## Reflection: Gradual Release Exploring Midpoint Quadrilaterals - Section 2: Independent Practice

When students were asked to determine whether HJKL had any congruent or parallel sides, several of them were unclear on how they should go about doing that. These students tended to call me over to their desk and say something like, "What do you want us to do here?"

My response was typically, "I don't want you to do anything...what is it that the directions are asking you to do?" In that way, I was trying to put the onus on the students to interpret the directions rather than me doing it for them.

The typical student response to my question would be "They want me to see if any of the sides are congruent."

My response: "What does it mean for two sides to be congruent?"

Student: "It means they're the same."

Me: "What about them is the same?....They're color?, Their smell? What?"

Student: "Oh their lengths are the same."

Me: "So how could you determine whether two segments are congruent?"

Student: "I could use a ruler and measure."

Me: "Yes, but in this exercise you will not have a ruler available to you; all you have is the coordinates of the vertices of HJKL. What could you do?"

So after this type of exchange, the student usually gets the idea that they should use the distance formula to determine if there are any congruent sides. Before I leave, though, I emphasize to the student that the type of questioning I put them through is the type of internal dialogue they need to be having with themselves as they make sense of the instructions and find a way to approach the task. I might, then, ask them to replay the logical sequence for me. That should go something like:

"I'm trying to determine if HJKL has any congruent sides. If there are congruent sides, then their lengths must be equal. I can use the distance formula to find the lengths of the sides and determine if any of them are equal to each other."

This experience reminds me that some students are very hesitant to take initiative when they have not been given explicit directions on what to do. Even though we practiced the distance formula in the Activating Prior Knowledge section, and even though it was not that much of a stretch to apply the formula to determine if there were congruent sides, the sheer fact of not being told explicitly what to do threw some students for a loop. I have no doubt that they understand the concepts; I just think they need to get more comfortable taking that first step to think about what is being asked and take the risk of trying to respond appropriately.

Getting students to take initiative
Gradual Release: Getting students to take initiative

Unit 2: Geometry Foundations
Lesson 4 of 14

## Big Idea: Simon Says? In this lesson students learn to apply the midpoint and distance formulas even when they aren't explicitly told to do so.

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80 minutes

### Anthony Carruthers

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