Helping All Children Become Proficient in Mathematics

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Seeking Common Ground Jeremy Kilpatrick Universi
ty of Georgia
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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
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Outline

• Whats the fuss about?
• Why seek common ground?
• What common ground?
• What complaints?
• Whats next?
• Where are the teachers?

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Whats the fuss about?
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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.
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Gurganuss authors 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. Didnt say not
  one word, just looked hard at us, every one us
  crying. We give him nice cool water from the
  dipper. . . .

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Gurganuss authors note A word to the reader
about historical accuracy

• After, didnt our owner or nobody credit it, but
  me and all my kin, we knowed. I still got the
  dipper to prove it.
• In reality, Lincolns 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

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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)

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New Math Mathematicians

• 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

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Lipman Bers
Andrew Gleason
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
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Math wars then and now

• 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 contentabstract structurespresented
  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 pedagogyactive learningwith
  meaningful content and investigations

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Standards-Based Reform

• Termed whole math, like whole language
• Termed new-new math, like new math
• Groups of parents and mathematicians formed

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Lynne Chaney June 1997
Kids are writing about What We Can Do to Save
the Earth, and inventing their own strategies
for multiplying. Theyre 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 nations
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//ourw
orld.compuserve.com/ homepages/mathman/index.htm
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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

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Why seek common ground?
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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

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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

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What common ground?
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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

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Article by Michael Pearson in Aug./Sept. FOCUS

• All students must have solid grounding in
  mathematics to function effectively in todays
  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

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Seeking Common Ground

• A process
• People working together
• Listening thoughtfully
• Valuing others opinions
• Taking time
• Agreeing on language
• Working hard toward a common goal

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What complaints?
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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 communitycurriculum and
  technology
• Before attempt consensus, need a level of respect
  in both communities

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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

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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

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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.

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Whats next?
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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?

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Where are the teachers?
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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