Reflection: Routines and Procedures Multiple Ways of Seeing - Section 3: Share and Debrief


When facilitating this whole class discussion, I knew I had to keep one of the biggest themes of the year in mind: transformations.  I hoped to hear students saying things like:

  • "whatever is on this side is on the other"
  • “I feel like I can split this down the middle”
  • “you can actually rotate the figure and see it the same way.” 

In one class, students didn't bring up these ideas, so I told them that students in the other classes had brought them up.  I needed students to hear these ideas because line and rotational symmetry are so foundational to our perspective on and understanding of geometry that I wanted to make sure it became part of the discussion early, especially as it will have significance in the Four Triangle Problem and potentially other tasks (like Definitely, Maybe and Who’s a Widget?)

During the whole class discussion, I posed a question to the class:

How did the people in your group help you to make sense of the image? 

This question was useful for two reasons:

(1) it helped me to reinforce my norms and expectations around group work and my belief that we learn more when we are really working in a mathematical community

(2) the question helped students to articulate certain assumptions they made about the image itself. 

For example, if students assumed they could “add a line,” then they saw FAR more triangles than were actually present.  If students assumed they could view the figure as if three dimensionally, then they too saw more triangles than were actually present.  What was interesting about this discussion is it really got at the heart of (1) the significance of definitions—why precision matters so much (MP6) and (2) making sure to clearly state assumptions made when solving a problem (MP3).    



  Facilitating the 1st Whole Class Discussion
  Routines and Procedures: Facilitating the 1st Whole Class Discussion
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Multiple Ways of Seeing

Unit 1: Creating Classroom Culture to Develop the Math Practices
Lesson 1 of 6

Objective: Students will be able to determine the number of triangles in a composite figure.

Big Idea: Students will engage in structured, collaborative small group and whole group discussions to see how multiple ways of seeing can deepen the class' collective understanding.

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