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									The Quality of U.S. and Florida Math
Instruction Compared with Singapore,
a Recognized World Leader
                                      Florida Mathematics Standards
                                                     September 2006
                                                 Tallahassee, Florida


                                                               Alan Ginsburg*
                                                  U.S. Department of Education



  *Opinions are those of the presenters and do not necessarily reflect the views   1
  of the U.S. Department of Education
     Presentation Outline

1.   Singapore’s world-class math performance
2.   Overview of Singapore’s education system
3.   Comparison of Singapore-Florida math standards
4.   Comparison of Singapore-U.S. on other math
     system components : textbooks, assessments and
     teachers
5.   Results of Singapore textbook pilots in the U.S.
6.   Implications for adopting/adapting Singapore
     approaches to improve Florida’s math results

                                                        2
Singapore Has a World-class Mathematics
System with Quality Components Aligned
to Produce Students Who Learn
Mathematics to Mastery
   Highly logical national mathematics standards

   Mathematically rich problem-based textbooks

   Challenging mathematics assessments

   Highly qualified mathematics teachers whose
    pedagogy centers on teaching to mastery

   Special assistance from an expert teacher to its
    mathematically slower students along with an
    alternative framework
                                                       3
1. Mathematics Performance
Why Care About U.S. Primary-Level?
    “In our K-12 we were doing okay at the
    fourth-grade level, we were doing middle-of-
    the-road in the eighth grade, and by twelve
    grade we were hovering near the bottom in
    international tests related to math.”

        Tracy Koon, Intel’s director of corporate
    affairs, quoted in T. Friedman, The World Is
    Flat (2005)
                                                    4
In fact, U.S. International Math Results
Are Below Average At Grade 4




 Source: TIMSS 2003 (Mullis, I., Martin, M., Gonzalez, E., and Chrostowski, S. (2004). TIMSS 2003 international mathematics
                                                                                                                      5
 report. http://timss.bc.edu/PDF/t03_download/T03_M_Front.pdf
        The U.S. International Math Gap
        Continues in Grade 8

                          Average Math Scores
                                                                                                  Percent Achieving Advanced Math
                               8th Grade
                                                                                                             8th Grade
650

                                                                           50
600

                                                                           40
550


500                                                                        30



                                                                           20
450


400                                                                        10



350                                                                         0

                  Chinese                                         United        Australia   Chinese Taipei   Hong Kong   Japan   Korea   Singapore   United States
      Australia           Hong Kong   Japan   Korea   Singapore
                   Taipei                                         States
                                                                                    7             38            31        24      35        44             7
        505        585       586      570      589       605       504


      Source: TIMSS 2003 (Mullis, I., Martin, M., Gonzalez, E., and Chrostowski, S. (2004). TIMSS 2003 international mathematics
                                                                                                                           6
      report. http://timss.bc.edu/PDF/t03_download/T03_M_Front.pdf
U.S. Students Do Much Better
in International literacy 2001




                                 7

Source: 2001 PIRLS
Mathematics Are Gateway Courses
to College and Jobs
   COLLEGE. 71 percent of low-income students
    who took algebra I and geometry went to
    college, only 27 percent of low-income students
    who did not take algebra I and geometry went
    on to college. (U.S. Dept. of Education)

   JOBS. An applicant for a production associate’s
    job at a modern automobile plant would have to
    score roughly 300 points or higher on the NAEP
    math test to meet company proficiency
    requirements -- almost half of all 17-year-olds
    cannot do math at that level. (Murnane & Levy,    8

    Teaching the New Basic Skills)
2. Singapore Education
Mission




Moulding the future of our nation


  The Singapore Education Service - Moulding the Future of Our Nation   9
Primary System Emphasis on
Learning Core Content
 Literacy & Numeracy
 Bilingualism
  English language as the medium
   of instruction
  Every child would have the
   opportunity to learn his/her mother
   tongue to as high a level as he/she
   is capable of
  The Singapore Education Service - Moulding the Future of Our Nation   10
Primary Education
    Primary School Leaving Exam



   EM1             EM 2              EM 3
   20%             70%               10%
       Orientation Stage (Primary 5 – 6)



    Foundation Stage (Primary 1 - 4)
   Language Learning & Mathematics
                                            11
Fewer School Dropouts



     20         19%
     18
     16                                       Pri
     14
 %   12     11%
                                              Sec

     10
      8
      6
      4                                2.7%
      2                             0.3%
      0                                                          Year
               80           90         2001
                                                                        12
  The Singapore Education Service - Moulding the Future of Our Nation
Is Singapore Too Different from the
U.S.?
   Size: 500,000 Pupils: A little bigger than the
    Chicago Public Schools and a little smaller than
    Connecticut.

   Population: Racially diverse student body: 75%
    Chinese, 15% Malaysian,and 10 % Indian

   Work ethic: Singapore students are 2.5 times as
    likely as U.S. students to receive high-levels of
    math homework (8th grade TIMSS).                   13
Singapore Workers Are Strong on
Implementation, Weaker on
Innovation
   “We come from a very conscientious culture.
    You tell our people what to do, they’ll follow
    the rules, they’ll do it. The downside is they
    are not as creative. We fixed that by having a
    U.S-based R&D team that’s doing more
    advanced research.”
                                     Sim Wong Hoo
           CEO Creative Technologies Singapore
                           Newsweek Feb. 21, 2005
                                                 14
3. Math Standards Should
    Aim to develop in students a set of desired
     mathematical proficiencies

    Logically and clearly organize math topics
        sequence around the internal logic of mathematics
        cover a few core math topics in-depth at each grade
        be specific and clear about content

    Provide for student diversity in learning math


                                                               15
Singapore’s Proficiencies Are
Centered Around Problem Solving




                        MATHEMATICAL
                          PROBLEM
                          SOLVING
Computation,
Mental Math,                                      Thinking Skills
Data Analysis                                     Heuristics


                Numbers, Geometry, Statistics, Algebra
                                                               16
Florida’s Desired Math
Proficiencies?




                         17
NCTM’s Proficiencies Focus on Similar
Content to Singapore, but Process
Priorities Emphasize 21st Century Skills
     NCTM’s Five Content             NCTM’s Process
      Priorities                       Priorities Are Focused on
         Numbers and operations       21st Century Skills
         Algebra
                                          Problem solving
         Measurement
                                          Reasoning and proof
         Geometry
                                          Communications
         Data and statistics
                                          Connections
                                          Representation



                                                                 18
Exposure to Math Topics and
Outcomes in Singapore and 7 U.S.
States : Grades 1–6
                                                           Avg. No. of
                              Avg. No. of                    Outcomes
               Total No. of      Topics/    Avg. No. of          /
                 Topics         Grade       Grades/Topic     Grade

                   (1)           (2)           (3)            (4)
 Singapore         40             15           2.3            39

 California        42             20                          51
                                               2.9
 Florida           54             39           4.2            107

 Maryland          46             29           3.8            69
 New Jersey        50             28           3.4            56
 N. Carolina       41             18           2.6            36

 Ohio              48             26           3.3            62
                                                                     19
 Texas             40             19           2.8            44
Fla. Numbers Standards Gr. 1:
Lack Focus




                                20
Fla. Numbers Standards Gr. 1:
Lack Focus




                                21
Singapore Numbers Pr. 1: Whole
Numbers and Basic Operations




                                 22
Singapore Numbers Pr. 1: Whole
Numbers and Basic Operations




                                 23
Fla. Geom. Gr. 1:
Vague outcomes




                    24
Singapore Geometry Pr. 1:
Shapes and Patterns




                            25
Singapore Logically Builds-up Math
Topics Across Grades: Numbers




                                     26
Singapore Logically Builds-up Math
Topics Across Grades: Geometry




                                     27
Singapore Logically Builds Math
Topics Across Grades: Statistics
(Note: does not teach probability)

  Tables and Graphs   1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
  Picture graphs         X     X
  Bar graphs                         XX
  Tables                                X
  Line graphs                                    X
  Pie charts                                           X
                                                            28
Singapore Limits Use of
Calculators in Early Grades;
Florida Does Not
   Singapore: calculators not allowed grades 1-
    6; 2007 will allow calculators grades 5-6.

   Florida Grade 1: uses calculators to explore
    addition, subtraction, and skip counting




                                                   29
Singapore’s Framework Addresses At-
risk Students: U.S. State Frameworks
(including Florida) Do Not
   Singapore                                  U.S.
     Identify students for                      State frameworks don’t
       supplementary after-school                  differentiate students.
       instruction by a specially-trained          Traditionally, compensatory
       teacher (Grade 1+).                         education is often taught by
                                                   untrained teacher aides.

       Weaker math students                       No Child Left Behind holds
        identified for special track with           students to same standards and
        more math instruction and                   highly-qualified teachers.
        similar content but at a slower
        pace (Grades 5-6)

       Students are streamed based                No Child Left Behind holds
        on their Primary School Leaving             schools rather than students
                                                                               30
        Exam scores(Grade 7+)                       accountable.
New Directions for Singapore Math
Standards
Think Things Through: Pr. 3-Squares
                         Draw the smallest
                          possible square.
                         Draw the biggest
                          possible square.
                         Draw all possible
                          squares and find the
                          area of each.


                                             31
New Directions for Singapore Math
Standards
T3: Pr. 3 -- Make a Graph
                       Write an interesting and
                        fun story based on the
                        graph.
                       Make up five questions
                        for your friends to
                        answer based on the
                        graph.



                                               32
New Directions for Standards:
China Integrates Science Into Math
to Foster Applications
   “In math during the middle school and high school period, China
    tries to link math more closely with science problems. The
    purposes of this are as follows:

       To adapt to the increasing tendency of science development.
        Chinese educators and scientists believe that integration could
        be one of the developmental directions.

       To make math more vivid and less boring. Math could not be just
        logical explanations and abstract signals any longer and might
        have something to do with everybody’s daily life.

       To train student scientific spirit. Students shall be prepared to
        develop creativity and be ready to solve practical problems, not
        just memorizing this and that.”
                                                                            33
                                                    MOE China
Science Examples Could
Support Different Math Strands
   Geometry: Vectors forces

   Algebraic equations: F=MA (linear); projectile
    motion (parabolic)

   Numbers: Speed of light

   Statistics and measurement: inquiry science
                                                  34
   A Meaningful Math-Science Example of
   “Concrete Models & Real-world Problems”




                                                                   35

Source: http://phet.colorado.edu/web-pages/simulations-base.html
4. Comparison of Singapore-U.S. on
other math system components

a.   Textbooks

b.   Assessments

c.   Teachers




                                     36
4a. Textbooks
Grade 1: Singapore Textbooks Have
Fewer Lessons, More Pages per
Lesson, and More Pages of Exercises

             #               Average   Pages of   Pages of
                    # Les-                                   Other
Textbook                     Pages/    Develop-    Exer-
           Topics    sons                                    Pages
                             Lesson     ment       cises



Sing-                                   174        261         62
            13       34        15
apore                                  (35%)      (53%)      (12%)


Scott                                   145        169        250
Fores-      25       157       4
                                       (26%)      (30%)      (44%)
man

                                                              37
Singapore Lesson: Fractions Pr. 2B




                                     38
Singapore Lesson: Fractions Pr. 2B




                                     39
Singapore Lesson: Fractions Pr. 2B




                                     40
Singapore Lesson: Fractions Pr. 2B




                                     41
Singapore Lesson: Fractions Pr. 2B




                                     42
Singapore Lesson: Fractions Pr. 2B




                                     43
Gr 6 Lessons by Content Area:
Singapore Stresses Number,
Measurement, and Geometry; U.S.
Algebra and Data
 Text-   Num-   Measure-   Geo-    Alge-
                                           Data
 book     ber    ment      metry    bra

Singa-
         63%     17%       13%     4%      4%
 pore


 Scott   41%      9%        9%     11%     11%




                                                  44
   Singapore’s Relative Strength Is
   Numbers and Measurement; U.S.
   Relative Strength is Data and
   Weakness is Geometry: TIMSS Gr. 8




                                       45
Source: Mullis et al., 2004
 Singapore’s Visual Approach to
 Building Conceptual Understanding
 Should Work Well for U.S. At-Risk
 and ELLS Students
  Example : Fraction of a set
      Concrete level : Use objects




      Pictoral level :          12

                        4       4     4
                            2
    Abstract level :          of 12 = 8
                            3
                                          46

Source: Singapore MOE
Visual Approach:
Use Model Drawing




                    47
Singapore Textbooks Use Scaffolding Within
Multi-step Problems :
Gr. 6 Pie Chart Problem Incorporating Angles




                                                                   48
Source: Singaporemath.com Inc (2003). Active Primary Math Series
U.S. Textbook Problems Emphasize
Mechanical Formulas:
Gr. 6 Pie Chart Requires Summing to a Total
   Cost of Raising a Child to Age 18 (for each $100)




                                                       49
4b. Assessments
What we examined
   Singapore Grade 6 Primary School Leaving
    Exam

   U.S. NAEP Grades 6 and 8

   Five State Assessments at Grades 6 and 8



                                               50
How Challenging Are the Singapore
and U.S. Assessments?
                                                  Finding an
                     % Multiple   % Multi-step   Intermediate
                      Choice                       Unknown
Singapore – 6           31            25            19%
Florida – 8             52            12             8%
New Jersey – 8          85            33             0%
North Carolina – 6      100            8             0%
North Carolina – 8      100            5             5%
Ohio – 6                74            17             4%
Texas – 6               100            7             2%
Texas – 8               100            6             2%
NAEP – 4                64            15             4%
NAEP - 8                60            21             8%         51
   A Singapore Grade 6 Hard Problem
   You Won’t See on U.S. Grade 8 State
   Assessments




                                         52
Source: Singapore MOE
Differences in Purpose of
Assessments
   Singapore:
       To determine at grades 4, 6, and 10 each
        student’s academic level for purposes of
        placement.
       Hence, assessments focus on differentiation at
        the upper-range of student performance.
   U.S.:
       To determine if students within each school are
        making adequate yearly progress
        Hence, assessments focus on ensuring that
        students meet minimum criteria for proficiency.   53
4c. Teachers
What we looked at
   Teacher preparation in Singapore’s National
    Institute of Education and U.S. typical
    schools of education.

   Professional development in Singapore and
    U.S.



                                                  54
What We Found At Different Stages of
Teacher Development
       Stage            Singapore                    U.S.


Screening of       1 institution with     Praxis 1 during college
education majors   high standards pays
                   students to become
                   teachers
Pre-service        Approx 12 semester     Average is one math
expectations       hours math methods     methods course

Certification      Completion of course   Praxis 2
requirements       work/no further exam

Induction          20% reduction          Differs by State with
                                          full-load common

Professional       Annual target of 100   Haphazard prof. devel.
Development        hours                  Less than 24 hours
                                                                    55
   Teacher Preparation to Teach Math:
   Grades 4 and 8

   Pecent of Grade 4 Teachers            Pecent of Grade 8 Teachers
  With a Major or Specialization in     With a Math as a Major Area of
          Math or Science                           Study

 100                                  100
   80                                   80
   60                                   60
   40                                   40
   20                                   20
       0                                     0
Singapore                     76      Singapore            86
U.S.                          28      U.S.                 48

                                                                         56
Source: Mullis et al., 2004
Singapore Gr. 6 Exam Is More
Difficult Than the U.S. Elementary
Teacher PRAXIS 2 Exam
   U.S. Elementary Teacher PRAXIS 2 Sample Questions:
   1. Which of the following is equal to a quarter of a million?
   (A)40,000 (B) 250,000 (C) 2,500,000 (D) 1/4,000,000
   (B) (E) 4/1,000,000

   2. Which of the following fractions is least?
   (A) 11/10    (B) 99/100 (C) 25/24          (D) 3/2                                            (E)
   501/500




   3. On the scale above, the arrow most likely indicates
   (A) 630½ (B) 635        (C) 660 ½    (D) 670        (E) 685
                                                                                                                             57
   Source. Ginsburg, Lienwand, Anstrom, and Pollock (2005). What the United States Can Learn From Singapore’s World-Class Mathematics
   System And What Singapore Can Learn From the United States.
   http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf
U.S. Lessons Fail to Develop
Conceptual Understanding




                               58
    U.S. Middle School Math Teachers
    Lack Content-based Professional
    Development




                                                                                             59

Source: National Longitudinal Study of NCLB: Teacher Survey (2006). U.S. Dept of Education
5. Results From 4 Singapore Math
Pilots in U.S. Primary Schools
        Pilot Site                       Characteristics                 Results

North Middlesex,                 Small district with stable   Large increase in % of high-
Mass                             population                   performing students
Baltimore City                   Program for gifted           Large increase in % high
Ingenuity Project                students                     performing students
Montgomery County,               Suburban school district     Two of 4 schools showed
MD.                              with mixed income            substantial gains, with
                                 population                   improvement tied to amount of
                                                              teacher professional
                                                              development; other two schools
                                                              made same gains as controls
Paterson, NJ                     Extremely poor school        Same gains as controls
                                 with over 40% annual
                                 student turnover

Source: Ginsburg, Leinwand, Anstrom, and Pollock (2005)
                                                                                         60
6. Implications and Actions:
Bottom Line
   Our major finding is that the components of
    Singapore’s system – frameworks,texts, tests
    and teacher prep – are carefully aligned AND all
    of these components reflect a higher quality than
    comparable components in U.S.

   But there are a few 21st Century features of the
    U.S. system that Florida should build upon, but
    we need to do a better job.

                                                       61
Implications of Singapore Math for
Florida’s Standards Reforms
   Adopt highly logical mathematics standards (e.g., Singapore)

       Define desired student mathematics proficiencies so as to balance
        mathematics concepts, skills, and strategies

       Organize standards to clearly and visually portray the sequencing of core
        mathematics topics across grades

       Identify fewer mathematics topics per grade and for each topic describe a
        deeper set of desired mathematics outcomes

       Sequence mathematical topics across grades to build on prior knowledge
        rather than repeat topics

   Consider standards that explicitly recognize the diversity in students’
    mathematics performance

   Leap ahead by incorporating standards that encourage the
    reinforcement of 21st Century mathematics proficiencies
                                                                                    62
Implications of Singapore Math for
Reforming Florida’s Mathematics
System
    Standards need to be made instructionally meaningful through
     aligned textbooks and assessments

    Teachers will require in-depth professional development in
     understanding and teaching the deeper mathematics content
    Consider launching
        Singapore Math textbook pilots in Florida
        Benchmarking Promising Practices in highly successful sites to guide
         improvements




                                                                                63
Please Email for further
information


   Email: alan.ginsburg@ed.gov




                                  64

								
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