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

Last Week’s Assignment: Extending the Coin Problem (Task #4) An opportunity to engage in actual work of teaching Developing “problem packages” different versions of a problem questions to use with a problem

Syllabus Reactions and Questions Assignments & readings check out & photocopy readings available from Erika Beck in room 4218 Notebooks Project details Final I’ll send an announcement of the date. Why place value? Office hours? Other?

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) 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 Widespread agreement that conventional methods and curriculum are inadequate International comparisons Effective with only a few

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?

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

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

Place Value Fundamental mathematical structure and set of ideas that spans K through calculus System of notation for both naming numbers and for supporting efficient procedures for computation. Ease of representation of both very large and very small numbers. Expands to represent all real numbers. Root of many student mathematical difficulties Central to school curriculum topics from K - 8

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)

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?

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?

Video Segment 9/19/89 (one week later) Write number sentences for 10. First wrote two-addend sentences Teacher asked for more than one term, other operations Later, during discussion: Lin proposes 200 - 190

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

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

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.