## Tuesday, April 19, 2016

### NCTM 2016 Day 1

Barbara Dougherty and Lisa Bendall
Take-aways:
• Motivation through games that are high interest, require collaboration or cooperation, and incorporate significant mathematical thinking (ex: Bowl-a-Fact and Find-a-Place)
• Using a high motivation Do Now as leverage for the rest of the class—if kids start excited and engaged, this sets them up for success in the rest of the lesson
• Public accountability for engagement—homework through expert groups or collaborative groups
What I am wondering now: What is the “just right” fit for skill level in games that require some sort of prerequisite knowledge? How do students get feedback to improve if they are consistently demonstrating misconceptions in these types of games? What are the characteristics of a game that is both engaging and builds mathematics?

### Cuisenaire Rods and Number Lines: Multiplication and Division of Fractions

Adam Harbaugh, Kurt Killion, and Gay Ragan (Powerpoint here)
Take-aways:
• Sequence of building understanding: word problem--> concrete model with Cuisinaire rods--> # line model --> matching pencil and paper algorithm
• They are only doing “sharing” division (how many 1/3’s in 3/4?) rather than “measurement” division (3/4 is 1/3 of what whole?)  because “measurement” contexts with two fractions are too contrived. Therefore, this leads to the development of the common denominator algorithm.
What I am wondering now: They require their students to make the model so that it is easily partitioned by both denominators. This makes the numbers come out nice and the model easier to use, but it does not promote sense-making. Where is the line between sense-making/flexibility and streamlining for success?

### Choosing Tasks for Productive Struggle, Not Frustration

Jackie Murawska (Powerpoint here)
Take-aways:
•  Characteristics of problems that are good for productive struggle:
• the problem solver must decide what math to bring in
• the task uses real life (often messy) data
• the task requires mathematical modeling
• “If I don’t ask you to guess, you don’t have a stake in it”
• “They’re not making mistakes because they aren’t thinking. They are making mistakes because they are thinking.”
What I am wondering now: These characteristics define a subset of problems that are engaging and good for productive struggle. But I think that the type of modeling problem described is only one type. How would I categorize the other types the are highly compelling?

### Linear or Quadratic? Engaging in Two Effective Math Teaching Practices

Amy Hillen and Jennifer Outzs
Take-aways:

• “In this figure as the step changes, the _____ also changes.”
•  For assessing questions stay and listen, for advancing questions walk away
What I am wondering now: I started my year building linear relationships with a lot of visual patterns work. I want to revisit that structure now and use this much more open prompt in order to review linear vs. non-linear.

Supporting Productive Struggle in Secondary Classes
Michael Steele
Take-aways:

• “Pencils down, brains on” One minute to think about the problem
• “[Students] eavesdropping [on other students] is a great sign because it means there’s something worth listening to”
• When students are starting to say “What if…” that is a good sign
What I am wondering now: What should help look like in my classroom?