Analyzing Shifts in Teacher Discourse and Mathematical Knowledge for Teaching Nanette Seago WestEd.
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Transcript of Analyzing Shifts in Teacher Discourse and Mathematical Knowledge for Teaching Nanette Seago WestEd.
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., [email protected])Lynn Goldsmith (P.I., [email protected])
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?