1. Overview of Class #2
Mathematics education in the US and the challenges of becoming a math teacher
Place value: core ideas, representations, teacher questions
Studying teacher moves, especially questions
Wrap up and assignments

2. Study Hall and Resource Center
Review, practice, extend, and discuss ideas presented in class
Examine resources for mathematics teachers
Work on assignments with colleagues
Ask questions about teaching mathematics

3. U.S. Mathematics Education in 2005
Mathematics achievement is inadequate
e.g., only 17% of grade 12 students performed above “basic” level of competence (2000 NAEP); approximately 42% of MI students met standards in math, whereas 78% of students met standard in reading (2005 MEAP)
Significant and persistent achievement disparities related to race and socioeconomic status
Many well-educated adults lack basic competence and confidence in mathematics (contrast with literacy)
Broad evidence that conventional methods and curriculum are ineffective
International comparisons
Effective with only a few
Changing goals and accountability
Broader and higher levels of mathematical proficiency required for life in the 21st century
Mathematical proficiency for all students, not just for a few (NCLB)

4. Challenges of Becoming a Teacher of Mathematics in 2005
Educated in one system, preparing to be a professional for another
If successful, dubious of criticisms; if not successful, may take personalized perspective
Lack of images of alternatives
Own mathematical knowledge product of current system, professional needs more and different for improved instruction
Dilemma: Do you prepare, as a beginner, to fit in to the system we have or to help make a better system?

5. How the Course Design Addresses these Challenges (1)
Guiding Principles
Domains of Practice
Attending to the integrity of the mathematics
Committing to the learning and achievement of all students
Establishing and managing a productive learning environment
Learning from and systematically improving practice
Eliciting, interpreting, and assessing students’ ideas
Modeling and representing mathematical ideas
Leading a whole class discussion
Designing,enact-ing, analyzing, improving lessons

6. How the Course Design Addresses these Challenges (2)
Choose topics and practices that:
Contribute to improvement in mathematics instruction
Are of high leverage for instruction
Can be mastered by beginning teachers
Focus on skillful performance through explicit instruction and repeated opportunities to practice and get feedback
Use records of practice
To study real practice, develop images, skills
Learn to learn from teaching
Emphasize collegial professional work for the development of improved knowledge and practice

7. Why is “Place Value” So Important?
Fundamental mathematical structure and set of ideas that spans kindergarten through calculus
Underpinning for system of notation, structure of number for computation, representation of number systems
Root of many student mathematical difficulties
Central to school curriculum topics from K - 8
Because it seems so obvious to adults, more attention required to teach it

8. Goals for Bundling Activity
Three layers of learning for you:
Major ideas of place value
Begin investigation of representational materials for modeling place value (bundling sticks)
Teacher questions as tool in instruction

9. Core Ideas of Place Value Today
Distinction between quantity and numeration
Grouping (tens, but could be other)
Fundamental “ten-ness”: “decimal notation”
Directionality
Representational materials (bundling sticks)
Close mapping between structure of grouping and notation we use

10. What stood out to you today about place value and the work of modeling it?

11. Studying Teacher Moves
Video clip from Lampert’s first day of class
Working on “inbetweenness” problems:

12. Focus for Viewing
What kinds of teacher questions do you see? What specific questions stand out?
More broadly, what other teacher “moves” do you see that are not questions?

13. Analysis of Teacher Moves
Can you give names to some of the recurrent teacher moves?
Pick a particular move. Name it, and speculate what purposes it may be serving.

14. Wrap-Up and Assignments
Assignment posted on website later today –– reading, more work on place value and teacher moves