The Quality of U.S. and Florida Math Instruction Compared with Singapore, a Recognized World Leader

1. 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 of the U.S. Department of Education

2. Presentation Outline • Singapore’s world-class math performance • Overview of Singapore’s education system • Comparison of Singapore-Florida math standards • Comparison of Singapore-U.S. on other math system components : textbooks, assessments and teachers • Results of Singapore textbook pilots in the U.S. • Implicationsfor adopting/adapting Singapore approachesto improve Florida’s math results

3. 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

4. 1. Mathematics PerformanceWhy 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)

5. 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 report.http://timss.bc.edu/PDF/t03_download/T03_M_Front.pdf

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

7. U.S. Students Do Much Better in International literacy 2001 Source: 2001 PIRLS

8. 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, Teaching the New Basic Skills)

9. TheSingapore Education Service - Moulding the Future of Our Nation 2. Singapore EducationMission Moulding the future of our nation

10. TheSingapore Education Service - Moulding the Future of Our Nation 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

11. Primary School Leaving Exam EM 2 70% EM 3 10% Primary Education EM1 20% Orientation Stage (Primary 5 – 6) Foundation Stage (Primary 1 - 4) Language Learning & Mathematics

12. TheSingapore Education Service - Moulding the Future of Our Nation Fewer School Dropouts % Year

13. 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).

14. 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

15. 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

16. Attitude Metacognition Skills Processes Computation, Mental Math, Data Analysis Thinking Skills Heuristics Concepts Numbers, Geometry, Statistics, Algebra Singapore’s Proficiencies Are Centered Around Problem Solving

17. Florida’s Desired Math Proficiencies?

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

19. Exposure to Math Topics and Outcomes in Singapore and 7 U.S. States : Grades 1–6

20. Fla. Numbers Standards Gr. 1: Lack Focus

21. Fla. Numbers Standards Gr. 1: Lack Focus

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

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

24. Fla. Geom. Gr. 1: Vague outcomes

25. Singapore Geometry Pr. 1:Shapes and Patterns

26. Singapore Logically Builds-up Math Topics Across Grades: Numbers

27. Singapore Logically Builds-up Math Topics Across Grades: Geometry

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

29. 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

30. Singapore Identify students for supplementary after-school instruction by a specially-trained teacher (Grade 1+). Weaker math students identified for special track with more math instruction and similar content but at a slower pace (Grades 5-6) Students are streamed based on their Primary School Leaving Exam scores(Grade 7+) U.S. State frameworks don’t differentiate students. Traditionally, compensatory education is often taught by untrained teacher aides. No Child Left Behind holds students to same standards and highly-qualified teachers. No Child Left Behind holds schools rather than students accountable. Singapore’s Framework Addresses At-risk Students: U.S. State Frameworks (including Florida) Do Not

31. Draw the smallest possible square. Draw the biggest possible square. Draw all possible squares and find the area of each. New Directions for Singapore Math StandardsThink Things Through: Pr. 3-Squares

32. New Directions for Singapore Math StandardsT3: 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.

33. 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.” MOE China

34. 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

35. A Meaningful Math-Science Example of “Concrete Models & Real-world Problems” Source: http://phet.colorado.edu/web-pages/simulations-base.html

36. 4. Comparison of Singapore-U.S. on other math system components • Textbooks • Assessments • Teachers

37. 4a. TextbooksGrade 1: Singapore Textbooks Have Fewer Lessons, More Pages per Lesson, and More Pages of Exercises

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. Singapore Lesson: Fractions Pr. 2B

44. Gr 6 Lessons by Content Area: Singapore Stresses Number, Measurement, and Geometry; U.S. Algebra and Data

45. Singapore’s Relative Strength Is Numbers and Measurement; U.S. Relative Strength is Data and Weakness is Geometry: TIMSS Gr. 8 Source: Mullis et al., 2004

46. 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 3 of 12 = 8 Abstract level : Source: Singapore MOE

47. Visual Approach: Use Model Drawing

48. Singapore Textbooks Use Scaffolding Within Multi-step Problems: Gr. 6 Pie Chart Problem Incorporating Angles Source: Singaporemath.com Inc (2003). Active Primary Math Series

49. 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)

50. 4b. AssessmentsWhat we examined • Singapore Grade 6 Primary School Leaving Exam • U.S. NAEP Grades 6 and 8 • Five State Assessments at Grades 6 and 8