Copyright 2007 Dr. Richard Bisk Singapore Primary Math Textbooks An Overview Richard Bisk Professor...

copyright 2007 Dr. Richard Bisk

Singapore Primary Math Textbooks

An Overview

Richard Bisk

Professor and Mathematics Department Chair

Worcester State College


Questions

1. What is the most important question in a math class?2. Why are people interested in Singapore Math?3. Why am I interested in Singapore Math?4. What’s different about Singapore Math?5. What are its key characteristics?6. What is mental math?7. What is model drawing?8. What do the books look like?9. Do teachers like it?10. Is there evidence that it’s effective?

wwwfac.worcester.edu/smip


But first … some math questions

9 ÷ 0 = ? And why?

Compute mentally: 13 x 98

David spent 2/5 of his money on a storybook. The storybook cost $12. How much money did he have at first?


TIMSS 2003 – Average Mathematics Scaled Scores by Country

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

Slovenia 479 Israel 496

Armenia 456 New Zealand 494

Norway 451 Slovenia 493

Iran, Islamic Republic of 389 Italy 484

Philippines 358 Armenia 478

Morocco 347 Serbia3 477

Tunisia 339 Bulgaria 476

Additional countries with 8th grade scores below Bulgaria’s are included in the complete study Hence the average of 466.


In 1983, prior to implementing this curriculum, Singapore ranked 17 out of 26 countries tested in eighth grade Mathematics.

Just twelve years later, in 1995, Singapore ranked number one out of 41 countries tested at that level and remained number one in both 1999 and 2003.


Professional Development

• “I never realized that I do not understand math until I had to teach mathematics from the Singapore textbooks.”

Teacher quoted in A.I.R. report prepared for U.S. DOE


The Big Issue “How vs. Why”

In our professional development program, we use the texts to help teachers develop a deep understanding of math so that they can teach for understanding.


What are the key characteristics of the K-8 Singapore books?

• Depth emphasized over breadth: More time is spent on each topic. Fewer topics are covered in a year. Greater focus on mastery.

Topics emphasized are consistent with the new NCTM Focal Points


Depth versus Breadth

Grade 1 Grade 3 Grade 6

Textbook Number of Lessons

Avg. pages/lesson

Number of Lessons

Avg. pages/lesson

Number of Lessons

Avg. pages/lesson

Singapore 34 15 42 12 24 17

Scott-Foresman

157 4 164 4 158 5

Everyday Math

110 2 120 2 113 4

(Source: American Institute for Research – “What the United States Can Learn From Singapore’s World-Class Mathematics System”)


What are the key characteristics of the K-8 Singapore books?

• Problem Solving Emphasis: Model drawing diagrams are used to promote understanding of word problems and provide a bridge to algebraic thinking.

• More Multi-Step Problems: Problems often require the use of several concepts.

• Mental Math: Techniques encourage understanding of mathematical properties and promote numerical fluency.


• Absence of Clutter and Distraction: Presentation is clean and clear and uses simple, concise explanations.

• Coherent Development: Topics are introduced with simple examples and then incrementally developed until more difficult problems are addressed.

• Teacher and Parent Friendly: Since mathematical content is clear, it is often easier for teachers to plan lessons. Parents can read the books and help children.

• Review of concepts is not explicitly incorporated into the curriculum. Students are expected to have mastered a concept once it has been taught.

• A high level of expectation is implicit in the curriculum.


Stress on Developing Conceptual Understanding: Students and teachers learn to focus on “why” not just “how.”


Emphasizes an understanding of place value and the distributive,

commutative and associative properties

MENTAL MATH


Compensation

99 + 28 = 99 + (1 + 27)= (99 + 1) + 27

---------------------------------------

72 – 59 = 73 – 60

Add 1 to each


MENTAL MATH

Multiplication facts with meaning

7 x 6 = (5 x 6) + (2 x 6)

8 x 6 = 2 x (4 x 6)

9 x 6 = (10 x 6) – (1 x 6)


PROBLEM SOLVING WITH MODEL DRAWING

The model drawing approach takes students from the concrete to the abstract stage via an intermediary pictorial stage.

Students create bars and break them down into “units.” The units create a bridge to the concept of an “unknown” quantity that must be found.

Students can learn to use this strategy in the primary grades and continue with it through the middle grades.


Bill has 7 cookies. He eats 4 cookies. How many cookies remain?

4?

7

Cookies


Maria has 10 cookies. Bill has 3 cookies. How many more cookies does Maria have?

Bill

Maria

3

10

?


Ali has $10. Joe has $2 more than Ali. How much do they have altogether.

Ali

Joe

$10

$2?


Example (grade 3): The sum of two numbers is 36. The smaller number is one-third of the larger number. Find the two numbers.

larger

smaller

4 units = 36

?

?

36

1 unit = 93 units = 27

The numbers are 9 and 27


Example (grade 4): David spent 2/5 of his money on a storybook. The storybook cost $12. How much money did he have at first?

Solution

David's Money ?

│-----12----│

2 units = 12 5 units = 30David started with $30.

1 unit = 6


Example (grade 5): Jill and Bob share $80 in the ratio 3:2. How much money did Bob get?

Jill

Bob

$80

?

5 units = 80 2 units =32

1 unit = 16 Bob gets $32


TEACHERS COMMENTS

• “I never realized that I do not understand math until I had to teach mathematics from the Singapore textbooks.”

• “Topics are taught for mastery. Fewer topics taught in greater depth. Review is usually done in the context of a new topic or through use of word problems. Emphasizes logic and visualization.”


“… mastery of basic algorithms is expected in the early grades…. The students also learn why certain formulas are used rather than just learn how to apply the formulas. The most valuable aspect of Singapore Math is that the program encourages active thinking and emphasizes the communication of math ideas.”


American Institute for Research Report Comparing US and Singapore Math Education Systems

• Table 7-1: Outcomes of Pilots Studies

• http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf

• Page 146 of Adobe document.

http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf



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