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

2. Alabama Quality Teaching Standards (AQTS)
Standard 1: Content Knowledge Standard 2: Teaching and Learning Standard 3: Literacy Standard 4: Diversity Standard 5: Professionalism
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.”

3. This is an opportunity to do just that!
As professionals, we should take ownership of our professional growth and continued improvement
This is an opportunity to do just that!
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)

4. Year One Reflection
What have you changed about your practice in response to implementing the College-and Career-Ready Math Standards ?
What are two priorities related to implementation of the CCRS Math you have identified for ?
How has incorporating the College-and-Career-Ready Math Standards into your classroom culture caused your students to learn and behave differently?
Say, “in order to take the next right steps, we need to think about where we’ve been and where we are.
Allow about 2 minutes for participants to review at the 2012 QM learning map before they do their year one reflection. Next allow 3-5 minutes for participants to write their individual responses to the above questions on their note-taking tool.
Allow a few participants to share-out whole group. Please be sure to have them focus on bullet #3 – the goals for

5. The discourse of a classroom – the ways of representing, thinking, talking, agreeing and disagreeing – is central to what students learn about mathematics as a domain of human inquiry with characteristic ways of knowing. NCTM 2000
Discuss the slide.

6. Outcomes Participants will: Discuss and define student discourse
Share the Outcomes of the sessions.

7. Discourse
Show slide
Ask participants to think about their classroom and the types of mathematical communication their students engage in during class as they read the slide.
Ask the question, “Do you think discussions are an important feature of mathematics classrooms? Why or why not?” Allow a few participants to share out. (5 minutes)

8. What is Discourse? How do you define student discourse?
How does discourse encourage reasoning and sense making in your classroom?
Ask participants:
“How do you define student discourse”
“How does discourse encourage reasoning and sense making in your classroom?”
Allow individual reflection time on the above questions on the T-chart provided. ( 3-5 minutes)
Once participants have reflected individually, have participants to discuss in their small groups and select characteristics from the individual list.
Provide each group with chart paper and have them draw a T-chart and make two lists title one list “IS considered student discourse” and the other list “IS NOT considered student discourse”
Facilitators should circulate and keep groups on task. Allow about 5-7 minutes for groups to chart out. Do not have the participants debrief or share out their charts just yet.

9. Unlocking Engagement Through Mathematical Discourse
Bring the group back together and have them read the article (“Unlocking Engagement Through Mathematical Discourse”) and highlight 2 or 3 big ideas that are interesting to them.
Once participants finish reading the article, in their groups, ask them to share the idea(s) they
highlighted and why they think it is important. Then have them revisit the chart on which they gave their initial definition (characteristics) of student discourse.
Say “Based on your reading and discussion of your thoughts in your group refine (if necessary) your lists using a different color marker.”
Share out whole group.

10. Making the Case for Meaningful Discourse
Show slide 10
Bring the small groups back to a whole-group and have them to look at the last paragraph of the article as you say “Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization

11. “Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions – the Mathematical Practices in action.”
Show slide 11
Have participants read the slide and reflect on the Standards of Mathematical Practice.

12. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
You will need speakers.
Show slide 12
As they reflect on the SMP have the watch the video clip “Mathematical Practices, Focus, and Coherence in the Classroom.” (The clip is 1:13 minutes in length) (The video is hyperlinked to title on the slide).
Allow a few participants to share 2-3 ideas after the video clip.
Have participants turn in their packets to the Standards for Mathematical Practice. Allow participants time to highlight/identify which of the 8 practices support or promote classroom discourse? (for example which have “communication of ideas” embedded within them? After 3-5 minutes ask participants to turn and talk to their shoulder partner and then share with the table group: Which of the 8 practices support or promote math discourse?

13. Making the Case for Meaningful Discourse: Standards for Mathematical Practice
Standard 1: Explain the meaning and structure of a problem and restate it in their words
Standard 2: Explain their mathematical thinking
Standard 3: Habitually ask “why”
Question and problem-pose
Develop questioning strategies ...
Justify their conclusions, communicate them to others and respond to the arguments of others
Listen to the reasoning of others
Compare arguments
Standard 4: Communicate their model and analyze the models of their peers
Standard 6: Communicate their understanding of mathematics to others
Use clear definitions and state the meaning of the symbols they choose
Standard 7: ...describe a pattern orally...
Apply and discuss properties
Wrap up the discussion with this slide.
Show slide 13 and discuss with participants changes in their thinking, what they better understand now, and what they want to do once back in their classroom (professional learning communities).

14. HOW IS A PREPARED GRADUATE DEFINED?
District and School Leadership Team Orientation
HOW IS A PREPARED GRADUATE DEFINED?
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, “What we looked at on the previous slide are all characteristics of a prepared graduate!”
Macon County Schools - September 6, 2013

15. Purposeful Discourse
Through mathematical discourse in the classroom, teachers “empower their students to engage in , understand and own the mathematics they study.”
(Eisenman, Promoting Purposeful Discourse, 2009)
Wrap up the discussion with the quote on slide 14.
Say, “This just reiterates the importance of having students talk both in small and large groups, as this gives them practice with learning to express their mathematical thinking and ideas.”

16. Outcomes Participants will: Discuss and define student discourse
Revisit outcome #1 and ask participants, by a show of thumbs, (Thumbs up, down, sideways): do you feel you are able to integrate some of today’s ideas into your classroom practice?

17. Exit Activity
Slide 16
As participants reflect on their learning about student discourse distribute the sorting activity (Ziploc bag- one per table group). Ask the groups to sort the classroom activities into two groups (Is considered discourse and Is Not considered discourse). Wrap this activity up by having one or two groups to share out their sorting.

18. LUNCH
Show slide 17
Tell participants to enjoy lunch and you will see them after lunch.

19. Welcome participants back from lunch.

20. Outcomes Participants will:
Identify advantages of planning lessons that focus of facilitating carefully constructed student engaged discourse.
Describe practices that teachers can learn in order to facilitate discourse more effectively.
Show outcomes for Session II.

21. Standard for Mathematical Practice
Through the Lens
Use the handout to make notes as you watch the video.
Observation Lens
Standard for Mathematical Practice
that was Supported
Teacher’s Questions
Student Discussions
Classroom Culture

22. Envision a Discourse Rich Math Class
How does teacher best practice produce student math practices?
What are you going to do to produce student discourse in your classroom?
What teacher and student behaviors occur in a classroom where the teacher promotes discourse?
Introduce the video.
This is an 8 minute video of a teacher building a discourse based classroom environment.
It’s a good idea to pre-load the video to be sure it runs smoothly. The link is:
You will need speakers.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

23. Teacher and Student Roles in Classroom Discourse
Figure 5.5
Teacher and Student Roles in Classroom Discourse
Teacher’s Role
Student’s Role
Poses questions and tasks that elicit, engage, and challenge each student’s thinking.
Listen to, respond to, and question the teacher and one another.
Listens carefully to student’s ideas.
Use a variety of tools to reason, make connections, solve problems, and communicate.
Asks students to clarify and justify their ideas orally and in writing.
Initiate problems and questions.
Decides which of the ideas students bring up to pursue in depth.
Make conjectures and present problems.
Decides when and how to attach math notation or language to students’ ideas.
Explore examples and counterexamples to investigate conjectures.
Decide when to provide information, when to clarify an issue, when to model, when to lead, and when to let different students struggle with a problem.
Try to convince themselves and one another of the validity of particular representations, solutions, conjectures, and answers.
Monitors student participation in discussions and decides when and how to encourage each student to participate.
Rely on mathematical evidence and argument to determine validity.
Wrap this discussion up with slide 23.
Show slide 22 and say, “Teachers (and others) must shift their perspectives about teaching, from that of a process of delivering information to that of a process of facilitating students’ sense making about mathematics.”
“That shift will require teachers in pre-K through grade 12 to be proficient in… orchestrating classroom discourse in ways that promote the explorations and growth of mathematical ideas… “
(Originally published as Professional Standards for Teaching Mathematics, 1991, p p. 5-6
Source: Adapted from information in Professional Standards for Teaching Mathematics, by the National Council of Teachers of Mathematics, 1991, Reston, VA; Author.
Kenney, Hancewicz, Heuer, Metsisto, Tuttle(2005).

24. What are the practices that will promote student discourse?
Allow participants to read the question on the slide.
Tell them that we are going to be look at a model for effective use of student thinking in whole-class discussions.
Say:
Research has shown that this model helps give teachers the power to have control over the productive student discourse in their classrooms, and helps them orchestrate discussions that move beyond showing and telling.
Supporting productive discourse can be made easier if teachers work with mathematical tasks that allow for multiple strategies, connect core mathematical ideas, and are of interest to the students.

25. Five Practices for Orchestrating Productive Mathematical Discussions
Say:
Teachers feel that they should avoid telling students anything, but are not sure what they can do to encourage rigorous mathematical thinking and reasoning.
Have participants turn to the handout on the 5 practices and read and highlight 2 or 3 big ideas that are interesting to them.
Once participants finish reading the handout, in their groups, ask them to share the idea(s) they
highlighted and why they think it is important.
Wrap up the table discussions by saying:
This model “Five Practices” will help teachers create a classroom of mathematical thinkers.

26. The Five Practices (+) 0. Setting Goals and Selecting Tasks
1. Anticipating (e.g., Fernandez & Yoshida, 2004; Schoenfeld, 1998)
2. Monitoring (e.g., Hodge & Cobb, 2003; Nelson, 2001; Shifter, 2001)
3. Selecting (e.g., Lampert, 2001; Stigler & Hiebert, 1999)
4. Sequencing (e.g., Schoenfeld, 1998)
5. Connecting (e.g., Ball, 2001; Brendehur & Frykholm, 2000)
Discuss the fact that these practices have been discussed separately by various authors as indicated on the slide. However, Smith and Stein’s contribution was to integrate them into a single package.
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

27. Purpose of the Five Practices
To make student-centered instruction more manageable by moderating the degree of improvisation required by the teacher during a discussion.
Have a participant read the slide to the group.
Ask:
How can this be accomplished? Say, through lesson planning. Ask the participants, “in your lesson planning to what extent do you focus on what you will do versus what students will do and think?”

28. Thinking Through a Lesson Protocol (TTLP) Planning Template
Remind participants about the protocol from last year (on slide).
Say, “The Purpose of the TTLP is”
To prompt teachers to think deeply about a specific lesson in order to consider how to advance students’ mathematical understanding
To focus on students’ mathematical thinking
To help anticipate a range of student solutions or solution strategies
To prompt the development of questions that will support students’ engagement and learning
To address ways to facilitate the learning of all students
To move beyond structural components of lesson planning

29. The Calling Plans Task
Company A charges a base rate of $5 per month, plus 4 cents for each minute that you’re on the phone. Company B charges a base rate of only $2 per month charges you 10 cents for every minute used. How much time per month would you have to talk on the phone before subscribing to company A would save you money?
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.
Once you have set a goal(s) for instruction and identified an appropriate task, then it is time to begin focusing on the five practices.
Have participants read the task on the slide and then locate the task in their participant packet Allow3-5 minutes for participants to individually work the task. Then give each table group two sheets of chart paper. As a group, have them solve the problem in as many ways as they can on one sheet. Ask them to consider how students might solve the problem. On the other sheet, have them identify errors or misconceptions that you would expect students to have as they worked on the task.

30. Mathematical Goals I want students to:
recognize that there is a point of intersection between two unique nonparallel linear equations that represents where the two functions have the same x and y values
understand that the two functions “switch positions” at the point of intersection and that the one that was on “top” before the point of intersection is on the “bottom” after the point of intersection because the function with the smaller rate of change will ultimately be the function closer to the x-axis
make connections between tables, graphs, equations, and context by identifying the slope and y-intercept in each representational form
Standards this task will address:
10. Analyze and solve pairs of simultaneous linear equations. [8-EE8]
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously. [8-EE8a]
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b]
Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c]
Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair
Create equations that describe numbers or relationships. (Linear, quadratic, and exponential (integer inputs only); for Standard 14, linear only.)
14. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. [A-CED3]
Example: Represent inequalities describing nutritional and cost constraints on combinations of different foods.

31. Mathematical Discourse
“Teachers need to develop a range of ways of interacting with and engaging students as they work on tasks and share their thinking with other students. This includes having a repertoire of specific kinds of questions that can push students’ thinking toward core mathematical ideas as well as methods for holding students accountable to rigorous, discipline-based norms for communicating their thinking and reasoning.”
(Smith and Stein, 2011)
A key challenge mathematics teachers face in enacting current reforms is to orchestrate discussions that use students’ responses to instructional tasks in ways that advance the mathematical learning of the whole class.
In particular, teachers are often faced with a wide array of student responses to complex tasks and must find a way to use them to guide the class towards deeper understandings of significant mathematics. .

32. Why These Five Practices Are Likely to Help
Provides teachers with more control
Over the content that is discussed
Over teaching moves: not everything improvisation
Provides teachers with more time
To diagnose students’ thinking
To plan questions and other instructional moves
Provides a reliable process for teachers to gradually improve their lessons over time

33. Outcomes Participants will:
Identify advantages of planning lessons that focus of facilitating carefully constructed student engaged discourse.
Describe practices that teachers can learn in order to facilitate discourse more effectively.
Thumbs up, down, sideways: do you feel you are able to integrate some of today’s ideas into your classroom practice?

34. Resources Related to the Five Practices
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.
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),