1. Overview of Class #2 Comments on last week’s assignment and syllabus
Mathematics education in the U.S. and becoming a teacher of mathematics
Introduction to place value
Introduction to classroom culture
Wrap up

2. Last Week’s Assignment: Extending the Coin Problem (Task #5)
An opportunity to engage in actual work of teaching
Developing “problem packages”
different versions of a problem
questions to use with a problem

3. Syllabus Reactions and Questions
Assignments & readings
check out & photocopy readings
available from Erika Beck in room 4218
Notebooks
Project details
Final
Thursday, December 11, from 10:00-12:00
Why place value?
Office hours?
Other?

4. U.S. Mathematics Education in 2003
Mathematics education in the U.S. in serious need of improvement
E.g., only 17% of grade 12 students performed above “basic” level of competence (2000 NAEP)
Significant and persistent achievement gaps related to race and socioeconomic status
Many well-educated adults lack basic competence and confidence in mathematics (contrast with literacy)
Widespread agreement that conventional methods and curriculum are inadequate
International comparisons
Effective with only a few
Changing goals
Broader and higher levels of mathematical proficiency required for life in the 21st century
Mathematical proficiency for all students, not just for a few

5. Challenges of Becoming a Teacher of Mathematics in 2004
Educated in one system, preparing to be a professional in another
If successful, dubious of criticisms
If not successful, may have personalized perspective
Lack of images of alternatives
Own mathematical knowledge product of current system, professional needs more and different for improved instruction
Instead of “theory” versus “practice,” maybe “teaching as it is” versus “teaching as it could be”
Dilemma: Do you prepare, as a beginner, to fit in to the system we have or to help make a better system?

6. How the Design of this Course Addresses these Challenges: COURSE CONTENT

7. How the Design of this Course Addresses these Challenges: COURSE APPROACH
Choose topics and foci that:
Contribute to improvement in mathematics instruction
Are of high leverage for instruction
Can be mastered by beginning teachers
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

8. Place Value
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

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)

10. Analysis of Questions
Review the list of questions asked by the teacher during this activity.
For each question, consider
What do you think the purpose or function of the question was?
What type of participation does the question allow? How might it affect students’ participation in mathematics?

11. Classroom Culture Norms, patterns of interaction, language, values
Our focus: elements of classroom culture that shape students’ participation in mathematics
Tasks, questions, and moves that shape classroom culture: Where are key areas of leverage?

12. Video Segment 9/19/89 (one week later)
Write number sentences for 10.
First wrote two-addend sentences
Teacher asked for more terms and other operations
Later, during discussion: Lin proposes

13. Focal Questions How is the teacher working to shape classroom culture?
What stands out about students’ mathematical participation in this segment?

14. Wrapping Up Comments Any questions?
Next week: Continue place value and classroom culture
Assignments (will be posted on website this afternoon)

15. Assignments Week #2 Readings: To hand in next week: Lampert, Chapter 4
Labinowicz (1987)
Professional Standards for Teaching: Standard 5: Learning Environment
To hand in next week:
Develop a list of specific teacher questions. (Sources: video clips, our class, your field placement, readings) For each one, analyze its purpose and consider how it might affect students’ participation in mathematics.
Analyze the problem “Write number sentences for 10” for its usefulness as a beginning of the year problem.

16. End of Class Comments Office hours? Reactions to today’s class
Mondays 3:30 - 4:30
Wednesdays 1:30 – 2:30
Fridays 1:30 – 2:30
Reactions to today’s class
Anything else?