The Current State of Mathematics in Our Nations Schools

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The Current State of Mathematics in Our Nations
Schools

• New York City Math Supervisors and Coaches
• May 26, 2009
• Zalman Usiskin
• The University of Chicagoz-usiskin_at_uchicago.edu

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The positive
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The positive

• Students are taking significantly more
  mathematics than ever before.

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Percents of 8th graders studying various levels
of mathematics curricula

• Alg Enr. Typ Rem.
• SIMS 13 11 66 10
• Alg PreA Reg Other
• NAEP 16 19 61 5
• NAEP 20 36 39 5
• G/AA Alg PreA Reg Other
• NAEP 3 25 31 37 5
• 2003 NAEP 5 28 29 33 5
• 2007 NAEP 7 34 30 25 4
• SIMS Second International Mathematics Study
• NAEP National Assessment of Educational
  Progress
• Alg Algebra Enr Enriched Typ Typical Rem
  Remedial
• PreA Pre-algebra Reg Regular G/AA
  Geometry or Advanced Algebra.

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NMAP (2008) statement

• All school districts should ensure that all
  prepared students have access to an authentic
  algebra course - and should prepare more students
  than at present to enroll in such a course by
  Grade 8. (p. 23)

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End w/ A or G
AA
FST
PDM
C
PDM
C
A or G
AA
FST
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End w/ A or G
AA
FST
PDM
C
PDM
C
A or G
AA
FST
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Percent of high school graduates with highest
level of mathematics
Source 2005 NAEP H.S. Transcript Study (Feb
2007)
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The positive

• Students are taking significantly more
  mathematics than ever before.
• Scores of students on national tests have been
  increasing for some time.

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8th grade NAEP scores 1990-2007
4th grade NAEP scores 1990-2007
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New York - Grade 4 (public) NAEP average scores
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New York - Grade 8 (public) NAEP average scores
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Mean SAT-I Math and ACT-Math scores

• Year SAT ACT
• 1990 501 19.9
• 1991 500 20.0
• 1992 501 20.0
• 1993 503 20.1
• 1994 504 20.2
• 1995 506 20.2
• 1996 508 20.2
• 1997 511 20.6
• 1998 512 20.8
• 1999 511 20.7
• 2000 514 20.7
• 2001 514 20.7
• 2002 516 20.6
• 2003 519 20.6
• 2004 518 20.7
• 2005 520 20.7
• 2006 518 20.8
• 2007 515 21.0

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1960
1980
2000
1990
1970
new math
back-to-basics
problem-solving
standards
NCLB
SAT-M
SAT-V
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NMAP statement (2008)

• During most of the 20th century, the United
  States possessed peerless mathematical prowess -
  not just as measured by the depth and number of
  the mathematical specialists who practiced here
  but also by the scale and quality of its
  engineering, science, and financial leadership,
  and even by the extent of mathematical education
  in its broad population . (Executive Summary, p.
  xi)

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Number of AP Calculus Exams 2000-2008

• Year AB BC
• 2000 137,276 34,142
• 2001 146,771 38,134
• 2002 157,524 41,785
• 2003 166,821 45,973
• 2004 175,094 50,134
• 2005 185,992 54,415
• 2006 197,181 58,603
• 2007 211,693 64,311
• 2008 222,835 69,103
• Source The College Board, AP Report to the
  Nation 2005-06-07-08

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Source David Bressoud www.macalester.edu/bress
oud/talks/CBMS.pdf
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Percents of students with each score on AP
Calculus Exams

• AB BC
  
• Year 2004 2005 2006 2007 2004 2005 2006 2007
• Score
• 5 20.4 20.9 22.3 21.0 39.8 43.8 41.9 43.5
• 4 19.9 19.5 20.5 18.7 18.8 17.0 19.7 17.9
• 3 19.0 17.7 18.6 19.1 20.9 20.1 19.7 18.8
• 2 17.6 16.7 15.5 15.4 7.7 6.8 6.4 6.4
• 1 23.0 25.2 23.2 25.7 12.8 12.3 12.3 13.5
• 3 59.3 58.1 61.3 58.8 79.6 80.9 81.3 80.2
• mean 2.97 2.94 3.03 2.94 3.65 3.73 3.72 3.71
• Source The College Board, AP Reports to the
  Nation 2005-06-07-08

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The negative
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The negative

• The gap between the mathematics performance of
  various groups is enormous and declining very
  little if at all.

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American Math Achievement
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Average NAEP scores by race/ethnicity, 1990-2005,
grade 4
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Average NAEP scores by race/ethnicity,
1990-2005, grade 8
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New York - Grade 4 (public) NAEP 2007 average
scores
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New York - Grade 8 (public)NAEP 2007 average
scores
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NMAP statement

• The use of real-world contexts to introduce
  mathematical ideas has been advocated A
  synthesis of findings from a small number of
  high-quality studies indicates that if
  mathematical ideas are taught using real-world
  contexts, then students performance on
  assessments involving similar real-world
  problems is improved. However, performance on
  assessments more focused on other aspects of
  mathematics learning, such as computation, simple
  word problems, and equation solving, is not
  improved . (p. xxiii and p. 49)

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Strong Standard Understand how real and complex
numbers are related, including plotting complex
numbers as points on a plane. Example Plot the
points corresponding to 3 2i and 1 4i. Add
these complex numbers and plot the result. How
is this point related to the other two? Weak
Standard Model and analyze real-world situations
by using patterns and functions. Source AFT,
Sizing Up State Standards, 2008
Time, Apr 27, 2009
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The negative

• The gap between the mathematics performance of
  various groups is enormous and declining very
  little if at all.
• The gap between what is offered in some schools
  and what is offered in others is enormous.

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Percent of high school graduates completing that
level of mathematics
Source 2005 NAEP H.S. Transcript Study (2007)
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The negative

• The gap between the mathematics performance of
  various groups is enormous and declining very
  little if at all.
• The gap between what is offered in some schools
  and what is offered in others is enormous.
• The mathematics teacher is beleaguered by
  conflicting expectations coming from all
  directions.

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Conflicting expectations

• the course syllabus
• the textbook
• college entrance tests (SATs, ACTs)
• state tests
• college placement tests
• parental expectations
• local customs
• a teachers own views and expectations

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The rational
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The rational

• NCLB - no public non-charter school given a free
  pass

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The rational

• NCLB - no public non-charter school given a free
  pass
• Move towards consistent standards

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The move towards national standards

• NCTM Standards (1989, 2000)
• No Child Left Behind legislation (2002)
• ASA K-12 Standards (2005)
• College Board standards for college success
  (Springboard et al.) (2006)
• American Diploma Project standards (Achieve)
  (2006)
• NCTM K-8 Focal Points (2006)
• NCTM focus on h.s. mathematics (2009, to appear)

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The rational

• NCLB - no (public, not charter) school given a
  free pass
• Move towards consistent standards
• Test as many students as possible to determine
  how we are doing

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The irrational
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The irrational

• NCLB- and state-mandated testing will improve
  scores overall.

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States currently testing in grades 3-8 Reading
and Math
Alaska
Washington
Maine
North Dakota
Minnesota
Montana
Vermont
New Hampshire
Oregon
Massachusetts
Wisconsin
South Dakota
New York
Rhode Island
Michigan
Idaho
Connecticut
Wyoming
New Jersey
Pennsylvania
Iowa
Nebraska
Ohio
Delaware
Indiana
West Virginia
Nevada
Illinois
Maryland
Utah
Colorado
District of Columbia (not pictured)
Virginia
Kansas
Missouri
California
Kentucky
North Carolina
Tennessee
South Carolina
Oklahoma
Arizona
New Mexico
Arkansas
Alabama
Georgia
Mississippi
Hawaii
Texas
Louisiana
Florida
Puerto Rico (not pictured)
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California and Illinois - Grade 4 (public)NAEP
average scores 1992-2007
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California and Illinois - Grade 8 (public)NAEP
average scores 1992-2007
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The irrational

• NCLB-mandated testing will improve scores
  overall.
• NCLB-mandated testing will reduce performance
  differences between high- and low-performing
  groups (the achievement gap).

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The irrational

• NCLB-mandated testing will improve scores
  overall.
• NCLB-mandated testing will reduce performance
  differences between high- and low-performing
  groups (the achievement gap).
• One size fits all.

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The many kinds of students

• the selective school college-bound
• the non-selective school college bound who will
  get a bachelors degree
• the college bound who will not finish college
• the work-force/technical school bound
• the dropout who gets a GED
• the student who will never attain high-school
  equivalency

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The irrational

• NCLB-mandated testing will improve scores
  overall.
• NCLB-mandated testing will reduce performance
  differences between high- and low-performing
  groups (the achievement gap).
• One size fits all.
• Some NCLB provisions are mathematically
  impossible to attain.

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Some Impossible NCLB provisions

• The Lake Wobegon Effect that all students can
  be brought up to grade level

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• "Isn't the purpose of public education to make
  sure every child reads at grade level? Right
  now, we're only seeing rates at 30 or 40
  percent...These gaps mean children aren't
  achieving and we have to target that.
• - Ron Tomalis, acting asst. secy, DOE, 2003

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• A Key Policy letter
• September 5, 2006
• Dear Chief State School Officers
• To meet the goal that all students will be on
  grade level in reading and mathematics by 2014,
  we need to pick up the pace in our efforts to
  ensure that all core academic subjects are taught
  by highly qualified and effective teachers.
  (long letter)
• Sincerely,
• Margaret Spellings
• Source NCLB website.

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Impossible NCLB provisions

• The Lake Wobegon Effect that all students can
  be brought up to grade level
• The Movement Paradox that moving students
  from a poor-performing school to a
  better-performing school will improve school
  performance

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Impossible NCLB provisions

• The Lake Wobegon Effect bringing all students
  up to grade level
• The Movement Paradox moving scores from one
  group to another does not necessarily lower the
  mean in one and raise the mean in the other
• The Upper Bound Effect that school mean
  scores can increase indefinitely

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The irrational

• NCLB-mandated testing will improve scores
  overall.
• NCLB-mandated testing will reduce performance
  differences between high- and low-performing
  groups (the achievement gap).
• One size fits all.
• Some NCLB provisions are mathematically
  impossible to attain.
• We have based virtually all of our K-12 policy
  decisions on curriculum on the assumption that
  the sole reason for teaching mathematics is for
  success in college mathematics classrooms.

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The imaginary
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The imaginary

• The U.S. mathematics curriculum is a mile
  wide and an inch deep. - Schmidt

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NMAP statement

• A focused, coherent progression of mathematics
  learning, with an emphasis on proficiency with
  key topics, should become the norm in elementary
  and middle school mathematics curricula. Any
  approach that continually revisits topics year
  after year without closure is to be avoided. (p.
  xvii and p. 22)

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Average Years of Coverage and Emphasis of Certain
Topics in the Mathematics Curriculum of Several
Countries

• Country Coverage Emphasis
• France 7 1
• Japan 5.5 4.5
• Norway 8 0.5
• Spain 5 1
• Switzerland 7 3
• United States 7.5 3.75
• average of years devoted to the following
  topics
• whole number, fractions/decimals,
  exponents/roots, and equations/formulas
• From Characterizing Pedagogical Flow, p. 52

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The imaginary

• The U.S. mathematics curriculum is a mile wide
  and an inch deep. - Schmidt
• Our standing on international tests has serious
  implications for our economy.

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Our students are falling behind their
counterparts in the rest of the world,
threatening the U.S.s economic future. - Walter
Isaacson, CEO, Aspen Institute
Time, Apr 27, 2009
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1963-64
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1963-64
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1980-81
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1980-81
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TIMSS 1994-95 8th grade means

• Statistically equal to U.S.
• New Zealand 508
• Norway 503
• United States 500
• Spain 487
• Iceland 487
• Statistically below U.S.
• Cyprus 474
• Portugal 454
• Iran 428

• Significantly higher than U.S.
• Singapore 643
• Korea 607
• Japan 605
• Hong Kong 588
• Belgium-Flemish 565
• Czech Republic 564
• Slovak Republic 547
• Switzerland 545
• France 538
• Hungary 537
• Russian Federation 535
• Ireland 527
• Canada 527
• Sweden 519

Mean score of countries meeting sampling
specifications 527
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TIMSS 1994-95 8th grade means

• Statistically equal to U.S.
• New Zealand 508
• Norway 503
• United States 500
• Spain 487
• Iceland 487
• Statistically below U.S.
• Cyprus 474
• Portugal 454
• Iran 428

• Significantly higher than U.S.
• Singapore 643
• Korea 607
• Japan 605
• Hong Kong 588
• Consortium 587
• Belgium-Flemish 565
• Czech Republic 564
• Slovak Republic 547
• Switzerland 545
• France 538
• Hungary 537
• Russian Federation 535
• Ireland 527
• Canada 527
• Sweden 519

Mean score of countries meeting sampling
specifications 527
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2003
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of top 27 countries at each grade level
2007
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The imaginary

• The U.S. mathematics curriculum is a mile wide
  and an inch deep. - Schmidt
• Our standing on international tests has serious
  implications for our economy.
• Singapore (or Japan or Korea) is a good model
  to emulate.

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Rating of the current state of mathematics
education in the U.S., on a scale from 0 to 10

• 6.5 3i

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The current state of mathematics education in the
U.S. is complex, better than it was, not as good
as we want, not as bad as critics charge, and
being dragged down by irrational goals and
actions fueled by imaginary views.
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Thank you!
z-usiskin_at_uchicago.edu