SUPPORTING CCSS-M

IMPLEMENTATION

from standards to practice

GOALS Deepen understanding of

mathematics content and practices.

Analyze instructional materials. Explore ways to increase

students’ access to mathematics through lesson planning.

Identify ways in which this professional learning module can be used to improve instructional practice in your district.

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Learner of this information

Facilitator of this information

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AGENDA8:00 - 8:15 Welcome and Goals8:15 - 8:45 Making Sense of the Mathematics

– Unit Perspective8:45 - 9:45 Making Sense of the Mathematics

– Progression Perspective9:45 - 10:00 Break10:00 - 11:00

Making Sense of the Mathematics – Across Units, Within a Grade

• Identify Mathematical Connections Across Units

11:00 - 11:45

Lunch

11:45 - 12:45

Mathematics as Represented in Your Materials• What concepts, procedures and practices

need to stay and what can go?• What concepts, procedures, and practices

appear to be missing?• Locate a Task in Your Materials

12:45 - 2:00 Lesson Goals and the “Launch”• Planning for access and learning

2:00 - 2:30 Reflections, and District Planning

What implications might this suggestion have in relation to: making sense

of mathematics teaching,

assessing, and learning?

MAKING SENSE OF THE MATHEMATICS UNIT PERSPECTIVE

The UNIT is the “optimal grain-size for the learning of mathematics” not a lesson or activity.

-Phil Daro (co-author of CCSS-M)

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1. Unit Themes• Graphic• Focus Questions• Intellectual Processes• Key Concepts

2. Content Standards• Abstract• CCSS Standards

3. Instructional Resources• Illuminations• Children’s Literature• Texas Instruments• References• Applets

4. Professional Resources• NCTM Articles• Books

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MAKING SENSE OF THE MATHEMATICS UNIT PERSPECTIVE

What do you notice is staying the same and what is changing with this mathematics?

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MAKING SENSE OF THE MATHEMATICS UNIT PERSPECTIVE

“A teacher or test designer seeing exclusively within the grade level will miss the point [of the number line]. Multi-grade progression views of standards can avoid many misuses of standards” (p.43).

What do you notice is staying the same and what is changing with this mathematics?

MAKING SENSE OF THE MATHEMATICS PROGRESSION PERSPECTIVE

How does this document help you deepen your understanding of the mathematics?

How might you use this document to support implementation in your district?

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BREAK

MAKING SENSE OF THE MATHEMATICSACROSS UNITS WITHIN A GRADE

Where might there be opportunities for students to make mathematical connections?

MAKING SENSE OF THE MATHEMATICSACROSS UNITS WITHIN A GRADE

Look in the units you selected to find examples that support these mathematical connections.

Same DifferentExample 1

Example 4

Example 6

Example 2

Example 3

Example 5

How did this activity help you think about teaching this content in your classroom?

How could this activity be used to help teachers understand the development of content within a grade level?

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Lunch

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Click icon to add picture

MATHEMATICS AS REPRESENTED IN YOUR MATERIALSExamine your instructional materials for today’s focus unit. Make notes about:

the CCSS concepts, procedures and practices represented (or not)

which sections should stay and which can go?

Identify a task/lesson that includes both CCSS content and practice standards.

How did this activity help you think about teaching this content in your classroom?

In what ways might this model be a useful design for you to use with colleagues?

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Research has suggested that an effective set-up phase (launch) of instruction clarifies both the final work product and how students should work (i.e., individually, in groups) to solve the problem (Boaler & Staples, 2008, Smith, Bill, & Hughes, 2008). We focus on complementary aspects of the set-up—in particular students’ understanding of the task statement.

--Jackson et al., 2011, NCTM Research Presession

LESSON GOALS AND THE “LAUNCH”

Video clips are examples, not exemplars. To spur discussion not criticism

Video clips are for investigation of teaching and learning, not evaluation of the teacher. To spur inquiry not judgment

Video clips are snapshots of teaching, not an entire lesson. To focus attention on a particular moment not what

came before or after Video clips are for examination of a

particular interaction. Cite specific examples (evidence) from the video

clip, transcript and/or lesson graph.

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NORMS FOR WATCHING VIDEO

I noticed… I wonder…

VIDEO OF A LAUNCHIn Ms. Chang’s class, Emile found out that his walking rate is 2.5 meters per second. When he gets home from school, he times his little brother Henri as Henri walks 100 meters. He figured out that Henri’s walking rate is 1 meter per second.

Henri challenges Emile to a walking race. Because Emile’s walking rate is faster, Emile gives Henri a 45-meter head start. Emile knows his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his brother will win.

How long should the race be so that Henri will win in a close race?

LAUNCHING COMPLEX TASKS

What key ideas about launching tasks did you find in the article?

VIDEO OF A LAUNCH

What do you notice or wonder about the way in which the teacher used key aspects of the launch from the article?

WHY IS THE LAUNCH CRUCIAL?A key reason why we view the set-up phase as crucial for supporting equitable learning opportunities in the classroom is because it provides teachers with an opportunity to:a) gauge what their students understand about a

given task statementb) take action to ensure that all students have

requisite understandings such that they can engage productively in solving the task at hand (cf. Boaler, 2002).

--Jackson et al., 2011, NCTM Research Presession

WHY IS THE LAUNCH CRUCIAL?

By engaging productively in solving a task, we mean in a manner that is likely to lead to the development of conceptual understanding of central mathematical ideas.

--Jackson et al., 2011, NCTM Research Presession

LAUNCHING A MATHEMATICAL TASKAs you begin to plan a launch for the task you identified, consider:

What is this task asking students to do? Are there any constraints or givens within

this task to which students need to pay attention?

What are the key mathematical ideas in this task?

What might students be unfamiliar with? How could students begin to work on this

task? What representation seems appropriate and efficient?

How can I ensure that I have maintained the cognitive demand of this task?

Implementation Planning for your district:

What? When? Who?

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END OF THE DAY REFLECTIONS Pick an idea that came up today

and that you found particularly interesting.  What is your current thinking about this idea?  What questions do you still have?

What is your reaction to the work we did today?  What seems promising and/or challenging at this point?

Adapted from Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving.

Geometric/Graphical

Verbal (written and oral)

Tabular

Contextual

Symbolic

Pictures

Oral Language

ManipulativeModels

Real-World Situations

WrittenSymbols

Representation Stars

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Thinking Through a Lesson Protocol (TTLP)

Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14, 132-138.

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