## Reflection: Developing a Conceptual Understanding Equations of Circles - Section 2: Equations of Circles

When I first taught this lesson, I thought I did a fair job of explaining the conceptual side of completing the square. But I walked away feeling that I could do a better job of it. I thought my explanation, though thorough, was overly clinical and too teacher-centered. I wanted to capture students' imaginations and involve them more in the process of sense-making. I also wanted to incorporate a piece that would hold them accountable for demonstrating their conceptual understanding of completing the square.

This is what spawned the fictional conversation between Dr. Blabbendorf and his 5 year-old granddaughter, Samantha.

I decided to make Samantha 5 years-old so that she would have license to ask totally naive questions that students themselves might relate to. At the same time, though, I didn't want students to relate to Samantha as a peer. I wanted students to see themselves as more experienced and more mathematically sophisticated than Samantha so that they would expect a deeper understanding from themselves than that which Samantha exhibited. So while it was perfectly ok for Samantha to dismiss all of her Grandfather's jargon and move on to wanting to play, I wanted to compel students to make sense of what Dr. Blabbendorf has said and demonstrate that understanding by responding to the writing prompt.

In terms of having the students role play, I think having them role play Samantha allows them to acknowledge the aspect of themselves that simply wants to dismiss things that appear to be too complicated and having them role play Dr. Blabbendorf allows them to take the perspective of a more mature expert. After this whole dramatic experience, I'm hoping that they will land themselves somewhere between those two extremes and leave having a conceptual understanding of completing the square.

Using drama to develop conceptual understanding
Developing a Conceptual Understanding: Using drama to develop conceptual understanding

# Equations of Circles

Unit 9: Analytic Geometry
Lesson 4 of 7

## Big Idea: "I'll take 80's sitcoms for \$1000, Alex." In this lesson, students learn how completing the SQUARE "PEGS" the center and radius of the round hole.

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70 minutes

### Anthony Carruthers

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