Professional Practice Norms

1
Professional Practice Norms

• Listening to and using others ideas
• Keeping records of professional work
• Adopting a tentative stance toward practice -
  wondering versus certainty
• Backing up claims with evidence and providing
  reasoning
• Talking with respect yet engaging in critical
  analysis of teachers and students portrayed
• Seago Mumme, 2003

2
Learning and Teaching Linear Functions Video
Cases for Mathematics Professional Development,
6-10 Conceptualizing and Representing Linear
Relationships Session Two
3
A Frame for Viewing Teaching

• Teaching is a practice that can be learned like
  playing soccer or performing dance.
• Teaching is complex. In complex practices there
  are many variables at play there are no simple
  solutions some things are unpredictable.
• Teaching and learning happen within a basic set
  of dynamic relationshipsteachers, students,
  content, and environment.

4
Teaching and Learning
Ball and Cohen (2000)
5
Foundation Module Map
We are here
6
Cubes in a Line Lesson Task

• How many faces (face units) are there when 2
  cubes are put together sharing a face? 10 cubes?
  100 cubes? t cubes?

7
Mathematical Task Questions

• Look over how you solved this problem. Why did it
  make sense to you to solve it this way? How is
  this like/unlike the Dots Problem?
• What are some of the ways students might solve
  it? How might they use the cubes to generate the
  number of faces for any number of cubes? What
  misconceptions might they bring?
• What might a teacher need to do to prepare to use
  this task with students?

8
Lesson Graph Questions

• What does this lesson graph tell you/not tell
  you about the mathematical point of the lesson?
• What clues (evidence) did you use from the
  lesson graph to make your claim?

9
Video Segment Focus Questions

• What moments or interchanges appear to be
  interesting/important mathematically?
• What about them makes this so?

10
Differentiating Instruction

• What are ideas that come to mind when you hear
  the phrase differentiated instruction?
• Where did you see evidence of differentiated
  instruction, either in relation to our charted
  list or otherwise, during this video clip or in
  the lesson graph?

11
Link to SAS

• How do you think MaryAnn considered the elements
  of SAS in planning and delivering the lesson?

12
Comparing Growing Dots 1 and Cubes in a Line
Video Segments

• What was similar/different about the segments
  from the Cubes in a Line and Growing Dots 1
  lessons?
• About the mathematics?
• About the student ideas?
• About the teachers apparent goals and use of
  student ideas?

13
Linking to Practice

• Work in grade-level groups to adapt the Cubes in
  a Line task to your grade level.
• Decide what you want to use this task to teach.
• Predict possible student responses.
• Develop questions to ask students.

14
Reflections

• What were the important mathematics ideas you
  encountered today?
• Did this experience generate any
  insights/connections related to teaching? (What
  about the day prompted these?)

15
Closing Discussion
16
Concept Map Discussion

• What were the mathematical goals of this session?
  
• What were the pedagogical goals of this session?

17
Concept Map Discussion

• Mathematical Goals
• Distinguish various symbolic representations of a
  situation and relate them to the geometry of the
  task.
• Examine explicit and recursive models for linear
  growth.
• Conceptualize linear growth as constant rate of
  change and slope as constant growth rate.

• Pedagogical Goals
• Promote the value of sustained professional
  development.
• Increase awareness of the role of facilitator of
  professional development.
• Begin to clarify, distinguish, and reconcile
  students mathematical representations,
  explanations, and reasoning.
• Examine mathematically important aspects of
  various solution strategies.

18
Facilitation Discussion

• Were there any facilitation moves that stood out
  to you throughout the morning?