combined petoskeyc2s7

Overview of Session 7

• Looking Back

– Value of Algorithms

– Value of Reasoning Strategies

• Goals of the Session

• Hexagon Train Problem

• Analysis of Catherine and David Case

• Facilitation of “Redefining Success”

• Reflection

Looking Back

• Value of Algorithms

– Efficient

– Reliable

– Universal

• Value of Reasoning Strategies

– Understand the structure of numbers,

operations, proportional

relationships, etc.

Goals of the Session

Pedagogical Goals

– To analyze the task for level of cognitive

demand

• To make connections to the MTF

– To analyze instruction

• To recognize the teacher moves that support and

undermine student learning

– To consider what it means to be successful in

doing mathematics and in teaching

mathematics

Hexagon Train Problem

• Compute the perimeter for the first 4 trains;

• Determine the perimeter for the tenth train without constructing it; and

• Write a description that could be used to compute the perimeter of any train in the pattern.

Train 1 Train 2 Train 3 Train 4

The Case of Catherine and David

What’s the Math?

• What are the mathematical goals?

• How would you describe the level of

the task?

Catherine’s and David’s Story

• Read The Case of Catherine Evans

and David Young (Focus on

paragraphs: 10-29 and 42-63.)

• Pay special attention to teacher

moves that support or undermine

student learning.

Focus Questions

• What instructor moves supported student learning?

• What instructor moves undermined student learning?

• How would you describe the level of the task as it is implemented in each of the classrooms?

Trapezoid and Hexagon Train Problem

• Build the fourth train;

• Build a larger train in the sequence,

such as the tenth or fifteenth, without

building all the trains in between; and

• Write an explanation for why the tenth

or fifteenth train looks as it does.

Train 1 Train 2 Train 3

“Redefining Success”

• What was your reaction to

Henderson’s alteration of tasks?

• How has Henderson’s definition of

successful teaching and learning

changed over time?

“Redefining Success”

• What do you take as evidence of

success as a teacher of

mathematics?

• What does it mean for students to

be successful in your classroom?

Mathematical Goals

– To identify and generalize patterns

– To explore relationships between

variables

– To make connections among

representations and solution methods

– To explain and justify solution

methods

Pedagogical Goals

– To analyze the task for level of cognitive

demand

• To make connections to the MTF

– To analyze instruction

• To recognize the teacher moves that maintain or

undermine the cognitive level of the task

– To consider what it means to be successful in

doing mathematics and in teaching

mathematics

Session 7 Dearborn & Petoskey 9/19/08 & 9/26/ 08

Adapted from Improving Instruction in Algebra: Using Cases to Transform Mathematics Teaching and Learning 9/15/08

Authors: Smith, Silver and Stein

Comparing Instructional Decisions and Their Impact:

The Case of Catherine Evans and David Young

How were the two classes the same and how they were different in terms of what was learned. Describe additional similarities and differences

that you noted as you compared the two classes. Be sure to cite specific evidence from the case (using paragraph numbers) to support your

claims.

Similarities Differences

Catherine Evans David Young

Session 7 Dearborn & Petoskey 9/19/08 & 9/26/ 08

Authors: Smith, Silver and Stein jf & nc

Comparing Instructional Decisions and Their Impact: The Case of Catherine Evans and David Young

How were the two classes the same and how they were different in terms of opportunities to learn? What teacher moves or decisions impacted

students’ opportunities to learn? Give 3 to 4 examples for each Catherine and David. Be sure to cite specific evidence from the case (using

paragraph numbers) to support your claims.

Catherine

Teacher moves that undermine student learning Teacher moves that support student learning

Session 7 Dearborn/Petoskey

9/19/08 & 9//26/08

Authors: Smith, Silver and Stein

The Hexagon Train Problem

Solve Trains 1, 2, 3, and 4 are the first 4 trains in the hexagon pattern. The first train in this pattern consists of one regular hexagon. For each subsequent train, one additional hexagon is added. For the hexagon pattern

o Compute the perimeter for the first 4 trains; o Determine the perimeter for the tenth train without constructing it; and o Write a description that could be used to compute the perimeter of any train in

the pattern. (Use the edge length of any pattern block as your unit of measure. If pattern blocks are not available, use the side of a hexagon as the unit of measure.)

Consider Find as many different ways as you can to compute (and justify) the perimeter.

Train 1 Train 2 Train 3 Train 4

- Michigan Mathematics and Science Teacher Leadership Collaborative -

Pictures From

Petoskey Session

Pictures From

Dearborn Session

combined petoskeyc2s7

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