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**Singapore Math: How It Can Help Improve U.S. Mathematics Learning**

Alan Ginsburg* U.S. Department of Education Chair, APEC Human Resources Development Presentation to Maryland State Board of Education May 28, 2009 *Opinions are those of the presenter and do not necessarily reflect the views of the U.S. Department of Education or APEC

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**Presentation Outline Importance of primary mathematics.**

Can we compare U.S. and Singapore? Results from U.S. pilots of Singapore Math. Comparing Singapore – U.S. math systems on: Frameworks Textbooks Assessments Teachers Singapore and other math standards online.

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Presentation Basis Ginsburg, Leinwand, 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. American Institute for Research

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**Neglect of U.S. Primary Mathematics Performance**

“In our K-12 we were doing okay at the 4th grade, we were doing middle-of-the-road in the 8th grade, and by 12th 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) NCES, National Academy of Sciences, and Business Roundtable have drawn similar conclusions about U.S. students’ primary-level international mathematics performance. Proposals to reform U.S. mathematics instruction have largely ignored primary grades.

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**U.S. Math Scores Are Substantially Below Asian Average at Grade 4**

Source: TIMSS 2007 (Mullis, I., Martin, M., Gonzalez, E., and Chrostowski, S. (2008). TIMSS 2007 international mathematics report.

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**Is Singapore too Different from the U.S. for Comparison?**

Size: 500,000 pupils, which is 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. Expectations: Singapore students are 2.5 times more likely than U.S. students to receive high-levels of math homework (8th grade TIMSS).

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**Results From U.S. Pilots of Singapore Math**

Pilot Site Characteristics Results North Middlesex, Mass Small district with stable population Large increase in percent of high-performing students (advanced level) Baltimore City Ingenuity Project Program for gifted students Large increase in high performing students and those above 75th percentile Montgomery County, MD Suburban school district with mixed income population Two of four schools showed substantial gains Paterson, NJ Poor school, over 40% annual student turnover No improvement over controls Washington, DC High-poverty, mostly LEP Large increase in proficiency Source: Ginsburg, Leinwand, Anstrom, and Pollock (2005); DC 2008 results reported under NCLB

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**Why is Singapore Math Successful in Singapore?**

The components of Singapore’s system – frameworks, texts, tests and teacher prep – are carefully aligned and reflect a higher quality than comparable U.S. components. See Education Commission of the States: International Benchmarking Toolkit (2009).

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**Math Frameworks: Singapore’s 2005 Topics and Outcomes Grades 1–6**

Total Topics Avg. Topics /Grade Avg. Grades /Topic Out-comes Avg. Outcomes /Grade No. Ratio to Sing. Ratio to Sing. Ratio to Singapore 40 15 — 2.3 232 39 California 42 20 1.3 2.9 305 51 Florida 54 2.6 4.2 1.8 640 107 2.7 Maryland 46 29 1.9 3.8 1.7 415 69 New Jersey 50 28 3.4 1.5 336 56 1.4 N. Carolina 41 18 1.2 1.1 217 36 .9 Ohio 48 26 3.3 370 62 1.6 Texas 19 2.8 265 44

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**Example: Singapore Exposure to Fractions Grades 2-6**

Primary 2: Concept of fraction as part of a whole Primary 3: Equivalent fractions Primary 4: Fraction of a set of objects Fraction of a quantity Improper fractions & mixed numbers Addition and subtraction of fractions Primary 5: Concept of fraction as division Product of fractions Primary 6: Concept of fractions as ratio

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**MD. VOLUNTARY STATE CURRICULUM – MATHEMATICS PREK – 3 **

KNOWLEDGE OF NUMBER RELATIONSHIPS AND COMPUTATION/ARITHMETIC Grade 1 Grade 2 Grade 3 2. Apply knowledge of fractions a) Read, write, and represent fractions as parts of a single region using symbols and models with denominators of 2 or 4 b) Read, write, and represent halves as parts of a set using pictures and models a) Read, write, and represent fractions as parts of a single region using symbols or models with denominators of 2, 3, or 4 b) Read, write, and represent halves or fourths as parts of a set using symbols, words, and models a) Read, write, and represent fractions as parts of a single region using symbols, words, and models· Assessment limit: Use fractions with denominators of 2, 3, or 4 b) Read, write, and represent fractions as parts of a set using symbols, words, and models· Assessment limit: Use fractions with denominators of 2, 3, or 4, and use sets of 2, 3, 4 items, respectively

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**Singapore and U.S. Treatment of At-Risk Students**

Supplementary after-school instruction lead by a specially-trained teacher (Grade 1+) Weaker math students identified for special track with more instruction and same content but at a slower pace (Grades 5-6) Students streamed based on Primary School Leaving Exam (Grade 7+) U.S. Compensatory education often taught by untrained teacher aides No Child Left Behind holds students to same standards and highly-qualified teachers. Hold schools rather than students accountable.

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**Textbooks: What We Examined**

Singapore’s two texts and two workbooks at each grade published by Ministry of Education U.S. Textbooks Traditional Text – Scott-Foresman Series (80% usage in elementary grades) Reform Text – Everyday Mathematics (20% usage in elementary grades)

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**Grade 1: Singapore Textbooks Have Fewer Lessons, More pages per Lesson, and More Pages of Exercises**

# Chapters # Lessons Total Pages Average Pages/ Lesson Pages of Development Pages of Exercises Other Pages Singapore 18 34 497 15 174 (35%) 261 (53%) 62 (12%) Scott Foresman 12 157 564 4 145 (26%) 169 (30%) 250 (44%) Ginsburg & Leinwand (2005). What the U.S. can learn from Singapore’s World-class mathematics system, AIR

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Singapore Math’s visual approach is well-suited for students whose first language Is not English

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**A Straight Forward U. S. Gr**

A Straight Forward U.S. Gr. 6 Pie Chart Problem Involving Summing to a Total Cost of Raising a Child to Age 18 (for each $100)

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A Singapore Gr. 6 Pie Chart Problem Requiring Strong Conceptual Understanding by Incorporating Angles Source: Singaporemath.com Inc (2003). Active Primary Math Series

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**How Challenging Are the Singapore and U.S. Assessments?**

% Multiple Choice % Multi-step Finding an Intermediate Unknown Singapore – 6 31 25 19% Florida – 8 52 12 8% New Jersey – 8 85 33 0% North Carolina – 6 100 8 North Carolina – 8 5 5% Ohio – 6 74 17 4% Texas – 6 7 2% Texas – 8 6 NAEP – 4 64 15 NAEP - 8 60 21

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**A Singapore Grade 6 Hard Problem You Won’t See on U. S**

A Singapore Grade 6 Hard Problem You Won’t See on U.S. Grade 8 State Assessments Source: Singapore MOE

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**Singapore Math Challenges U.S. Teachers in the Following Ways:**

Automaticity (e.g. mental math). Deep understanding of math concepts. Student-centered rather than teacher-centered textbook – fill-in omitted lesson materials. Builds on prior concepts. Vision of how to teach lessons.

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**Singapore & Other Math Standards**

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**Singapore’s Math is Good, but Their Food is Even Better!**

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Thank you If you have additional comments or questions, please contact me at: Alan Ginsburg (202)

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