2. Reflecting on Practice: Making Connections that Support Learning
Unit 3, Session 4
2016
Reflecting on Practice
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3. Park City Mathematics Institute
“Students’ experiences have strong effects on their beliefs about themselves as well as their abilities to remember information and use it spontaneously to solve new problems” (How Students Learn: Mathematics in the Classroom, 2005, p. 238)
Reflecting on Practice
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4. Park City Mathematics Institute
Using PollEverywhere
What are the beliefs you think students have about mathematics? Post your ideas to the PollEverywhere. 3 separate rooms:)
Reflecting on Practice
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5. Park City Mathematics Institute
“Supporting metacognitive thinking and attitudes goes beyond reflection and coordination of alternative mathematical representations and strategies. It includes creating a classroom atmosphere in which students feel comfortable to explore, experiment, and take risks in problem solving and learning”
How Students Learn: Mathematics in the Classroom, 2005, p. 373
Reflecting on Practice
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6. Park City Mathematics Institute
Is this statement true or false? “In an isosceles triangle a median divides the triangle into two regions of equal area.”
Reflecting on Practice
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7. Park City Mathematics Institute
Tom’s class
What evidence do you see in this class of students thinking about their own thinking and that of their classmates? [Round Robin at your tables]
What evidence do you see in this class of Tom's thinking about his students' thinking and his own thinking? 
Reflecting on Practice
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8. Park City Mathematics Institute
Lyle’s class
What evidence do you see in this class of students thinking about their own thinking and that of their classmates? [Round Robin at your tables]
What evidence do you see in this class of Tom's thinking about his students' thinking and his own thinking?
Reflecting on Practice
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9. Park City Mathematics Institute
Reflect on your classroom in terms of discussion,responsibility and independence teacher< >student
Reflecting on Practice
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10. Park City Mathematics Institute
Part of being able to think about your own thinking is to know the norms for being able to share your thinking with others in the class.
Read "Nurturing the Development of a Learning Community" paragraphs on pp
At your table, brainstorm strategies for making these norms a part of your classroom to produce a Lyle-like classroom.
Reflecting on Practice
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11. Park City Mathematics Institute
Establishing norms
Classroom norms do not happen without explicit conversation with students about your expectations.
Students need to see the norms modeled and teachers need to call attention to them.
Students need to be recognized when they are following the norms you want in your room.
Reflecting on Practice
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12. Park City Mathematics Institute
Share one norm per table that at least one of you will try to implement in your classroom next fall.
Reflecting on Practice
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13. Park City Mathematics Institute
Peter Liljedahl
4:30pm in here Groups of 3 will be working on a math problem, then discuss with Peter
A little more than five, a little less than ten
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14. Setting norms: Deborah Ball
One of the things that's very important is that if one person in the class is talking other people need to listen, because people say things that can help you think about the problems.
Shekira said some interesting things, and so did Liz, but lots of people were not listening to them.
I know it's because you're finding more solutions yourself.
But, one of the things that I would really like you to, to see you doing is to be listening really hard when someone else has an idea, because it might help you with your thinking.
Transcript of 3rd Grade Class, Deborah Ball, 2001

15. Setting norms: Kathy Humphreys
“TEACHER: . . group one at a time and say what ideas you might have. And let’s practice doing what we were doing before where one person talks and everyone listens and everyone gets a chance to talk and if you don’t have an idea, you can pass. So, starting with the person, like in Kimberly’s position at the….., what you’ll do is go in a clockwise direction and if you have an idea, tell your group, and people that are listening, I’d like you to respond.
I notice from watching videotapes that sometimes somebody’ll say something in the group and no one’ll say anything. And it’s sort of like being completely ignored. So when someone comments, when you, when you make a statement or someone makes a statement to you, there should be some kind of response, like, h-huh, or I don’t understand what you mean, or something to acknowledge..”.
Boaler & Humphreys, 2005