially powerful tool for coming to common understanding of the math practices
  • Are some math practices more likely to occur together in a single task? Here was the correlations for this group

6 x 2/3 or 2/3 x 6: Using Structure & Precision to Build Understanding of Fraction Multiplication – Ryan Casey

  • Structure across the table: each row goes from iterating --> partitioning --> associative property --> distributive property
  • “Students must be taught structure explicitly”—planning and being aware of it yourself isn’t enough, but annotations can be used to help students look for and make use of structure
  • Because students are already in the mode of partitioning/iterating, 2 1/3 x 15 is easier for students than 2/3 x 15 (and 16÷3 is easier to evaluate than 2÷3)


Let’s Be Detectives: The Search for Rules, Patterns, And Understanding with SMP 7 & 8 in the Early YearsSusan Looney

  • The number line is already too abstract for some students. A beaded number line is more concrete and really helps the students see and understand what value mean. Can go from beaded number line (concrete) --> number line (pictorial) --> computations (abstract)
  • “Structure: When I look at 7 is there a doubles fact hiding in there? What do I notice about all of these numbers?”
  • “Repeated Reasoning: Does this always work? And why or why not? Are there patterns to the way we say and write our numbers?”

Get Strategic: A Thoughtful Progression of Addition  & Subtraction Strategies – Susan Jensen

  • Computation Strategy: purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another vs. Computation Algorithm: a set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly
  • Activities to do with kids: counting center (estimate the # of something then put it into ten frames), 10-frame build it (flash a quick image and then have students recreate on 10 frame, use some sort of interesting progression ex: all have a value of 6), shake and spill (5 red/yellow counters in a cup, shake and spill, how many red and how many yellow?), macaroni squeeze (10 noodles in a bag, line in the middle, what are all the possible combinations)
  • Progressions Document for single digit addition and subtraction

Early Number Operations: Important Understandings for All K-2 Students – Kathleen Lynch-Davis and Chrystal Dean

  • 65-36 alternative algorithms: subtracting in parts, counting on by 10s, and compensation
  • Disrupting people’s conceptions about standard algorithms: when dividing a fraction by another fraction, it does work to divide the numerators to get the numerator of the quotient and divide the denominators to get the denominator of the quotient (ex: 6/21 ÷ 2/3 = 3/7)

Seeing Students Who HideCathy Yenca

  • In regards to only a subset of students participating, went from feeling indifferent --> insulted --> inspired (maybe not a linear progression)
  • How can you access the students who hide?
    • Ask everyone (anonymize and project answers)
    • Include everyone (everyone works a problem and puts it up)
    • Make insulting moments inspiring
    • Let them talk
    • Let them create
  • Students care what their peers think and they compare what they think to their peers

Mathematical Heart – Anarupa Ganguly

  • K-12 50/50 math achievement M/F, but post-secondary 75/25 or worse
  • Maybe this is because we are missing an explicit effort to humanize math, so try:
    • Pose a pursue questions that catalyze emotional resonance (not just about the past and present, but future)
    • Empower our students to make and explore conjectures

Math Play: A Few ThoughtsKassia Omohundro Wedekind

  • Play is characterized by diminished consciousness of self, improvisational potential, continuation desire
  • Goals of play: ownership and identity in math

The Art of Mathematical Anthropology  - Geoff Krall

  • Growth mindset tells us that effort leads to ability, but it’s hard for students to see that when they are always being compared to a changing standard. Students need an opportunity to zoom out and see how they have grown over time
  • Students can see this through the following iterative process: assign complex tasks that produce complex work, written reflection, conversation

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