1. Overview of Class #2
The context in which you are learning to teach mathematics, and the accompanying challenges
Comments & questions about the syllabus and the course
Place value: core ideas, representations, teacher questions
Studying teacher moves, especially questions
Wrap up and assignments

2. U.S. Mathematics Education in 2006
U.S. mathematics achievement is inadequate
Broad evidence that conventional methods and curriculum are ineffective
Changing goals and accountability
As a beginning teacher, you have been educated in one system, but are 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
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)

3. 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
Leading a whole class discussion about mathematics
Representing mathematical
ideas
Assessing students’ knowledge, skill, and dispositions
Planning mathematics lessons

4. 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

5. Syllabus Questions Major assignments & final exam
Assignment sheet posted to course website by end of night on Thursday
Notebooks - pick up on Friday mornings in crate outside of Tim’s office suite
Digital recorders
Can check them out from Tech Services
Purchase suggestions: ipod, Olympus, Sony
can compare online at sites like Amazon
Be able to download recorded files to a computer
Recommended file formats: AAC, m4a or mp3, WMA, or DSS.
NCTM trail membership (

6. Major Assignments Professional practice pieces:
Three in the field: (1) Teach a mini-problem; (2) Student thinking interview; (3) Audio tape while circulating during lesson
Culminating performance assessments
Teach a lesson
Meet with instructor before lesson
Lesson needs to include a whole class discussion
End of class assessment
Modeling an algorithm (part of final)
Final exam
Includes oral and written questions; to be completed in class
Details about tasks and grading will be handed out with each assignment; try to complete during specified dates

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 tonight –– reading, more work on place value and teacher moves
Study Hall starts next week
Mondays from 3-5 and Fridays from 12-2
Not collecting notebooks this week; Tim will collect them next week
Comment cards