US Mathematics Education: Challenges & Strategies for Math Teachers

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)

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