1. CCRS Quarterly Meeting # 2 Promoting Discourse in the Mathematics Classroom
Welcome participants to 1st Quarterly Meeting for school year

2. Instructional Leaders and Effective Teachers
The CCRS meetings
support professional
study for Instructional
Leaders and Effective
Teachers.
Read the slide.
Professional Study
Professional Study

3. Emphasizing CCRS helps it ALL fit together!
College and Career Ready Students
CIP
Professional Learning
EducateAlabama
LEADAlabama
Alabama Quality Teaching Standards
Formative Assessment
Professional learning connecting standards-based instruction and formative assessment is the vehicle by which teachers design and deliver rigorous and relevant learning experiences for all students.
Briefly show slides 2 and 3. These slides will help set the stage for today’s learning.
Say this “Research provides compelling evidence relating student achievement to teachers’ use of appropriate instructional strategies selected from a rich repertoire based on research and best practice.
Current research relates teacher collaboration, shared responsibility for student learning, and job-embedded learning in professional communities to higher levels of student achievement. Teachers have formerly worked in isolation and independent of other. We have to personally commit to continuous learning and improvement.”
EdAl provides an opportunity to make tight connections. A teacher’s PLP should indicate how they are learning more about the CCRS and how they are making that change in their instruction.
Again, it is our job as leaders to make sure our puzzle pieces fit together and to discard them if they don’t.

4. CCRS-Implementation Team This is an opportunity to do just that!
As a team of professionals, we should take ownership of our learning community’s professional growth and continued improvement
Wrap up these two slides by saying, “You love learning or you would not have chosen to make a living in a field that requires constant learning. Use this process (the CCRS Quarterly Meetings) to continually reflect on your strengths and your areas for growth.”(2 minutes)
This is an opportunity to do just that!

5. What is he learning at school right now?
“As we move into the second decade of the twenty-first century, one thing is clear: Our country needs highly trained workers who can wrestle with complex problems. Gone are the days when basic skills could be counted on to yield high-paying jobs and an acceptable standard of living. Especially needed are individuals who can think, reason, and engage effectively in problem solving.” (Smith and Stein, 2011)

6. District and School Leadership Team Orientation
Is what our children are learning today preparing them for life after graduation?
District and School Leadership Team Orientation
Possesses the knowledge and skills needed to enroll and succeed in credit-bearing, first-year courses at a two- or four-year college, trade school, technical school, without the need for remediation.
Possesses the ability to apply core academic skills to real-world situations through collaboration with peers in problem solving, precision, and punctuality in delivery of a product, and has a desire to be a life-long learner.
Say, “The quote on the previous slide describes characteristics of a prepared graduate!”
Macon County Schools - September 6, 2013

7. Outcomes Participants will:
analyze a vignette in which the practice of anticipating is being used and determine the impact on teaching and learning
Say, “Teachers must be several steps ahead of the student in order to lead them where they need to go for mastery.”

8. The Five Practices (+) 0. Setting Goals and Selecting Tasks
1. Anticipating student responses to challenging mathematical tasks;
2. Monitoring students’ work on and engagement with the tasks;
3. Selecting particular students to present their mathematical work;
4. Sequencing the student responses that will be displayed in a specific order and
5. Connecting different students’ responses and connecting the responses to key mathematical ideas.
Say:
“Note the beginning of this process is to always start with the standard(s). The “0” practice shows that setting instructional goals and selecting rigorous tasks precedes the five practices. The critical staring point for planning is to specify clearly and explicitly the mathematical goals for the lesson or unit; what are the understandings that the students should come away with? Practice “0” is the foundation on which the five practices are built. The next step in practice “0” is to select a task that involves high-level thinking and reasoning and aligns well with the goal of the lesson. ”
Teachers feel that they should avoid telling students anything, but are not sure what they can do to encourage rigorous mathematical thinking and reasoning. This model “Five Practices” will help teachers create a classroom of mathematical thinkers. These practices can help teachers to use students’ responses to advance the mathematical understanding of the class as a whole by providing them with a measure of control over what is likely to happen in a discussion as well as more time to make instructional decisions by shifting much of the decision making to the planning phase of the lesson. Today we will spend time unpacking the practice of anticipation.
Say
"Ensuring that students have the opportunity to reason mathematically is one of the most difficult challenges that teachers face. A key component is creating a classroom in which discourse is encouraged and leads to better understanding. Productive discourse is not an accident, nor can it be accomplished by a teacher working on the fly, hoping for a serendipitous student exchange that contains meaningful mathematical ideas. While acknowledging that this type of teaching is demanding, Smith and Stein present five practices that any teacher can use to implement coherent mathematical conversations. By using the five practices, teachers will learn to teach effectively in this way.”
The five practices are:
Anticipating likely student responses to mathematical tasks
Monitoring students’ responses to the tasks during the explore phase
Selecting particular students to present their mathematical response during the discuss-and- summarize phase
Purposefully sequencing the student responses that will be displayed
Helping the class make mathematical connections between different students’ responses

9. Reflection
What are the advantages of anticipating students’ responses to cognitively demanding tasks during the lesson planning process?
Say, “Anticipating is an activity that is likely to increase the amount of time spent in planning a lesson. What would be the advantages for this investment of time?” Have participants turn to their reflection handout in the participant’s packet. Allow about 2-3 minutes for participants to reflect individually on the question on the slide and their note-taking tool.
Once participants have reflected individually, have them form pairs and then discuss their responses with one another. Allow 2 minutes for pairs to share. Then each pair will join another pair, creating a square to again share their responses. Allow 4 minutes for squares to share. Do not have the participants debrief or share out whole group just yet.

10. Anticipating
The first practice is for teachers to anticipate the different ways the mathematical task can be solved. This requires considering how students might mathematically interpret a problem, the array of strategies – both correct and incorrect – they might use to solve it, and how those strategies and interpretations might relate to the mathematical ideas the teacher would like his or her students to learn.
While anticipating requires that the teacher do the problem as many ways as she can, it is often helpful to expand on what one might be able to do individually by working on the task with other teachers, reviewing responses to the task that might be available (e.g., work produced by students the previous year, responses that are published along with tasks in supplementary materials), and consulting research on student learning of the mathematical ideas embedded in the task.

11. likely student responses to mathematical problems
1. Anticipating
likely student responses to mathematical problems
It involves considering:
The array of strategies that students might use to approach or solve a challenging mathematical task
How to respond to what students produce
Which strategies will be most useful in addressing the mathematics to be learned
It is supported by:
Doing the problem in as many ways as possible
Doing so with other teachers
Drawing on relevant research
Documenting student responses year to year
Anticipating requires considering the different ways the
task might be solved. This includes anticipating factors such
as how students might mathematically interpret a problem,
the array of correct and incorrect strategies students might
use to solve it, and how those strategies might relate to the
goal of the lesson (M. Smith & Stein, 2011). Anticipating can
support teachers’ planning by helping them to consider, in advance,
how they might respond to the work that students are
likely to produce and how they can use those strategies to address
the mathematics to be learned.
The first practice is for teachers to make an effort to actively envision how students might mathematically approach the instructional task (s) that they will be asked to work on. This involves much more than simply evaluating whether a task will be at the right level of difficulty or of sufficient interest to students, and it goes beyond considering whether or not they are getting the ‘right answer.’
[Click to INVOLVES]
Anticipating students’ responses involves developing considered expectations about how students might mathematically interpret a problem, the array of strategies—both correct and incorrect—they might use to tackle it, and how those strategies and interpretations might relate to the mathematical concepts, representations, procedures, and practices that the teacher would like his or her students to learn.
[Click to SUPPORTED and read/explain, making reference to their experience solving the calling plan/caterpillar problem as helping them make sense of the vignette and the student work]

12. Leaves and Caterpillar Task
A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars?
Use drawings, words, or numbers to show how you got your answer.
Solve the task in as many ways as you can, and consider other approaches that you think students might use to solve it.
Identify errors or misconceptions that you would expect to emerge as students work on this task.
Note we started with a standard from the Math COS Grade 4 – We chose this task to fit the standard. We will come back at the end.

13. Leaves and Caterpillars: The Case of David Crane
Read Vignette
Record Notes
Discuss and Compare
Adjust Charts
Say, “We will use the vignette Leaves and Caterpillars: The Case of David Crane to compare your thinking with the experience of another teacher.”

14. Journal Reflection
What could you do differently in your own practice to improve your ability to anticipate student responses?

15. Leaves and Caterpillars Task Mathematical Goals
Recognize that the relationship between caterpillars and leaves is multiplicative and not additive.
Students will recognize that there are three related strategies for solving the task – unit rate, scale factor, and scaling up.

16. Content Standards
Which CCRS Mathematics Content Standards does the Leaves and Caterpillars task address?
Does it address all parts of the standard(s)?
What do you notice about the verbs used in the standard(s)?
What does the verb convey to you about expectations for students?

17. Practice Standards
What is the connection between the cognitive demand of the task and the alignment of the task to the Practice Standards?

18. “Mathematics reform calls for teachers to engage students in discussing, explaining, and justifying their ideas. Although teachers are asked to use students’ ideas as the basis for instruction, they must also keep in mind the mathematics that the class is expected to explore.” (Sherin, 2000, p. 125)

19. Outcomes Participants will:
analyze a vignette in which the practice of anticipating is being used and determine the impact on teaching and learning
Thumbs up, down, sideways: Do you feel you are able to integrate some of today’s ideas into your classroom practice?
Take the time now to record your thoughts about the first session on the sheet that you will be taking back for your team planning.

20. LUNCH
Tell participants to enjoy lunch and you will see them after lunch.

21. Welcome participants back from lunch.

22. Outcomes Participants will:
work on setting goals (standards), selecting tasks, and anticipating student responses in small groups with grade level colleagues

23. “During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organize the classroom, what routines to use, and how to adapt instruction to support individual students.”
Fennema & Franke, 1992, p. 156
Ask a participant to read the quote.
(SAY) As educators, it is easy to focus on all the things outside our control. This quote reminds us that there are many decisions to be made every day that are our responsibility. Focusing on these elements of lesson planning and instruction that are within our control will have a tremendous impact on student learning.

24. Setting Goals and Selecting a Task Selecting, Sequencing
Anticipating
Connecting
The graphic on the screen shows the ways in which the five practices are embedded within the TTLP. Although there is clearly more to the TTLP than the five practices, they are in fact a significant subset of the work of planning. Smith and Stein have argued that before teachers can begin enacting the five practices, they must first set goals for the lesson and select a task (click to bring in goal setting). Also prominent in the TTLP is anticipating (click). This includes both anticipating the way in which a student might solve a task (both correctly and incorrectly) as shown in part 1 of the TTLP, and the questions that teachers might develop that would prepare them to respond to the things that students do as they work the task (the first set of bullets in part 2 of the TTLP). In part 3, of the TTLP we explicit attention to the selecting, sequencing, and connecting (click, click) and this work is a large part of what the teacher must do in planning for productive student discourse. One thing that is noticeable by its absence in the TTLP is any connection to monitoring. Monitoring is a process that happens during instruction, and while it is facilitated by carefully anticipating prior to the lesson, little additional planning can support this activity other than the creation of a monitoring sheet such as that created by Nick Bannister/David Crane. Today we will focus on the practices of setting goals, selecting task, and anticipating. Smith and Stein, 2011, p. 80)

25. Thinking Through a Lesson Protocol Backwards Planning
Share, Discuss, and Analyze
Set Up
Explore
What mathematical concepts (standards) will be developed in the implementation of this task?
What do you expect your students to do as they engage in the lesson?
What will you see or hear that lets you know students are developing understanding of the concepts?
What questions will you need to ask to build mathematical understanding?
SAS Secondary Mathematics Teacher Leadership Academy, Year 1

26. This slide sets up the task activity coming up in the next slide.
Note the progression at the top in green that the standard precedes the selection of the task.
Right now in QM #2 we are looking at anticipating. We will look at these other areas in QM #3 and #4.
Handout the tri-fold anticipating chart to use in the activity. Use the 2nd session trifold here to work with the task that you have selected at your grade band.

27. Selecting Standards and Setting Goals
What are your mathematical goals for the lesson?
What do you want students to know and understand about mathematics as a result of this lesson?
Give each table group their grade band packet of standards (i.e. K-2, 3-5, 6-8, 9-12). Allow the grade band table groups to discuss and select standards.

28. Solve the Task (Private Think Time )
Work privately on the task.
Once they have selected the standards, distribute the task and have participants turn to handout #8. Allow participants 8 minutes of private think time to solve the task.
Note: Once they have selected the standard, distribute the task associated with the standards.
Say, “the task has been selected with specific Standards for Mathematical Content and Practice in mind.”
Solution paths refers to all the possible ways the task is solved.

29. Solve the Task (Partner Time)
Work with a partner at your table.
Compare your solution paths, and consider other approaches that you think students might use to solve it.
Allow table partners 7 minutes to compare solution paths and consider other approaches. Say, “If you both used the same method to solve the task, see if you can come up with a different way.”

30. Solve the Task (Table Group Time)
Discuss in your table groups :
What are all the ways the task can be solved?
Which of these methods do you think students will use?
What misconceptions might students have?
What errors might students make?
What questions you will ask to –
Focus students thinking
Assess students’ understanding
Advance students’ understanding
Identify student solutions that will be useful in addressing mathematical goals
Distribute “anticipating tablemats” and have participants turn to handout #8a as you discuss the slide. Say, “notice how this slide parallels handout #8a. Space is provided for you to collect your thoughts in each category as a group.”
Allow participants 17 minutes to discuss and complete the tablemat.

31. Multiple Representations
Pictures
Written
Symbols
Manipulative
Models
Real-world
Situations
Oral
Language
(SAY) Many of you moved between and among representations when solving and discussing the solution paths to the task. (Remember chart #1 for the calling plan task.)
Research has shown that some of the better problem solvers are those who, when they are struggling to figure out a problem, have the resources or know how to use different representations in order to solve a problem. If this is true, then what are the implications for instruction in our classrooms?

32. “The effectiveness of a lesson depends significantly on the care with which the lesson plan is prepared.”
Brahier, 2000
One of the main goals of lesson planning is prepare:
Student discussions provides opportunities for students to:
Share ideas and clarify understandings
Develop convincing arguments regarding why and how things work
Develop a language for expressing mathematical ideas
Learn to see things for other people’s perspective

33. Next Steps Identify standards and select a high level task.
Plan a lesson with colleagues.
Anticipate student responses, errors, and misconceptions.
Write assessing and advancing questions related to student responses. Keep copies of planning notes.
Teach the lesson. When you are in the Explore phase of the lesson, tape your questions and the students responses, or ask a colleague to scribe them.
Following the lesson, reflect on the kinds of assessing and advancing questions you asked and how they supported students to learn the mathematics.
Ask participants to bring student work from bridge to practice assignment.

34. likely student responses to mathematical problems
1. Anticipating
likely student responses to mathematical problems
It involves considering:
The array of strategies that students might use to approach or solve a challenging mathematical task
How to respond to what students produce
Which strategies will be most useful in addressing the mathematics to be learned
It is supported by:
Doing the problem in as many ways as possible
Doing so with other teachers
Drawing on relevant research
Documenting student responses year to year
Tips for anticipating:
Not to be used with drill and practice worksheets (i.e 30 problems per page)
Great for collaborating with colleagues across grade level to generate solution paths
To get started set an achievable goal for anticipating – focus on one challenging mathematical task each week or use 10 minutes of math time to focus on effectively implementing student discourse
In the case of the of Nick Bannister, we saw a teacher who, as a result of his anticipating is ready for monitoring and orchestrating a discussion of the Calling Plan task that builds on the students thinking.
Use this after working the task to address strategies for the time issue.
Anticipating requires considering the different ways the
task might be solved. This includes anticipating factors such
as how students might mathematically interpret a problem,
the array of correct and incorrect strategies students might
use to solve it, and how those strategies might relate to the
goal of the lesson (M. Smith & Stein, 2011). Anticipating can
support teachers’ planning by helping them to consider, in advance,
how they might respond to the work that students are
likely to produce and how they can use those strategies to address
the mathematics to be learned.
The first practice is for teachers to make an effort to actively envision how students might mathematically approach the instructional task (s) that they will be asked to work on. This involves much more than simply evaluating whether a task will be at the right level of difficulty or of sufficient interest to students, and it goes beyond considering whether or not they are getting the ‘right answer.’
[Click to INVOLVES]
Anticipating students’ responses involves developing considered expectations about how students might mathematically interpret a problem, the array of strategies—both correct and incorrect—they might use to tackle it, and how those strategies and interpretations might relate to the mathematical concepts, representations, procedures, and practices that the teacher would like his or her students to learn.
[Click to SUPPORTED and read/explain, making reference to their experience solving the calling plan/caterpillar problem as helping them make sense of the vignette and the student work]

35. Outcomes Participants will:
work on setting goals, selecting tasks, and anticipating student responses in small groups with grade level colleagues
Thumbs up, down, sideways: do you feel you are able to integrate some of today’s ideas into your classroom practice?

36. Wrapping up….. With your district team think about your next steps.
Record your thoughts on this template and share with the rest of your team when you join them in a few minutes.

37. .
Resources
Brahier, D.J. (2000). Teaching Secondary and Middle School Mathematics. Boston: Allyn & Bacon
Fennema, E. & Franke, M. (1992). Teachers’ knowledge and its impact. In Douglas Grouws (Ed.). Handbook of research on mathematics teaching and learning (pp ). Indianapolis, IN: Macmillan Publishing Inc.
Kenney, J.M., Hancewicz, E., Heuer, L., Metsisto, D., Tuttle, C. (2005). Literacy Strategies for Improving Mathematics Instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

38. Resources
Sherin, M. G., Mendez, E. P., Louis, D. A. (2000) Talking About Math Talk. Learning Mathematics for a New Century: Yearbook of the NCTM. Reston, VA: National Council of Teachers of Mathematics.
Smith, M. S., & Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics and Thousand Oaks, CA: Corwin Press.
Smith, M.S., Hughes, E.K., & Engle, R.A., & Stein, M.K. (2009). Orchestrating discussions. Mathematics Teaching in the Middle School, 14 (9),