CCRS Quarterly Meeting # 1 Promoting Discourse in the Mathematics Classroom

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

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

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

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 2013-2014? • How has incorporating the College-and-Career-Ready Math Standards into your classroom culture caused your students to learn and behave differently?

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

6. Outcomes Participants will: • Discuss and define student discourse

7. Discourse

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

9. Unlocking Engagement Through Mathematical Discourse

10. Making the Case for Meaningful Discourse

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.”

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.

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

14. 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. 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.

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)

16. Outcomes Participants will: • Discuss and define student discourse

17. Exit Activity

18. 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.

21. Through the Lens Use the handout to make notes as you watch the video.

22. Envision a Discourse RichMath Class • How does teacher best practice produce student math practices? • What are you going to do to produce student discourse in your classroom?

23. 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?

25. Five Practices for Orchestrating Productive Mathematical Discussions

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)

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.

28. Thinking Through a Lesson Protocol (TTLP) Planning Template

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.

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

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)

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.

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), 549-556.