1. 1 Overview of Class #2 Today’s goals Comments on syllabus and assignments Mathematics education in the U.S. and becoming a teacher of mathematics Introduction to classroom culture Introduction to place value Teaching segments Wrapping up

2. 2 Syllabus Reactions and Questions Due dates and advance notice Will I have sufficient time in my classroom to complete projects? Final exam date; mixed returns. Assignments; placement complications Several comments about the goal of learning to promote equity Readings –– where, when due Other?

3. 3 Assignments Due dates Use of web Methods of submitting assignments Communication via email or phone with any questions or problems

4. 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. 5 Challenges of Becoming a Teacher of Mathematics in 2004 (compared with 1974) 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 “Theory-practice” divide is often actually “existing” versus “need for change” Dilemma: Do you prepare, as a beginner, to fit in to the system we have or to help make a better system?

6. 6 How the Course Design Addresses these Challenges (1)

7. 7 How the Course Design Addresses these Challenges (2) 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. 8 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?

9. 9 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

10. 10 Focal Questions What is the teacher doing, and how does it seem to shape student participation in mathematics? What stands out about students’ mathematical participation in this segment?

11. 11 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

12. 12 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)

13. 13 Place Value Please answer the following questions on the index card provided. (Be sure to write your name and the date on the card.) 1.Given our work today, what mathematical topics and ideas would you say are included in “place value”? 2.Why do you think place value was selected as the mathematical focus of this course?

14. 14 Teaching Segments Commitment of the course to practicing teaching --- not just talking about it “Slices” of teaching practice that–– –are things teachers do all the time –you can learn, practice, and get really good at –are crucial for beginning teachers to be able to do Apply what you are learning about students, mathematics, and equity Work closely with your cooperating teacher

15. 15 Schedule for Teaching Segments Teaching SegmentAssignedDue #1: End-of-class checkClass #2Class #4 #2: Read aloudClass #3Class #5 #3: Warm up problemClass #7Class #9 #4: Homework designClass #9Class #11 #5: Homework correctionClass #10Class #12

16. 16 End-of-Class Check A short question or prompt to check where your students are at the end of a lesson Purposes: –to help students reflect on their learning –to see what students think about their work that day –to check on students’ understanding of content –to reinforce skills or concepts Examples from our class -- comment cards, place value prompts

17. 17 Practice for End-of-Class Check 1.Design an end-of-class check for a lesson taught by you or your cooperating teacher. 2.Carry out the end-of-class check with students. 3.Review and analyze student responses. 4.Write an entry about your work on this teaching segment.

18. 18 Wrapping Up Assignments Comments Other questions Next week: Continue place value and classroom culture; bring teacher’s guide for your grade level

19. 19 Assignments Reading: Read and respond to questions Reflection: Teacher questions and their purposes Teaching Segment #1 (due in 2 weeks)