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Singapore Math

Singapore Math . Chris Susanto For Trends and Issues in Education Layer A Assignment. In the beginning…. Traditional/classical math. Concepts: Based on direct instruction S tudents are shown one standard method of performing a task in a standard sequence

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Singapore Math

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  1. Singapore Math Chris Susanto For Trends and Issues in Education Layer A Assignment

  2. In the beginning…

  3. Traditional/classical math • Concepts: • Based on direct instruction • Students are shown one standard method of performing a task in a standard sequence • A task is taught in isolation rather than as only a part of a more complex project • Criticisms: • Over-emphasizes memorization and repetition • Fails to promote conceptual understanding • Fail to present math as creative or exploratory • Too few students master even algebra; many do well enough for standardized tests, not much beyond that

  4. Along comes …

  5. New math • Concepts: • Short lived in the 1960s, after the Sputnik crisis • Emphasized mathematical structure through abstract concepts like set theory and number bases other than 10 • Some focus was seen as exaggerated, even dogmatic. • Functions, diagrams, modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra • Criticisms: • Too far outside of students' ordinary experience • Teachers were required to teach material they did not fully understand • Parents could not help their children with homework

  6. Then (reluctantly) comes…

  7. Reform math • Concepts: • Algorithmic dependence is de-emphasized • Focus students' attention on the process leading to the answer, rather than the answer itself • Children in reform classes perform at least as well as children in traditional classes on tests of calculation skill, and considerably better on tests of problem solving • Criticisms: • Decreased focus on basic computation skills • Increased emphasis on exploration causes confusion • Abandoning teaching of standard arithmetic methods such as regrouping or common denominators

  8. Inevitably…

  9. Math Wars • Started with 1989 “Curriculum and Evaluation Standards for School Mathematics” from the National Council of Teachers of Mathematics (NCTM) • Debates: • How explicitly children must be taught skills based on formulas or algorithms • How much inquiry-based approach should be taught • Computation skills vs. reasoning skills • Fluency in calculations vs. conceptual understanding • When to start each, how much emphasis on each

  10. Cold War? • Reports/studies calming the dispute: • NCTM’s Principles and Standards for School Mathematics (2000) • NCTM’s Curriculum Focal Points (2006) There is inconsistency in the grade placement of mathematics topics, in how they are defined, and what students are expected to learn • National Mathematics Advisory Panel (2008) Recommendations that instruction should be entirely 'student centered' or 'teacher directed' are not supported by research Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other

  11. In a faraway land…

  12. Singapore • A small country in Southeast Asia • Size: 272 sqmi (smaller than Kansas City) • Population: 5.1 million (barely smaller than Missouri) • Multicultural country • 36% of population is foreign-born • Many languages: Malay, Chinese Mandarin, Cantonese, Tamil, etc. • Education represents 20% of the government’s budget • Several education tracks or streams: "Special", "Express", "Normal (Academic)", or "Normal (Technical)“ • Ideology: meritocracy and bilingualism; criticism: elitism • Ratio of students to teaching staffs: between 17 to 21 pupils • Special ed. Students is exempted from compulsory education, and there are no public schools for such children.

  13. Singapore Math • Rationale and development: • Singapore used to import textbooks and methods • Curriculum Development Institute of Singapore (CDIS) started publishing own textbooks in 1982 • In 1983, Singapore ranked 17 out of 26 countries tested in eighth grade Mathematics • By 1995, Singapore ranked number one out of 41 countries • Actually closer to traditional math, just ‘tweaked’ • Places greater focus on developing mathematical concepts and fostering mathematical problem solving • Consistent with NCTM Curriculum Focal Points

  14. Achievements: from TIMSS 2003 Average Math Scaled Scores by Country

  15. Singapore Math • Concepts: • Depth emphasized over breadth: more time on each topic • Fewer topics covered in a year; greater focus on mastery • Math concepts are exceptionally clear and simple so that ESL students (common in Singapore) can read it easily • Greater emphasis on mental math and word problems • Each semester builds upon preceding levels • Focuses on essential math skills, not re-teaching/remediation • Students master essential math skills at a more rapid pace • Uses a lot more multi-step process, pictorial, bar models • No frills: absence of clutter and distractions in textbooks • Clever sequencing of the topics minimizes the need for drills

  16. Attitude Metacognition Skills Processes Computation, Mental Math, Data Analysis Thinking Skills Heuristics Concepts Numbers, Geometry, Statistics, Algebra Singapore Math • Proficiencies

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

  18. Singapore Math teachesWHY THE MATH WORKS… not just the how.

  19. Strategies not Tricks! 12 • Number bonds help students learn math facts • Specific lessons develop mental math strategies 34.73 + 14.98 = 34.73 + 15 - .02 =49.71 • Bar modeling is used to solve word problems 3 ? 7 4 4 units = 12 1 unit = 12/4 = 3 3 units = 3 x 3 = 9

  20. Singapore Math • Pros • Great for visual learners: bar models, pictorials • Great for tactile learners: manipulatives and hands-on activities that build concrete understanding • Emphasis on conceptual understanding (“why” and “how”) • Cons: • Successes in the US has been limited to smaller districts; gains were not as impressive on average • It can be deceptively simple; needs work to cover the basics • Harder for those who learn from small pieces, then build up • Easier for those who learn and never forget, harder for some • Books direct from Singapore uses SI

  21. Opinion

  22. Opinion • There are many approach to solve math problems (usually) • Younger students DO need an anchor, something reliable • Once they develop the basic skills, then introduce more complex math and other approaches • Consistency is paramount: unlearning a set way is confusing, difficult, and often painful • Mental math skills can be useful, if nothing else to tip accurately • In all seriousness, the skill can be developed and can be useful in life • Singapore method may be good for students who learn by looking at the “big picture” then breaking it to pieces • It’s a whole new way of looking at math, needs adjustment time • Any method needs practice and guidance for mastery

  23. Ultimately Even Rebecca Black knows math can be…

  24. References and Links Bisk, R. (2007). Singapore Primary Math Textbooks: An Overview. PowerPoint. Ginsburg, A. (2006). The  Quality of U.S. and  Florida Math Instruction  Compared with Singapore,  a Recognized World Leader. PowerPoint. SMART Training (2010). What is Singapore Math and Why is My Kid Using It?. PowerPoint. http://en.wikipedia.org/wiki/Mathematics_education_in_the_United_States http://en.wikipedia.org/wiki/Math_wars http://en.wikipedia.org/wiki/Reform_mathematics http://en.wikipedia.org/wiki/Singapore_math http://en.wikipedia.org/wiki/Traditional_mathematics

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