Seeking Common Ground Jeremy Kilpatrick University of Georgia

1. Seeking Common Ground Jeremy Kilpatrick University of Georgia

2. NCSSM Precalculus “Teaching and Learning Cross-Country Mathematics: A Story of Innovation in Precalculus,” by J. Kilpatrick, L. Hancock, D. S. Mewborn, & L. Stallings In S. A. Raizen & E. D. Britton (Eds.), Bold Ventures, Vol. 3: Case Studies of U.S. Innovation in Mathematics Education. Dordrecht, the Netherlands: Kluwer, 1996

3. Outline • What’s the fuss about? • Why seek common ground? • What common ground? • What complaints? • What’s next? • Where are the teachers?

4. What’s the fuss about?

5. The New Math Benjamin DeMott, “The Math Wars.” In Hells and Benefits: A Report on American Minds, Matters, and Possibilities. New York: Basic Books, 1962.

6. Gurganus’s author’s note: A word to the reader about historical accuracy • 1930s Federal Writers’ Project found that many former slaves recalled seeing Lincoln in the South during the Civil War • Fanny Burdock (91): “We been picking in the field when my brother he point to the road and then we seen Marse Abe coming all dusty and on foot. . . • He so tall, black eyes so sad. Didn’t say not one word, just looked hard at us, every one us crying. We give him nice cool water from the dipper. . . .

7. Gurganus’s author’s note: A word to the reader about historical accuracy • “After, didn’t our owner or nobody credit it, but me and all my kin, we knowed. I still got the dipper to prove it.” • In reality, Lincoln’s foot tour of Georgia could not have happened, but such scenes were told by hundreds of slaves • “Such visitations remain, for me, truer than fact” • The South is a realm where fact and fable are both true

8. California Dreaming: Reforming Mathematics EducationSuzanne Wilson Why the new math reforms “failed”: • Weak mathematical knowledge of leaders: “Not everyone was a mathematician, and some of the mathematicians . . . were not highly respected” (p. 14) • Misguided reforms: “The mathematics was inappropriate . . . the wrong mathematicians were involved” (p. 16)

9. David Blackwell Robert Dilworth Mary Dolciani Andrew Gleason John Kelley Edwin Moise Peter Hilton Henry Pollak George Pólya Mina Rees Norman Steenrod Marshall Stone Albert Tucker Gail Young New Math Mathematicians

10. Andrew Gleason Lipman Bers Edwin Moise Morris Kline George Pólya Marshall Stone Lars Ahlfors Max Schiffer Paul Rosenbloom Garrett Birkhoff Henry Pollak E. G. Begle Marston Morse R. C. Buck Robert Dilworth Richard Bellman Mina Rees André Weil Critic* *Signed “On the Mathematics Curriculum of the High School,” Amer. Math. Monthly 69 (1962), 189-193: Math. Teacher 55 (1962), 191-195. New Math Reformer* *Participated in at least one project

11. New math era Mathematicians push for reform Gulf between school and university mathematics; political and military competitiveness Opposed by teachers, parents, and some mathematicians Emphasis on content—abstract structures—presented logically and formally Standards era Teachers (NCTM) push for reform Gulf between U.S. and international performance; economic and technological competitiveness Opposed by mathematicians, parents, some teachers, and policy makers Emphasis on pedagogy—active learning—with meaningful content and investigations Math wars then and now

12. Standards-Based Reform • Termed “whole math,” like “whole language” • Termed “new-new math,” like “new math” • Groups of parents and mathematicians formed

13. Lynne Chaney June 1997 Kids are writing about “What We Can Do to Save the Earth,” and inventing their own strategies for multiplying. They’re learning that getting the right answer to a math problem can be much less important than having a good rationale for a wrong one. Sometimes called “whole math” or “fuzzy math,” this latest project of the nation’s colleges of education has some formidable opponents. In California, where the school system embraced whole math in 1992, parents and dissident teachers have set up a World Wide Web site called Mathematically Correct to point out the follies of whole-math instruction. http://ourworld.compuserve.com/ homepages/mathman/index.htm

14. Controversy • New rhetoric: “Fuzzy math” “Parrot math” • Stories of students not learning basic facts • January 1998: Richard Riley, U.S. Secretary of Education, calls for a cease fire in the “math wars”

15. Why seek common ground?

16. Richard SchaarTexas Instruments • Managed TI calculator business since 1986, marketing graphing calculators for mathematics education along with the needed support programs for teachers • Frustrated over the lack of progress in K-12 mathematics education • Worked with other Texans on an initiative under the auspices of the Business Roundtable to help move the states forward in improving mathematics education • Saw the math wars as a major stumbling block to progress • After talking with Jim Milgram (Stanford mathematician), decided to convene a small group of people to find a middle ground in the conflict • Got support from NSF and then MAA

17. “Peace commission” • Richard Schaar, Texas Instruments, convener • Deborah Ball, University of Michigan • Joan Ferrini-Mundy, Michigan State University • Jeremy Kilpatrick, University of Georgia • James Milgram, Stanford University • Wilfried Schmid, Harvard University

18. What common ground?

19. Article by Michael Pearson in Aug./Sept. MAA FOCUS • The MAA hopes to help encourage and facilitate constructive discourse between mathematicians and mathematics educators to seek common ground in efforts to improve K-12 mathematics teaching and learning • Success of two pilot meetings: • At NSF in December 2004 • At the MAA offices in June 2005 • Document can serve as starting point for future conversations • See http://www.maa.org/common-ground/or Notices of the AMS, October 2005

20. Article by Michael Pearson in Aug./Sept. FOCUS • All students must have solid grounding in mathematics to function effectively in today’s world • Premises: • Basic skills with numbers continue to be vitally important for a variety of everyday uses • Mathematics requires careful reasoning about precisely defined objects and concepts • Students must be able to formulate and solve problems • Areas of agreement: automatic recall of basic facts, use of calculators in lower grades, learning algorithms, fractions, teaching mathematics in “real world” contexts, instructional methods, teacher knowledge

21. Seeking Common Ground A process: • People working together • Listening thoughtfully • Valuing others’ opinions • Taking time • Agreeing on language • Working hard toward a common goal

22. What complaints?

23. K-12 Mathematics Education: How Much Common Ground Is There?Anthony Ralston • A valuable exercise, with results unexceptional to almost all FOCUS readers, but fraught with difficulties: • Blandness • Ambiguity • Disagreement in community—curriculum and technology • Before attempt consensus, need a level of respect in both communities

24. K-12 Mathematics Education: How Much Common Ground Is There?Anthony Ralston • Ambiguity • “Certain procedures and algorithms in mathematics are so basic and have such wide application that they should be practiced to the point of automaticity” • “Calculators can have a useful role even in the lower grades, but they must be used carefully, so as not to impede the acquisition of fluency with basic facts and computational procedures”

25. K-12 Mathematics Education: How Much Common Ground Is There?Anthony Ralston • Disagreement in community • “By the time they leave high school, a majority of students should have studied calculus” • “Students should be able to use the basic algorithms of whole number arithmetic fluently, and they should understand how and why the algorithms work” • “The arithmetic of fractions is important as a foundation for algebra”

26. “By the time they leave high school, a majority of students should have studied calculus” • Although some should, and already do, take a full course in calculus, most students should learn at least certain fundamental ideas of calculus, such as rate of change, limit, and derivative • Some 70% of the countries in TIMSS cover the topics of elementary analysis (infinite processes and change) at grade 12, and many address these topics in grades 9 through 11 • A project involving incentives and district-wide commitment in ten inner-city Dallas high schools has resulted in a nine-fold increase to 330 out of 4161 graduates from 1995 to 2005 in the number of students receiving a score of three or better on the AB Calculus Advanced Placement exam.

27. What’s next?

28. March meeting in Indianapolis • Probability and data analysis in the elementary curriculum • Algorithms in the curriculum • Technology in general • Calculus in high school • Algebra for all • Gap between policy (high standards) and teacher beliefs and capacity • How can international studies and information be used? • How should we weigh class size versus teacher knowledge and capabilities?

29. Where are the teachers?

30. Mathematics Teachers • Are they in this fight? • What might they add to the conversation? • Calculus as goal • Role of definitions • Applications as motivation • Curriculum structure