Reflection: Rigor Polygons: Introduction & Investigation - Section 1: What is a Polygon?


A task doesn't need a lot of bells and whistles to be a rich task.  This period of dialogue and debate about the definition of a simple polygon became very high level in my classroom.  Achieving this level of rigorous discourse requires a few simple things, in my personal experience.  

The teacher should:

  • be willing to entertain questions that they themselves may find perplexing
  • never tell a student, "No, that's not a -----," but instead, when presented with a student error/misunderstanding, should ask guiding questions to eventually lead them to a change in thinking.  (What makes you say that?  What is the definition of a simple polygon?  What kind of sides do you see on your polygon? and so on).
  • encourage students who persist when they hit the point of cognitive dissoance
  • be willing to sometimes say, "I don't know" or "I'm not sure" and then elaborate upon the steps s/he will take to find the needed information
  • model the fun in thinking about perplexing questions and the limits of definitions (the arbitrary point at which a line becomes a really thin rectangle - conceptually very abstract)

The students should:

  • explain their reasoning in complete sentences
  • be allowed to attempt to justify a "wrong" answer. The student who thought he could draw a 2 sided polygon is a great example of the productive use of "incorrect" thinking. His illustrations on the board led to very rich conversations in my class.

  A Rich Conversation About Simple Polygons - Constructing Viable Arguments & Critiquing the Reasoning of Others
  Rigor: A Rich Conversation About Simple Polygons - Constructing Viable Arguments & Critiquing the Reasoning of Others
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Polygons: Introduction & Investigation

Unit 11: Geometry in Architecture
Lesson 1 of 9

Objective: SWBAT compare attributes of regular and irregular pentagons, hexagon, heptagons and octagons. They will construct viable arguments about what is/isn't a polygon and critique the reasons of other students who are doing the same.

Big Idea: Interacting with polygons and testing the definitions can be engaging, fun and build a powerful, individualized understanding. (Lesson updated: January 6, 2015)

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10 teachers like this lesson
Math, Geometry, engineering
  60 minutes
concave pentagon
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