VIEWS: 29 PAGES: 64 POSTED ON: 1/2/2012 Public Domain
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