National Council of Supervisors of Mathematics Indianapolis, Indiana April 11, 2011
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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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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 - PowerPoint PPT Presentation
Transcript of National Council of Supervisors of Mathematics Indianapolis, Indiana April 11, 2011
Developing Mathematics PD Sessions: Planning Conversations and Instructional Decisions that Lead to Improved MKT in District Leaders.
National Council of Supervisors of MathematicsIndianapolis, Indiana
April 11, 2011
Melissa Hedges, MathematicsTeaching Specialist, MTSDBeth Schefelker, Mathematics Teaching Specialist, MPSConnie 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.
Session Goals
We Are Learning To…build 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.
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?
A decision-making process
Identifying the math to be discussed
Connecting to standards
Completing the task
Looking at student work to push thinking
Process of development
Identify the needListening to math leadersLooking at dataReviewing student work with teachers
Identify a Domain as outlined in CCSSDecide on the cluster of standards that
connects to the needNarrow the focus to specific standard(s).
Why focus on proportional reasoning?
Proportional reasoning has been referred to asthe capstone of the elementary curriculum andthe cornerstone of algebra and beyond.
Van de Walle,J. (2009). Elementary and middle school teaching developmentally.Boston, MA: Pearson Education.
Connect to the CCSS
Narratives from grade 6 and grade 7Cluster 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)
Never ending question….
What are teachers expected to know and do to make sure students develop proportional reasoning?
A Definition of Proportionality
When two quantities are relatedproportionally, the ratio of one quantity to the other is invariant, or the numericalvalues of both quantities change by thesame factor.
Developing Essential Understandings of Ratios, Proportions & Proportional Reasoning, Grades 6-8. National Council of Teachers of Mathematics, 2010, pg. 11.
Essential Understanding
A proportion is a relationship of equalitybetween two ratios.
3 girls to 4 boys is the same ratio as 6 girls to 8 boys
Essential Understanding
A rate is a set of infinitely many equivalentratios.
Cassandra’s Faucet
Cassandra has a leaky faucet in her bathtub. She put a bucketunderneath the faucet in themorning and collected datathroughout the day to see howmuch water was in the bucket.
Use the data Cassandra collected to determine how fast the faucet was leaking.
Time Amount of Water
7:00 a.m. 2 ounces
8:30 a.m. 14 ounces
9:30 a.m. 22 ounces
11:00 a.m. 34 ounces
2:00 p.m. 58 ounces
5:30 p.m. 86 ounces
9:30 p.m. 118 ounces
Engaging in a task
Complete the task Cassandra’s FaucetShare 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
partner’s reasoning?
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.
Cassandra’s Faucet Student Work
How did student’s 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?
Making decisions about using student work
Which papers would drive conversations around the big math ideas of proportional reasoning? Why?
Student work A
Student work B
Student work C
Student work D
Student Work E
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
Think About…
Proportional reasoning may at first seemstraightforward, but developing anunderstanding of it is a complex processfor students.
How do we support ourteachers’ understanding of proportionalreasoning?
Deliberate decision-making process
Identifying the math to be discussed
Connecting to standards
Completing the task
Looking at student work to push thinking
Why pay attention to MKT?
“Knowing mathematics for teaching often entails making sense of methods and solutions different from one’s own and so learning to size up other methods, determine their adequacy and compare them is an essential mathematical skill for teaching…”
-D. Ball
Thank you for coming!
Melissa Hedges, MathematicsTeaching Specialist, Mequon-Thiensville School [email protected]
Beth Schefelker Mathematics Teaching Specialist, Milwaukee Public [email protected]
Connie LaughlinMathematics Consultant,
Milwaukee [email protected]
Thank You for coming!
Find the power point for this session on two websites:
NCSM conference website
Milwaukee Mathematics Partnership website: mmp.uwm.edu
