1. Today is 9/27. Problem of the Day
How many different 3-digit numbers can you make with the digits 9, 2, and 7?
Can you show that you have all the possibilities?
“Warm up problem.” Couple of minutes. No discussion. Anticipating TS #3, and also today’s video viewing.

2. Overview of Class #3
Continue work on place value with bundling sticks: representing quantities, notation
Purposes of teacher questions
Studying records of practice: context and rationale
Classroom culture
Teachers’ questions
Study video clip (9/12, permutations)
Mathematical tasks
Teaching Segment #2: Read-Aloud
Wrapping up

3. Core Ideas of Place Value
LAST WEEK
Distinction between quantity and numeration
Grouping (tens, but could be other):”Place value”
Fundamental “ten-ness”: “decimal notation”
Directionality (rt. to left)
Representational materials (bundling sticks, …)
WHERE WE’RE HEADED
Close mapping between structure of grouping and decimal notation (today)
Modeling the meaning of algorithms
Efficiency for computation
Launch into second fishbowl lesson with bundling sticks.

4. What stood out to you today about place value and the work of modeling it?
In notebooks; reflection on bundling stick lesson.

5. Purposes for Teacher Questions
Get students “into” a task
Probe students’ understanding
Scaffold students’ work or thinking
Get students back on task
Management of student error (correction, probing, converting)
Focus students to listen and respond to others’ ideas
Guide students to reason mathematically
Strengthen students’ thinking by posing a “what if” or incorrect idea for them to respond to
Support students to take intellectual risks
Demonstrate interest in students’ thinking
Encourage students to develop mathematical expression and fluency
15 minute whole group discussion, then BREAK

6. Studying Records of Practice: Context and Rationale
WHAT DO THESE RECORDS OF PRACTICE OFFER?
Continuous record of “real practice”
Regular public school classroom with diverse student population
Serious effort to teach with respect for mathematics, for student thinking, and for collective work, but not “model” teaching
Responsible for covering the curriculum, making sure students did well on testing
WHY STUDY RECORDS IN LEARNING TO TEACH?
Common “text”
Record offers more access than some
Learn to look and listen more closely
Study mathematics, students, teaching
Expand pedagogical “taste” and critical sophistication and skill
Develop ideas for one’s own practice: e.g., moves, problems, questions, pacing
HANDOUT: FREQUENTLY-ASKED QUESTIONS

7. Video Clip – September 12, 1989
Problem of the day: Today’s date is 9/12. How many three-digit numbers can you make with 9, 1, and 2?
Second day of school, day after two-coin problem; this problem designed to help them develop systematic way to prove that they had all the solutions
Setting up and clarifying the problem: Start with 2-digit numbers you can make with 5 and 9; Jillian: 14
Clip: We have six solutions. How can we be sure we have them all?
9 1/2 min clip

8. Focus for Viewing
What other kinds of teacher questions do you see? What specific questions?
The mathematics task and its extension: what do they offer?

9. Criteria for Tasks at the Beginning of the Year
Offer the teacher a way to learn about students’ mathematics concepts, skills, practices, dispositions
Convey to students what doing mathematics in this class is going to be like
Accessible to students who are at different levels
Will not immediately distinguish conventional conception of “good at math” from “not good at math” and perhaps even change those ideas
Help to build norms for independent and collective mathematical work
Avoid math problems that are win-lose, competition
Problems that are tangible, accessible

10. Why Read Mathematics Books?
Increase students’ opportunities to engage with mathematics
Launch problems or other mathematical work
Review concepts
Expose students to content not covered in regular curriculum
Support development of literacy by reading books that appeal to different interests
We’re focusing on the first bullet
Ask students for other reasons?

11. Things to Do when Reading Aloud
Introduce the book:
Read the title and author
Orient students to mathematical topic
Provide focus for listening
Hold the book so that students can see the pictures as you read, or show the pictures before turning the page.
Read clearly in a strong, engaging voice, with inflections and pauses in appropriate places
Engage students in the reading (e.g., make eye contact, ask questions, have them make predictions)
One possibility would be to
****go through this slide while modeling a read aloud*****
Note about holding the book: Remember students are sitting in various spots in the room so you may need to take a moment to move the book from side to side.
Ask students for other things they do when reading aloud

12. Preparing to Read Aloud
Read the book yourself, and size up the mathematical ideas involved
Choose a goal and emphasis for your read-aloud
Decide how to introduce the book
Identify places where you plan to stop reading and ask students questions
Practice reading the book aloud
Talking about the assignment

13. Practice for Teaching Segment #2
Select a book, and confirm your choice with your cooperating teaching
Prepare for your read-aloud
Read the book to the class, finding a way to secure another perspective on the experience (an observer or tape)
Write an entry about your work on this teaching segment
Talking about the assignment

14. Compiling a List of Mathematics Literature
Be on the lookout for other good books to add to your list
You might find it useful to create a file on mathematics literature:
Title and author
Mathematical content
Length
Age range
How you have used the book
Ideas for future uses
Handout for TS #2 includes a list of books

15. Classroom Culture: What Have You Learned?
Subtlety and importance of teachers’ questions to shape norms, talk, values, participation, what it means to be “good at math”
Some particular questions to use
The role of mathematical tasks in shaping norms, talk, values, participation, what it means to be “good at math”
Some particular tasks and criteria for others
Pacing and allowing time for students to talk, think, express themselves
Developing sense of collective work of verifying mathematical ideas and solutions (basis in reasoning) -- confidence, retention of concepts and skills
10 min SKIP THIS IF SHORT ON TIME

16. Wrapping Up Assignments on website later today
Next week: begin work on students’ thinking (start thinking of a student for your project)
Interest in going to MCTM (October in Detroit)?