1. 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?
Use drawings, words, or numbers to show how you got your answer.
Please try to do this problem in as many ways as you can, both correct and incorrect. What might a 4th grader do?
5 minutes

2. 5 Practices for Orchestrating Productive Mathematics Discussions
Margaret S. Smith
Mary Kay Stein
A key challenge mathematics teachers face in enacting current reforms is to orchestrate discussions that use students’ responses to instructional tasks in ways that advance the mathematical learning of the whole class.
In particular, teachers are often faced with a wide array of student responses to complex tasks and must find a way to use them to guide the class towards deeper understandings of significant mathematics.
We are proposing a model for effective use of student thinking in whole-class discussions that we think has the potential to make such teaching manageable for more teachers AND HELP TEACHERS ORCHESTRATE DISCUSSIONS THAT MOVE BEYOND SHOWING AND TELLING.
Talk is based on a paper that we have written in collaboration with Mary Kay Stein and Elizabeth Hughes.

3. WHAT’S LACKING IN OUR MATH CLASSROOMS?
NOT ENOUGH PROBLEM SOLVING
Textbook problems are not really “problems”
NOT ENOUGH SOCIAL INTERACTION
“Research tells us that complex knowledge and skills are learned through social interactions.”
Traditional model of [teacher lectures, kids take notes  guided practice  homework] has its place every now and then, but it can’t be the mainstay
Textbook problems are exercises
A math classroom that’s always quiet should concern us – how is that possible?
It’s important to communicate

4. WHAT TEACHERS CAN DO
Find problems that are conducive to problem solving (cognitively demanding tasks)
Orchestrate the discussions by guiding and supporting the students
Launch the problem
Explore the problem
Discuss and summarize the problem
challenging and high-level, “low entry, high exit”, they can be solved using multiple strategies
a. teacher’s role: What is the problem about, what tools are available, what is the nature of the desired products
b. student’s role: allow students to work individually, in pairs, or in small groups
2. c. finding the right balance between what students are held accountable for and what they can contribute. You might not want to say to the class, “You must participate or say something; otherwise you won’t get a grade.

5. THE CASE OF DAVID CRANE Read pages 3-4 of Introduction
After reading, at your table group, please discuss and record two things:
What did Mr. Crane do well?
What could he have done differently?
Whole group sharing
Set timer for 4 minutes to read.
Allow 5 minutes for small groups.
Allow 10 minutes for whole group sharing: from each group, record (on chart paper) 1 item from each of 2 questions

6. Introducing the Five Practices
CHAPTER 1
Introducing the Five Practices

7. The Five Practices Anticipating Monitoring Selecting Sequencing
Connecting
Chris
Maria
Fawn
Tomorrow Andrew will cover chapter 2 on setting goals and selecting a task
Maria will take you through chapter 3 which is another overview of the five practices as seen through one teacher’s lesson
Chris will cover chapter 4 which is on anticipating and monitoring
I will be back cover chapter 5 which includes the last three practices

8. Anticipating How students might interpret the problem
The different strategies they might use
How these strategies relate to the math they are to learn
How is the “doing math” support one or more of the 8 CCSS math practices
Our warm-up problem was your anticipating
Attending workshops helps teachers to do the problems and share with other teachers
Reading up on research
Document student responses – blogging, journaling

9. Monitoring Circulating while students work
Recording interpretations, strategies, other ideas
(Resisting urge to help!)
Sitting at our desk is not monitoring
Pretending to monitor fools no one

10. Selecting
Choosing particular students because of strategies used and/or the mathematics in their responses
Gaining some control over the discussion content
Your anticipating step would support this step

11. Sequencing
Ordering presentations to facilitate the building of mathematical content
Scaffolding
Think about time also!

12. Connecting Encouraging students to make connections between presenters
Making the key mathematical ideas of the task prominent
Follow up with a non-graded formative assessment?

13. GOING BEYOND SHOW AND TELL

14. If you don't make mistakes, you're not working on hard enough problems
If you don't make mistakes, you're not working on hard enough problems. And that's a big mistake. — Frank Wilczek, MIT Physics professor, Nobel laureate
-2004
-we need to challenge our kids, be less helpful to them, and embrace their mistakes.

15. Dyads Six Discussion Questions
Quiet time to read through all 6, then choose 2 to answer.
(5 minutes)
Then, we’ll do a dyad and share like this… (4 minutes total)