Analyzing Shifts in Teacher Discourse and

Mathematical Knowledgefor Teaching

Nanette Seago WestEd

Examine what it might mean to learn mathematical knowledge for teaching

(MKT) through the analysis of two sets of PD video of teachers’ pre-post discourse (same facilitator, same PD curriculum,

different teacher groups).

Focus of the Session

Turning to the Evidence Project*

*This work was supported by the National Science Foundation under Grant No. 0231892. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect

the views of the National Science Foundation.

Nanette Seago (P.I., nseago@wested.org)Lynn Goldsmith (P.I., Lgoldsmith@edc.org)

Research Questions:What do teachers learn by participating in professional development that uses classroom records and artifacts?

What aspects of their learning do teachers apply to their classroom practice?

• Examine & engage with the PD materials

• Define Mathematical Knowledge for Teaching

• Examine & analyze two sets of pre-post teachers’ discourse (two different PD settings)

• Discuss implications for leaders of PD

Agenda for this session

The PD Materials

Videocase centered

Modular

Sequenced PD curriculum

Learning and Teaching Linear Functions

Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

Session 7

Session 8

Growing Dots 1 Lesson Task

At the beginning At 1 minute At 2 minutes

Describe the pattern. Assuming the sequence continues in the same way, how many dots are there at 100 minutes? For any number of minutes?

Sample Solution Methods

1

dots = t(4) +1 dots = 4t + 1

where t = number of minutes

At 2 minutes At 2 minutes

# of min = # of dots in each of the 4 “arms”

# of min = # of squares; 4 dots(vertices) in each “square”

1

“Arms” Method “Squares” Method

We drop in

Situating the Video Segment Within the

Lesson

Video Segment Questions

What important mathematical issues arise for the teacher and students within this segment of classroom interaction?

Kirk

Linear Functions

context

Danielle & James

Whole class

Levels of the study of teaching and learning (Adapted from Ball & Cohen, 1999)

Shifting our Attention:From Classroom to Professional Development

Levels of the study of teaching and learning (Adapted from Ball & Cohen, 1999)

Mathematical knowledge required for teaching that is different from other mathematics-intensive professions such as research mathematics,

engineering, or financial modeling.

MKT emerges within core activities of teaching such as: Figuring out what students understand Analyzing methods and solutions different from one’s own, determine their

adequacy and compare them Unpacking familiar mathematical ideas, procedures and principles in ways

to make them more accessible to students Choosing representations to effectively convey mathematical ideas Figuring out student errors Designing and modifying mathematical tasks

Mathematical Knowledge for Teaching

Ball & Bass, 2000

PD Group 1Context:

24 middle school mathematics teachers

Large urban school district

Session 1 of Learning and Teaching Linear Functions

Foundation Module

Large group discussion of 1st video clip

Teachers have worked on and discussed the mathematics in the dots problem

Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

Session 7

Session 8

Predict

What might teachers tend to in the video?

What might they not tend to?

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

Session 1 Video Clip

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

PD Group 1; Session 8Context:

Five months later: Session 8 of Learning and Teaching

Linear Functions Foundation Module

Teachers have revisited and discussed the mathematics in the dots problem

Large group discussion of 1st video clip

Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

Session 7

Session 8

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are the teachers

working on?

Session 8 Video Clip

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

PD Group 2Context:

6 middle school, 3 high school mathematics teachers

Medium-sized urban school district

Session 1 of Learning and Teaching Linear Functions

Foundation Module (October)

Teachers have worked on and discussed the

mathematics in the dots problem

We drop in on the large group discussion of 1st video clip

Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

Session 7

Session 8

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

Session 1 Video Clip

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

PD Group 2; Session 8Context:

Five months later: Session 8 of Learning and Teaching

Linear Functions Foundation Module

Teachers have revisited and discussed the mathematics in the dots problem

Large group discussion of 1st video clip

Session 1

Session 2

Session 3

Session 4

Session 5

Session 6

Session 7

Session 8

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

Session 8 Video Clip

Video Focus

• Use the MKT worksheet to focus on:– What are the teachers talking about as they

analyze the video segment?– What core activities of teaching are teachers

working on?

Implications

As leaders of professional development, what has this session raised for you in terms of:

Teacher learning of MKT?

Facilitating the learning of MKT?