Singapore Math

Chris SusantoFor Trends and Issues in Education

Layer A Assignment

In the beginning…

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

Along comes …

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

Then (reluctantly) comes…

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

Inevitably…

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

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 researchConceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other

In a faraway land…

Singapore• A small country in Southeast Asia

– Size: 272 sq mi (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.

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

Fourth grade Eighth grade

CountryAverage

score CountryAverage

score

International average 495 International average 466

Singapore 594 Singapore 605

Hong Kong SAR1,2 575 Korea, Republic of 589

Japan 565 Hong Kong SAR1,2 586

Chinese Taipei 564 Chinese Taipei 585

Belgium-Flemish 551 Japan 570

Netherlands2 540 Belgium-Flemish 537

Latvia 536 Netherlands1 536

Lithuania3 534 Estonia 531

Russian Federation 532 Hungary 529

England2 531 Malaysia 508

Hungary 529 Latvia 508

United States2 518 Russian Federation 508

Cyprus 510 Slovak Republic 508

Moldova, Republic of 504 Australia 505

Italy 503 United States 504

Australia2 499 Lithuania3 502

New Zealand 493 Sweden 499

Scotland2 490 Scotland1 498

Achievements:from TIMSS 2003Average MathScaled Scoresby Country

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

Singapore Math• Proficiencies

MMMAAATTTHHHEEEMMMAAATTTIII CCCAAALLL PPPRRROOOBBBLLLEEEMMM SSSOOOLLLVVVIII NNNGGG

Numbers, Geometry, Statistics, Algebra

Computation,Mental Math, Data Analysis

Thinking Skills Heuristics

17

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

Textbook #Topics

# Les-sons

Average Pages/Lesson

Pages of Develop-

ment

Pages of Exer-cises

Other Pages

Sing-apore 13 34 15 174

(35%)261

(53%) 62 (12%)

Scott Fores-man

25 157 4 145 (26%)

169 (30%)

250 (44%)

Singapore Math teaches

WHY THE MATH WORKS… not just the how.

Strategies not Tricks!

• 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

4

3

7

12

?

4 units = 121 unit = 12/4 = 3 3 units = 3 x 3 = 9

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

Opinion

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

UltimatelyEven Rebecca Black knows math can be…

References and LinksBisk, 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_Stateshttp://en.wikipedia.org/wiki/Math_warshttp://en.wikipedia.org/wiki/Reform_mathematicshttp://en.wikipedia.org/wiki/Singapore_math http://en.wikipedia.org/wiki/Traditional_mathematics