1. Wesnesday, January 30, 2013 PS 153 Paul Perskin CFN 204

2. Agenda Warm Up How tall is my mom? Anticipating Solution Paths, Misconceptions, and Challenges to Inform Instruction The Case of David Crane The Case of Nick Bannister Closing

3. Warm Up The Height Dilemma I just found this picture of my parents. Cute, aren’t they? I remember my dad saying that he is 6 feet 2 inches tall, but I cannot remember how tall my mom is. Mathematically determine how tall my mom is. Convince me that your strategy and reasoning are mathematically sound. Make any connections/generalizations that you can. The Height Dilemma I just found this picture of my parents. Cute, aren’t they? I remember my dad saying that he is 6 feet 2 inches tall, but I cannot remember how tall my mom is. Mathematically determine how tall my mom is. Convince me that your strategy and reasoning are mathematically sound. Make any connections/generalizations that you can.

4. Warm Up, cont.

5. Warm Up, extension I just saw the movie, Honey, I Shrunk The Kids. If my dad was shrunk to 10% of his size, what size would my dad be? His pockets contained a brand-new, unsharpened pencil and an index card that were also “shrunk” to 10% of their size. What would be the new size of these items?

6. G UIDING Q UESTION How can anticipating student solution paths and misconceptions inform the planning of questioning and discussion?

7. What does a Common Core math classroom look and sound like? Level 1: Teachers can tell students important basic ideas of mathematics such as facts, concepts, and procedures. Level 2: Teachers can explain the meanings and reasons of the important basic ideas of mathematics in order for students to understand them. Level 3: Teachers can provide students opportunities to understand these basic ideas, and support their learning so that the students become independent learners. from presentation by Dr. Akihiko Takahashi at CFI Mathematics Content Seminar, Oct 26, 2012

8. Why Level 3? Our country needs highly trained workers who can wrestle with complex problems – especially those who can think, reason, and engage effectively in quantitative problem solving. 8 Adapted from 5 Practices for Orchestrating Productive Mathematics Discussions by Margret S. Smith and Mary Kay Stein (2011), p.2

9. An example of the Level 3 teaching Show and Tell Beyond Show and Tell “Neriage” from presentation by Dr. Akihiko Takahashi at CFI Mathematics Content Seminar, Oct 26, 2012

10. High-quality discussions support student learning of mathematics by: Helping students learn how to communicate their ideas Making students’ thinking public so it can be guided in mathematically sound directions, and Encouraging students to evaluate their own and each other’s mathematical ideas. 10 Adapted from 5 Practices for Orchestrating Productive Mathematics Discussions by Margret S. Smith and Mary Kay Stein (2011), p.1

11. 5 P ractices 1. Anticipating likely student responses to challenging mathematical tasks 2. Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups) 3. Selecting particular students to present their mathematical work during the whole-class discussion 4. Sequencing the student responses that will be displayed in a specific order 5. Connecting different students’ responses and connecting the responses to key mathematical ideas. 11 Adapted from 5 Practices for Orchestrating Productive Mathematics Discussions by Margret S. Smith and Mary Kay Stein (2011), p.8

12. Activity Case Study: David Crane Shows implementation of a 4 th grade task Case Study: Nick Bannister Shows planning of an 8 th grade task 12

13. Anticipating Involves carefully considering: 1. What strategies students are likely to use to approach or solve a challenging mathematical task (e.g., a high-level task) 2. How to respond to the work that students are likely to produce, and the challenges they might have 3. Which student strategies are likely to be most useful in addressing the mathematics to be learned 13 Adapted from 5 Practices for Orchestrating Productive Mathematics Discussions by Margret S. Smith and Mary Kay Stein (2011), p.7

14. The importance of planning Instead of focusing on in-the-moment responses to student contributions, the practices emphasize the importance of planning. Through planning, teachers can anticipate likely student contributions, prepare responses that they might make to them, and make decisions about how to structure students’ presentations to further their mathematical agenda for the lesson. 14 Adapted from 5 Practices for Orchestrating Productive Mathematics Discussions by Margret S. Smith and Mary Kay Stein (2011), p.7

15. 4 th Grade – Leaves & Caterpillars The Case of Mr. Crane

16. 4 th Grade – Leaves & Caterpillars Students in Mr. Crane’s fourth-grade class were solving the following problem: “A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?” Mr. Crane told his students that they could solve the problem any way they wanted, but he emphasized that they needed to be able to explain how they got their answer and why it worked. Students in Mr. Crane’s fourth-grade class were solving the following problem: “A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?” Mr. Crane told his students that they could solve the problem any way they wanted, but he emphasized that they needed to be able to explain how they got their answer and why it worked.

17. 4 th Grade – Leaves & Caterpillars Share and discuss possible solution paths as well as misconceptions and challenges. Identify related 4 th grade content standards and practices Read “Leaves and Caterpillars: The Case of David Crane” and look at student work. (pg 3-4) Consider the following two questions: 1. What did the teacher do well? 2. What opportunities were missed? Share and discuss possible solution paths as well as misconceptions and challenges. Identify related 4 th grade content standards and practices Read “Leaves and Caterpillars: The Case of David Crane” and look at student work. (pg 3-4) Consider the following two questions: 1. What did the teacher do well? 2. What opportunities were missed?

18. 4 th Grade – Leaves & Caterpillars How could David Crane move beyond the show and tell (Level 1)? Read “Analyzing the Case of David Crane”. Discuss authors’ analysis and compare to our own analysis. How could David Crane move beyond the show and tell (Level 1)? Read “Analyzing the Case of David Crane”. Discuss authors’ analysis and compare to our own analysis.

19. Re-imagine the case of David Crane Discuss as a table and chart ideas How could the ‘Caterpillar and Leaf problem’ have been used to connect the important mathematical ideas and deepen understanding? What would David Crane have to do differently to better advance student thinking? How would those changes affect the learning?

20. Break

21. 8 th Grade Plans: The Case of Nick Bannister

22. 8 th Grade – Calling Plans

23. Share and discuss possible solution paths as well as misconceptions and challenges. Identify related 8 th grade content standards. Read about Nick Bannister’s anticipation. (pg. 32-34)

24. 8 th Grade – Calling Plans Discuss planning and preparation in the case of Nick Bannister. How might anticipating student approaches and challenges position Nick to facilitate a productive mathematical discussion in his class? Read authors’ analysis. (pg. 35-36) How does the authors’ analysis compare to your own?

25. Revisiting the Case of David Crane. Consider how your thinking about the case might have changed after examining the practice of Nick Banister. Think about the following questions: How does the case of Nick inform our analysis of David? How would you coach and support David Crane?

26. Goodbye, Farewell Next meeting will be Wednesday, March 20, 2013 PS 29, College Point