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.

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

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.

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

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

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

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

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?

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

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?

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

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

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

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

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

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 29-30 in Detroit)?