Developing Mathematics PD Sessions: Planning Conversations and Instructional Decisions that Lead to Improved MKT in District Leaders.

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Developing Mathematics PD Sessions Planning
Conversations and Instructional Decisions that
Lead to Improved MKT in District Leaders.
National Council of Supervisors of
Mathematics Indianapolis, Indiana April 11,
2011 Melissa Hedges, MathematicsTeaching
Specialist, MTSD Beth Schefelker, Mathematics
Teaching Specialist, MPS Connie Laughlin,
Mathematics Instructor, UW-Milwaukee
The Milwaukee Mathematics Partnership (MMP), an
initiative of the Milwaukee Partnership Academy
(MPA), is supported with funding by the
National Science Foundation.
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Session Goals

• We Are Learning Tobuild Math Knowledge of
  Teaching (MKT) about proportional reasoning.
• We will be successful when we can look at student
  work that will strengthen teacher content
  knowledge about proportional reasoning.

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Questions we ask ourselves

• What is the critical content idea that leaders
  needed to understand?
• How much content can be explored in a 90-minute
  professional development session?
• What learning experiences can be used to launch,
  explore, and summarize the content idea?
• What connections can be made to current work?

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A decision-making process
Identifying the math to be discussed Connecting
to standards Completing the task Looking at
student work to push thinking
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Process of development

• Identify the need
• Listening to math leaders
• Looking at data
• Reviewing student work with teachers
• Identify a Domain as outlined in CCSS
• Decide on the cluster of standards that connects
  to the need
• Narrow the focus to specific standard(s).

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Why focus on proportional reasoning?
Proportional reasoning has been referred to
as the capstone of the elementary curriculum
and the cornerstone of algebra and beyond.
Van de Walle,J. (2009). Elementary and middle
school teaching developmentally.Boston, MA
Pearson Education.
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Connect to the CCSS

• Narratives from grade 6 and grade 7
• Cluster statements
• Understand ratio concepts and use ratio reasoning
  to solve problems (6.RP.3)
• Analyze proportional relationships and use them
  to solve real world and mathematical problems.
  (7.RP.2)

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Never ending question.

• What are teachers expected to know and do to make
  sure students develop proportional reasoning?

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A Definition of Proportionality

• When two quantities are related
• proportionally, the ratio of one quantity to
• the other is invariant, or the numerical
• values of both quantities change by the
• same factor.
• Developing Essential Understandings of Ratios,
  Proportions Proportional Reasoning, Grades 6-8.
  National Council of Teachers of Mathematics,
  2010, pg. 11.

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Essential Understanding
A proportion is a relationship of
equality between two ratios. 3 girls to 4 boys
is the same ratio as 6 girls to 8 boys
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Essential Understanding
A rate is a set of infinitely many
equivalent ratios.
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Cassandras Faucet
Cassandra has a leaky faucet in her bathtub. She
put a bucket underneath the faucet in the morning
and collected data throughout the day to see
how much water was in the bucket. Use the
data Cassandra collected to determine how fast
the faucet was leaking.
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Engaging in a task

• Complete the task Cassandras Faucet
• Share out your thinking with the person next to
  you.
• In what way did you use proportional reasoning in
  your thinking?
• Is your reasoning the same as your partners
  reasoning?

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What should student work look like?
Turn and talk In order to know if students
understand proportions, what traits would you
want to see demonstrated on their work? Share
out ideas with the whole group.
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Cassandras Faucet Student Work

• How did students make sense of the table?
• What were the various entry points?
• What conclusions can you make about how students
  are thinking as they engaged in purposeful
  struggle to understand rate?

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Making decisions about using student work
Which papers would drive conversations around
the big math ideas of proportional reasoning?
Why?
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Student work A
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Student work B
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Student work C
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Student work D
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Student Work E
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Purposefully selecting student work

• Student A shows the start of proportional
  reasoning by using additive thinking
• Student B multiple equivalent rates and
  checking more than one time interval
• Student C multiple representations to prove an
  answer
• Student D a right answer, but explanation needs
  clarity
• Student E proportional thinking but with some
  assumptions

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Think About
Proportional reasoning may at first
seem straightforward, but developing
an understanding of it is a complex process for
students. How do we support our teachers
understanding of proportional reasoning?
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Deliberate decision-making process
Identifying the math to be discussed Connecting
to standards Completing the task Looking at
student work to push thinking
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Why pay attention to MKT?

• Knowing mathematics for teaching often entails
  making sense of methods and solutions different
  from ones own and so learning to size up other
  methods, determine their adequacy and compare
  them is an essential mathematical skill for
  teaching
• -D. Ball

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Thank you for coming!

• Melissa Hedges, MathematicsTeaching Specialist,
  Mequon-Thiensville School District
• mhedges_at_mtsd.k12.wi.us
• Beth Schefelker
• Mathematics Teaching Specialist, Milwaukee
  Public Schools
• schefeba_at_milwaukee.k12.wi.us

• Connie Laughlin
• Mathematics Consultant, Milwaukee WI
• laughlin.connie_at_gmail.com

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Thank You for coming!

• Find the power point for this session on two
  websites
• NCSM conference website
• Milwaukee Mathematics Partnership website
  mmp.uwm.edu