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Promoting Discourse in Mathematics Classroom

This CCRS Quarterly Meeting aims to promote discourse in the mathematics classroom by analyzing vignettes, discussing guidelines for selecting and sequencing student work, and analyzing the impact of the Share, Discuss, and Analyze phase on student learning.

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Promoting Discourse in Mathematics Classroom

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  1. CCRS Quarterly Meeting # 4Promoting Discourse in the Mathematics Classroom http://alex.state.al.us/ccrs/

  2. Alabama Quality Teaching Standards 1.4-Designs instructional activities based on state content standards 2.7-Creates learning activities that optimizeeach individual’s growth and achievement within a supportive environment 5.3-Participates as a teacher leader and professional learning community member to advance school improvement initiatives

  3. Outcomes Participants will: • analyze a vignette in which the practice of selecting and sequencing is being used and determine the impact on the Share, Discuss, and Analyze Phase of the lesson • discuss guidelinesor “rulesof thumb”for selecting and sequencingstudent work that target the mathematical goal ofthe lesson • analyze student work samples to determine how to select and sequence student work for discussion in the Share, Discuss, Analyze Phase • analyze a vignette and determine the impact of the Share, Discuss, and Analyze Phase of the lesson on student learning • prepare to share resources with district - LEA team and colleagues

  4. Morning Session Participants will: • analyze a vignette in which the practice of selecting and sequencing is being used and determine the impact on the Share, Discuss, and Analyze Phase of the lesson • discuss guidelinesor “rulesof thumb”for selecting and sequencingstudent work that target the mathematical goal of the lesson

  5. Next Steps (to prepare for QM#4) The QM #4 goal is to be able to select, sequence and connect student work in order to orchestrate a whole-class discussion that targets the mathematical purpose(s) of the lesson. Identify standards and select a high level task and plan a lesson to implement that task. 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, monitor what students are doing. Identify/record the approaches that can help advance the mathematical discussion later in the lesson Collect student work samples and bring to the next Quarterly Meeting.

  6. Journal Reflection How did the practice of monitoring during the “Explore Phase,” help you assess and advance students’ learning? Explain.

  7. Mathematical Thinking “Orchestrating discussions that build on students’ thinking places significant pedagogical demands on teachers and requires an extensive and interwoven network of knowledge. Teachers often feel that they should avoid telling students anything, but are not sure what they can do to encourage rigorous mathematical thinking and reasoning.” (Stein, M.K., Engle, R., Smith, M., Hughes, E. 2008. Orchestrating Productive Mathematical Discussions: Five Practices)

  8. The Five Practices (+) 0. Setting Goals and Selecting Tasks 1. Anticipatingstudent 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.

  9. Selecting, Sequencing Setting Goals and Selecting a Task Anticipating Connecting

  10. Part 3: Sharing and Discussing the Task“Share, Discuss, and Analyze Phase” Part III of the TTLP: Model and share Make sense of the mathematical ideas Make connections between different strategies Focus the Discussions on Key Mathematical Ideas Look for patterns and form generalizations

  11. Journal Reflection How did you select which students would share out? Does it really matter who presents a solution? Why or why not?

  12. Select and Sequence the Ideas to Be Shared in the Discussion

  13. Institute for Learning “When observing and interacting with your students as they are working on a task, it is very easy to get pulled down various “mathematical pathways.” This is why it is critical to keep in mind the mathematical goals of the lesson so you can set a course to support your students in getting to the goals. In the course of teaching, we have to make quick decisions on multiple occasions about which student ideas to pursue and which ideas to put on hold and return to at a later time. Our guidepost in making these decisions is knowing what the goal of the lesson is.”

  14. The Case Of Nick Bannister How would you select and sequence the work of Nick Bannister’s class?

  15. The Case Of Nick Bannister Which solutions did Nick Bannister select to share? How did Nick Bannister sequence (order) the whole class discussion?

  16. “Rules of Thumb” for Selecting and Sequencing Student Work

  17. “Rules of Thumb” for Selecting and Sequencing Student Work

  18. Journal Reflection What are the benefits of usingthe“rulesofthumb”as aguidewhenselectingandsequencingstudentwork for the Share, Discuss, and Analyze Phase of the lesson?

  19. Selecting and Sequencing (Smith and Stein, 2011) “There are many different ways that student responses could be selected and sequenced that could be equally productive. The point is that the method selected must support the story line that the teacher envisions for the lesson so that the mathematics to be learned emerges in a clear and explicit way.”

  20. How does this task align to standards?

  21. No Place Like Home Task Solve the task in as many ways as you can. Discuss the solution paths with colleagues at your table. If only one solution path has been used, work together to create others. Consider possible misconceptions or errors that we might see from students.

  22. LUNCH

  23. Afternoon Session Participants will: • analyze student work samples to determine how to select and sequence student work for discussion in the Share, Discuss, Analyze Phase • analyze a vignette and determine the impact of the Share, Discuss, and Analyze Phase of the lesson on student learning • prepare to share resources with district - LEA team and colleagues

  24. The Structure and Routines of a Lesson • Who is sharing? • What is “the cycle?” • What is the focus of the discussion?

  25. Analyzing Student WorkPrivate Think Time Use the student work to further your understanding of the task. Consider What do the students know? How did the students solve the task? How did their solution paths differ from each other?

  26. Essential Understandings(Mathematical Concepts) Reflect on the task and complete the first column

  27. Monitoring(SmallGroupDiscussion) • Examine the students’ solution paths. • Determine which solution paths you want to share during the class discussion; keep track of your rationale for selecting the pieces of student work. • Determine the sequencein which work will be shared; keep track of your rationale for choosing a particular order for sharing the work. Record the group’s decision on the chart in your participant handouts

  28. Selecting Students’ Work The teacher selected work from Groups V, II, and III for the Share, Discuss, and Analyze Phase of the lesson. Consider the following: Why might the teacher have chosen these pieces of student work for this lesson phase? What mathematical concepts can be targeted by the teacher using the student work he/she chose?

  29. Analyzing Teaching and Learning No Place Like Home Task Vignette Students in a classroom are solving and discussing solution paths to the No Place Like Home Task . • Read the transcript • What are students learning? • What made it possible for this learning to occur?

  30. Pressing for Mathematical Understanding Let’s focus on one piece of student work for the Share, Discuss, and Analyze Phase of the lesson. Assume that a student has explained the work and others in the class have repeated the ideas and asked questions. Now it is time to “FOCUS” the discussion on an important mathematical idea. What assessing and advancing questions might you ask the class as a whole to focus the discussion?

  31. Group Reflection • Each group write on chart paper one assessing and one advancing question • Reviewquestions • Whatare somesimilaritiesamongthe questions? • Whatare somedifferencesbetweenthequestions?

  32. Reflection “Teachers’ questions are crucial in helping students make connections and learn important mathematics concepts. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding.” (Weiss & Pasley, 2004)

  33. Outcomes Participants will: • analyze a vignette in which the practice of selecting and sequencing is being used and determine the impact on the Share, Discuss, and Analyze Phase of the lesson • discuss guidelinesor “rulesof thumb”for selecting and sequencingstudent work that target the mathematical goal of the lesson • analyze student work samples to determine how to select and sequence student work for discussion in the Share, Discuss, Analyze Phase • analyze a vignette and determine the impact of the Share, Discuss, and Analyze Phase of the lesson on student learning • prepare to share resources with district - LEA team and colleagues

  34. Wrapping up…..

  35. . 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. 147 - 164). 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.

  36. Resources • Sherin, M. G., Mendez, E. P., Louis, D. A. (2000) Talking About Math Talk. Learning Mathematics for a New Century: 2000 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), 549-556.

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