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**CCRS Quarterly Meeting # 1 Promoting Discourse in the Mathematics Classroom**

Welcome participants to 1st Quarterly Meeting for school year

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**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.”

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**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)

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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

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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.

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**Outcomes Participants will: Discuss and define student discourse**

Share the Outcomes of the sessions.

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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)

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**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.

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**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.

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**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

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“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.

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**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?

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**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).

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**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

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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.”

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**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?

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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.

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

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**Welcome participants back from lunch.**

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**Outcomes Participants will:**

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

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**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

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**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. (The video is hyperlinked to picture on the slide). It’s a good idea to pre-load the video to be sure it runs smoothly. The link is: https://www.teachingchannel.org/videos/sorting-classifying-equations-overview You will need speakers. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

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**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).

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**What are the practices that will promote student discourse?**

We are going to preview a model for effective use of student thinking in whole-class discussions that research has shown to have the power to put teachers in control of productive student discourse AND HELP TEACHERS 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 (Franke, Kazemi, & Battey, 2007).

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**Five Practices for Orchestrating Productive Mathematical Discussions**

Teachers feel that they should avoid telling students anything, but are not sure what they can do to encourage rigorous mathematical thinking and reasoning. We are going to preview a model for effective use of student thinking in whole-class discussions that research has shown to have the power to put teachers in control of productive student discourse AND HELP TEACHERS ORCHESTRATE DISCUSSIONS THAT MOVE BEYOND SHOWING AND TELLING. "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.“

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**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) The five practices are: Anticipating likely student responses to mathematical tasks While students working on the tasks (in pairs or small groups), Monitoring students’ actual responses to the tasks Selecting particular students to present their mathematical responses during the whole class discussion Purposefully sequencing when these student responses are shared during the discussion Helping the class make mathematical connections between different students’ responses As you can see, each of these has been discussed separately by various authors; Smith and Stein’s contribution was to integrate them into a single package. 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 Teaching in a manner that productively makes use of students’ ideas and strategies that are generated by high-level tasks is demanding. It requires knowledge of mathematics content, knowledge of student thinking, knowledge of pedagogical “moves” that a teacher can make to lead discussions, and the ability to rapidly apply all of these in specific circumstances (M. Smith & Stein, 2011). To support teachers in this endeavor, Smith and Stein suggested five practices that are intended to make student-centered instruction more manageable. This is done by moderating the degree of improvisation required from the teacher in the midst of a discussion. Rather than providing an instant fix for mathematics instruction, the five practices provide “a reliable process that teachers can depend on to gradually improve their classroom discussions over time” (Stein, Engle, Smith, & Hughes, 2008, p. 335). The first two of the five practices are anticipating students’ solutions to a mathematics task and monitoring students’ actual work on the task as they work in pairs or groups.

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**0. Setting Goals It involves:**

Identifying what students are to know and understand about mathematics as a result of their engagement in a particular lesson Being as specific as possible so as to establish a clear target for instruction that can guide the selection of instructional activities and the use of the five practices It is supported by: Thinking about what students will come to know and understand rather than only on what they will do Consulting resources that can help in unpacking big ideas in mathematics Working in collaboration with other teachers This slide will be hidden. Review this slide. Remind participants that our focus last year was on selecting task, setting goals, and thinking through lesson planning. Hiebert, Morris, Berk, and Jansen (2007, p.51) argue that this level of specificity is critical to effective teaching: Without explicit learning goals, it is difficult to know what counts as evidence of students’ learning, how students’ learning can be linked to particular instructional activities, and how to revise instruction to facilitate students’ learning more effectively. Formulating clear, explicit learning goals sets the stage for everything else.

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**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 This slide will be hidden. 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 caterpillar problem as helping them make sense of the vignette and the student work]

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**students’ actual responses during independent work**

2. Monitoring students’ actual responses during independent work It involves: Circulating while students work on the problem and watching and listening Recording interpretations, strategies, and points of confusion Asking questions to get students back “on track” or to advance their understanding It is supported by: anticipating student responses beforehand Using recording tools This slide will be hidden. Monitoring, as described by M. Smith and Stein (2011), is attending to the thinking of students during the actual lesson as they work either individually or collectively on the task. This involves not only listening to students’ discussions with their peers, but also observing what they are doing and keeping track of the approaches students are using. Monitoring can support teachers by allowing them to help students get ready for the classroom discussion (e.g., asking students to have an explanation prepared that uses mathematically precise language). It can also help teachers identify strategies that will advance the “collective reflection” (Cobb, Boufi, McClain, & Whitenack, 1997) of the classroom community and prepare for the end-of-class discussion (M. Smith & Stein, 2011) [Click INVOLVES] Monitoring student responses involves paying close attention to the mathematical thinking that students actually use as they work on the problem. Commonly, this is done by circulating around the classroom while students work . Lampert summarizes it – “If I watch and listen during small-group independent work, I am able to use my observations to decide what and who to make focal” during the discussion that follows [Click SUPPORTED and read quickly, referring to handout ***REFER TO BY COLOR ONCE I KNOW IT***] Returning to Leaves and Caterpillar Vignette, While the teacher understood who got correct answers and who did not, and that a range of strategies had been used, his sharing at the end of the class suggests he had not particularly monitored the specific mathematical learning potential available in any of the responses. [IF TIME] Targeting responses in advance just makes it easier to hone in on the math during the discussion since it is not totally improvisational.

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**student responses to feature during discussion**

3. Selecting student responses to feature during discussion It involves: Choosing particular students to present because of the mathematics available in their responses Making sure that over time all students are seen as authors of mathematical ideas and have the opportunity to demonstrate competence Gaining some control over the content of the discussion (no more “who wants to present next”) It is supported by: Anticipating and monitoring Planning in advance which types of responses to select This slide will be hidden. One of the primary features of a discussion-based classroom is that, instead of doing virtually all of the talking, modeling, and explaining themselves, teachers must encourage and expect students to do so. To do this effectively, teachers need to organize students’ participation (National Council of Teachers of Mathematics, 1991). After monitoring the work of students as they explore the task (described above), teachers can select and sequence the ideas to be shared in the discussion (M. Smith & Stein, 2011). Selecting involves deciding which particular students will share their work with the rest of the class to get “particular pieces of the mathematics on the table” (Lampert, 2001, p. 140). Selecting which solutions will be shared by particular students is guided by the mathematical goal for the lesson and by the teacher’s assessment of how each contribution will contribute to that goal. Sequencing is deciding on what order the selected students should present their work. Teachers can maximize the chances that their mathematical goals for the discussion will be achieved by making purposeful choices about the order in which students’ work is shared (M. Smith & Stein, 2011). Smith and Stein suggested that teachers can also benefit from a set of moves that will help them lead whole-class discussions. Specifically, they focused on a set of “talk moves” that can be used to support students as they share their thinking with one another in respectful and academically productive ways. Selecting is about determining what math students will have access to beyond what they were able to consider individually or in small groups. It is about both WHO and WHAT to make focal. [Click INVOLVES] Having monitored the available student strategies in the class, the teacher can then select particular students to share their work with the rest of the class in order to get “particular piece[s] of mathematics on the table,” thus giving the teacher more control over the discussion as well as more time to plan A typical way to do this is to call on specific students (or groups of students) to present their work as the discussion proceeds. Alternatively, the teacher may let students know in advance of the discussion that they will be presenting their work. [If time] In a hybrid variety, a teacher might ask for volunteers but then select a particular student that he or she knows is one of several who has a particularly useful idea to share with the class. This is one way of balancing the tension between “keeping the discussion on track and allowing students to make spontaneous contributions that they consider…to be relevant.” [Click SUPPORTED and quickly say what’s there] Returning to Leaves and Caterpillar Vignette IF we look at the strategies that were shared we note that Kyra and Janine had similar strategies that used the idea of unit rate – finding out the # of leaves needed for one caterpillar. Given that, there may not have been any added mathematical value to sharing both. In fact, if Mr. Crane wanted to students to see the multiplicative nature of the relationship, he might have selected Janine as her approach clearly involved multiplication. Also, there may have been some payoff in sharing the solution produced by Missy and Kate and contrasting it with the solution produced by Melissa which also used addition.

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**student responses during the discussion**

4. Sequencing student responses during the discussion It involves: Purposefully ordering presentations so as to make the mathematics accessible to all students Building a mathematically coherent story line It is supported by: Anticipating, monitoring, and selecting During anticipation work, considering how possible student responses are mathematically related This slide will be hidden. [Click INVOLVES & SUPPORTED BY] Having selected particular students to present, the teacher can then make decisions about how to sequence the students’ presentations. By making purposeful choices about the order in which students’ work is shared, teachers can maximize the chances that their mathematical goals for the discussion will be achieved. - For example, the teacher might want to have the strategy used by the majority of students presented before those that only a few students used in order to help validate the work that students did and make the beginning of the discussion accessible to as many students as possible. - Or, if there is a common misconception that underlies a strategy that several students used, the teacher might want to have it addressed first so the class can clear up that misunderstanding in order to be able to work on developing more successful ways of tackling the problem. - In addition, the teacher might want to have related or contrasting strategies be presented right after one another in order to make it easier for the class to mathematically compare them. More research needs to be done to compare the affordances of different sequencing methods, but we want to emphasize here that particular sequences can be used to advance particular goals for a lesson. - In addition, the teacher might want to have related or contrasting strategies be presented right after one another in order to make it easier for the class to mathematically compare them.

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**student responses during the discussion**

5. Connecting student responses during the discussion It involves: Encouraging students to make mathematical connections between different student responses Making the key mathematical ideas that are the focus of the lesson salient It is supported by: Anticipating, monitoring, selecting, and sequencing During planning, considering how students might be prompted to recognize mathematical relationships between responses This slide will be hidden. The first four of the five practices mentioned above (Anticipating, Monitoring, Selecting, and Sequencing) work to set up the discussion, whereas Connecting is primarily meant to occur during the discussion. Rather than having mathematical discussions that consist of separate presentations of different strategies and solutions, the goal is “to have student presentations build on one another to develop powerful mathematical ideas” (Smith & Stein, 2011, p. 11). The teacher supports students in drawing connections between their solutions and other solutions in the lesson. The discussion should come to an end with some kind of summary of the key mathematical ideas. The students ideally leave with “residue” from the lesson, which provides a way of talking about the understandings that remain when the activity is over (Hiebert et al., 1997). [Click INVOLVES] Finally, teachers can help students draw connections between their mathematical ideas as represented in the strategies and representations that they use . They can help students to make judgments about the consequences of different approaches for: the range of problems that can be solved, one’s likely accuracy and efficiency in solving them, and the kinds of mathematical patterns that can be most easily discerned. So, rather than having mathematical discussions consist of separate presentations of different ways to solve a particular problem, the goal is to have student presentations build on each other to develop powerful mathematical ideas. [Click SUPPORTED and read them out]

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**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?”

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**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

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**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.

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**Mathematical Goal I want students to:**

recognize that the relationship between caterpillars and leaves is multiplicative.

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Students might: make tables showing the relationship of leaves to caterpillars draw pictures write explanations count by 1’s or 5’s use unit rate use scaling up multiply

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**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. .

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**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

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**Outcomes Participants will:**

Identify advantages of planning lessons that focus on 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?

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**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),

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The Greater Los Angeles Mathematics Council

The Greater Los Angeles Mathematics Council

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