copyright 2007 Dr. Richard Bisk Singapore Primary Math Textbooks An Overview Richard Bisk Professor and Mathematics Department Chair Worcester State College

copyright 2007 Dr. Richard Bisk 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

copyright 2007 Dr. Richard Bisk 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?

copyright 2007 Dr. Richard Bisk TIMSS 2003 – Average Mathematics Scaled Scores by Country Fourth gradeEighth grade Country Average scoreCountry Average score International average495International average466 Singapore594Singapore605 Hong Kong SAR 1,2 575Korea, Republic of589 Japan565Hong Kong SAR 1,2 586 Chinese Taipei564Chinese Taipei585 Belgium-Flemish551Japan570 Netherlands 2 540Belgium-Flemish537 Latvia536Netherlands Lithuania 3 534Estonia531 Russian Federation532Hungary529 England 2 531Malaysia508 Hungary529Latvia508 United States 2 518Russian Federation508 Cyprus510Slovak Republic508 Moldova, Republic of504Australia505 Italy503United States504 Australia 2 499Lithuania New Zealand493Sweden499 Scotland 2 490Scotland Slovenia479Israel496 Armenia456New Zealand494 Norway451Slovenia493 Iran, Islamic Republic of389Italy484 Philippines358Armenia478 Morocco347Serbia Tunisia339Bulgaria476 Additional countries with 8 th grade scores below Bulgaria’s are included in the complete study Hence the average of 466.

copyright 2007 Dr. Richard Bisk 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.

copyright 2007 Dr. Richard Bisk 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

copyright 2007 Dr. Richard Bisk 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.

copyright 2007 Dr. Richard Bisk 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

copyright 2007 Dr. Richard Bisk Depth versus Breadth Grade1 3 6 TextbookNumber of Lessons Avg. pages/ lesson Number of Lessons Avg. pages/ lesson Number of Lessons Avg. pages/ lesson Singapore Scott- Foresman Everyday Math (Source: American Institute for Research – “What the United States Can Learn From Singapore’s World-Class Mathematics System”)

copyright 2007 Dr. Richard Bisk 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.

copyright 2007 Dr. Richard Bisk 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.

copyright 2007 Dr. Richard Bisk Stress on Developing Conceptual Understanding: Students and teachers learn to focus on “why” not just “how.”

copyright 2007 Dr. Richard Bisk Emphasizes an understanding of place value and the distributive, commutative and associative properties MENTAL MATH

copyright 2007 Dr. Richard Bisk Compensation = 99 + (1 + 27) = (99 + 1) – 59 = 73 – 60 Add 1 to each

copyright 2007 Dr. Richard Bisk 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)

copyright 2007 Dr. Richard Bisk 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.

copyright 2007 Dr. Richard Bisk Bill has 7 cookies. He eats 4 cookies. How many cookies remain? 4? 7 Cookies

copyright 2007 Dr. Richard Bisk Maria has 10 cookies. Bill has 3 cookies. How many more cookies does Maria have? Bill Maria 3 10 ?

copyright 2007 Dr. Richard Bisk Ali has $10. Joe has $2 more than Ali. How much do they have altogether. Ali Joe $10 $2 ?

copyright 2007 Dr. Richard Bisk 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 = 9 3 units = 27 The numbers are 9 and 27

copyright 2007 Dr. Richard Bisk 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 ? │ │ 2 units = 12 5 units = 30 David started with $30. 1 unit = 6

copyright 2007 Dr. Richard Bisk Example (grade 5): Jill and Bob share $80 in the ratio 3:2. How much money did Bob get? Jill Bob $80 ? 5 units = 802 units =32 1 unit = 16Bob gets $32

copyright 2007 Dr. Richard Bisk 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.”

copyright 2007 Dr. Richard Bisk “… 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.”

copyright 2007 Dr. Richard Bisk American Institute for Research Report Comparing US and Singapore Math Education Systems Table 7-1: Outcomes of Pilots Studies ore%20Report%20(Bookmark%20Version ).pdf ore%20Report%20(Bookmark%20Version ).pdf Page 146 of Adobe document.