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 Districtmhedges@mtsd.k12.wi.us

Beth Schefelker Mathematics Teaching Specialist, Milwaukee Public Schoolsschefeba@milwaukee.k12.wi.us

Connie LaughlinMathematics Consultant,

Milwaukee WIlaughlin.connie@gmail.com

Thank You for coming!

Find the power point for this session on two websites:

NCSM conference website

Milwaukee Mathematics Partnership website: mmp.uwm.edu