CCRS Quarterly Meeting # 2 Promoting Discourse in the Mathematics Classroom

1. CCRS Quarterly Meeting # 2Promoting Discourse in the Mathematics Classroom http://alex.state.al.us/ccrs/

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

3. Emphasizing CCRS helps it ALL fit together! CIP 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. Formative Assessment Professional Learning College and Career Ready Students Alabama Quality Teaching Standards EducateAlabama LEADAlabama

4. As a team of professionals, we should take ownership of our learning community’s professional growth and continued improvement CCRS-Implementation Team 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. Is what our children are learning today preparing them for life after graduation? 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. 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.

7. Outcomes Participants will: • analyze a vignette in which the practice of anticipating is being used and determine the impact on teaching and learning

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. Reflection What are the advantages of anticipating students’ responses to cognitively demanding tasks during the lesson planning process?

10. Anticipating

11. 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

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.

13. Leaves and Caterpillars: The Case of David Crane • Read Vignette • Record Notes • Discuss and Compare • Adjust Charts

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

20. 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

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

25. Thinking Through a Lesson ProtocolBackwards 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?

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?

28. Solve the Task(Private Think Time ) • Work privately on the task.

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.

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

31. Pictures Manipulative Models Written Symbols Real-world Situations Oral Language Multiple Representations

32. “The effectiveness of a lesson depends significantly on the care with which the lesson plan is prepared.” Brahier, 2000

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.

34. 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

35. Outcomes Participants will: • work on setting goals, selecting tasks, and anticipating student responses in small groups with grade level colleagues

36. Wrapping up…..

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. 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.

38. 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.