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

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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

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As professionals, we should take ownership of our professional growth and continued improvement

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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?

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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

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Outcomes Participants will: Discuss and define student discourse

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Discourse

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What is Discourse? How do you define student discourse? How does discourse encourage reasoning and sense making in your classroom?

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Unlocking Engagement Through Mathematical Discourse

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Making the Case for Meaningful Discourse

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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.

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Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

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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

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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. HOW IS A PREPARED GRADUATE DEFINED? 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. 14

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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)

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Outcomes Participants will: Discuss and define student discourse

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Exit Activity

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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.

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Through the Lens Use the handout to make notes as you watch the video. Observation Lens Standard for Mathematical Practice that was Supported Teachers 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?

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Figure 5.5 Teacher and Student Roles in Classroom Discourse Teachers RoleStudents Role Poses questions and tasks that elicit, engage, and challenge each students thinking. Listen to, respond to, and question the teacher and one another. Listens carefully to students 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. 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?

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Five Practices for Orchestrating Productive Mathematical Discussions

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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 (+)

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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

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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

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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

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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

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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

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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

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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.

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Thinking Through a Lesson Protocol (TTLP) Planning Template

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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 1s or 5s 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)

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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.

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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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