MTL MeetingDecember 6, 2011

Hank Kepner Connie LaughlinLee Ann Pruske Beth SchefelkerMary Mooney Rosann Hollinger

We are learning to deepen our understanding of ratio.

reflect on teacher moves to probe student thinking.

Capture the general tone and substance of an interaction between yourself and a student around the heartbeat problem.

Prepare a short reflection on your conversation to share at December’s meeting.

In your triad, use the Wheel of Protocol to share your reflections around your Professional Practice: 3 min/2 min

What did you find in common/unique?

Each table share one commonality or one unique aspect to their conversations.

• Deepen our understanding of the Standards for Mathematical Practice with a focus on: #1 Make sense of problems and persevere in

solving them.#3 Construct viable arguments and critique the

reasoning of others.#6 Attend to precision.

• Develop an understanding of various progressions of mathematics development.

use and justify various strategies to solve a ratio/rate problem,

recognize possible teacher moves to uncover student thinking.

If the small gear turns clockwise, which direction does the big gear turn? Why?

If you turn the small gear a certain number of times, does the big gear turn more revolutions, fewer, or the same amount? How can you tell?

You have turned the gears until they have returned to their original position.

How many revolutions does the small gear make?

How many revolutions does the big gear make?

Find a way to keep track of the number of revolutions both gears make until they return to their original position.

Students need to make a transition from focusing on only one quantity to realizing that two quantities are important.

Some found out that when the small gear turns 5 times, the big gear turns 3 times. What are some other rotation pairs for the gears?

Students need to make a transition from making an additive comparison to forming a ratio between two quantities.

Think back to Part I: Find a way to keep track of the number of revolutions both gears make until they return to their original position.

Form pairs of teacher-student roles.

Student explains their thinking while teacher asks probing questions.

use and justify various strategies to solve a ratio problem,

recognize and use teacher moves to uncover student thinking.

As you reflect on today’s problem and the dialogs between teacher and students, how will you support a teacher in probing students’ thinking?