Cathy Carroll

1

Supporting Teachers Mathematical Reasoning in
Secondary Level Mathematics Professional
Development

• Cathy Carroll
• WestEd

2
This Session

• Provides an opportunity to consider the coach/PD
  leader work of supporting teachers mathematical
  reasoning in mathematics professional development
  for secondary teachers

3
Agenda

• Engage in a videocase from the Learning to Lead
  Mathematics Professional Development materials
• Do a mathematics task
• View and discuss a video of mathematics
  professional development
• Step back and consider implications for
  coaches/PD leaders practice

4
Aspects of Leadership
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Assumptions about mathematics professional
development

• It is complex
• It involves an understanding of mathematics -
  childrens mathematics mathematics used in
  teaching
• Inquiry, analysis and reflection build greater
  understanding and the ability to improve
  practice
• It involves a dynamic relationship among
  teaching, learning and content.

6
We are looking at this
We are here
7
Why Videocases?

• Authentic examples - familiar but safe
• Stop-action - can be played and re-played to
  examine
• Allow freedom to study - removed from
  in-the-moment demands of a session

8
Working with Videocases
9
Crossing the River Task

• Work on the task individually (about 5 minutes)
• When ready, talk with your group about how you
  are thinking about the task
• Try to find more than one rule for figuring out
  the number of trips to get any number of adults
  (a) and two children across the river
• How do you think middle grade teachers might
  approach this task?

10
Sharing Solutions

• How many trips does it take for 8 adults and 2
  children?
• What rule(s) did you get for any number of adults
  and 2 children?
• How did you build your rule?
• How are the rules related?
• What might be the purpose(s) for using this task
  with middle grade teachers?

11
About This Case

• Videocase of real mathematics PD situation
• Unstaged
• Not intended as model or exemplar, but as an
  object of inquiry
• Intended to focus leaders on mathematics PD design

12
Context

• 1-day workshop focusing on algebraic thinking
• 19 secondary teachers
• The morning begins with a discussion of algebraic
  thinking
• Teachers then worked individually on the Crossing
  the River task for a few minutes
• Teachers begin discussing the task in small
  groups
• Mary Alice is the PD leader

We drop in here
13
Caveat

• Mary Alice and the teachers are offering us a
  gift of allowing us to carefully examine a real
  instance of practice. We are examining their
  practice, not critiquing them.

14
Mary Alice
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Viewing the Case

• We will look at this video twice
• First, we will look at a clip to focus on the
  mathematics and teachers thinking.
• Then we will watch part of the clip again to
  focus on the role of the PD leader.

16
Frame for Viewing

• What mathematical ideas are at play?

Suggestion Use transcript to think about issues
after viewing the video
17
What mathematical ideas are at play?
18
Small Group Discussion

• How did Sally appear to be building her rule?
• How did Cathy appear to be building her rule?
• How do you think Sherry and Fiona approached the
  task?

19
Whole Group Discussion

• How do you think the group members were reasoning
  about the task?

20
Frame for Viewing

• Assume that the PD leaders goal was to promote
  teachers mathematical reasoning by helping them
  to see relationships among multiple expressions.
  
• As you watch the clip, consider
• What is the PD leader doing and how might that
  contribute to teachers mathematical reasoning?

21
What is the PD leader doing and how might that
contribute to teachers mathematical reasoning?
22
Small Group Discussion

• What moves did the PD leader make with this
  group?
• How might her moves be related to the goal of
  mathematical reasoning?

Be sure to cite your evidence.
Whole group
23
Whole Group Discussion

• How are you thinking about the PD leaders moves
  in relationship to her possible goal of helping
  teachers to see relationships among multiple
  expressions?

24
Connecting to Practice

• Still assuming the goal of promoting mathematical
  reasoning by seeing multiple expressions, use the
  recording tool to identify
• Mary Alices move at line 121 and at one other
  line
• Some potential benefits/drawbacks of her move
• Some alternate possible moves
• Some potential benefits/drawbacks of the
  alternative moves

Small Group
25
Connecting to Practice

• What alternative moves did you suggest?
• What are some potential benefits or drawbacks of
  those moves?

Whole Group
26
Reflecting on the Experience

• How does this case help us think about the
  coach/PD leader work of supporting teachers
  mathematical reasoning?

Pairs/Whole Group
27
For More Information

• Contact
• ccarroll_at_wested.org