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Try Singapore Math Textbooks

Your students will learn Math

By Jerome Dancis, Ph.D. (math)

Associate Professor Emeritus

Math Dept, Univ of Maryland

College Park, MD 20742-4015

Math Education Website: www.math.umd.edu\

301 345 2973 (c) 301 448 8132

The only really good K-6 math textbooks in English are the Singapore Math textbooks, available at the new website

Warning, Grade 5 Singapore Math is comparable, but better than Grade 6 here.

Also it builds on Grade 4 Singapore Math, which builds on grade 3 Singapore Math.

Just noticed on the website, there are "Elementary Mathematics for Teachers" books, for use in conjunction with the Singapore Grades 3-6 Math Books, first half of each year only. (http://www.singaporemath.com/Elementary_Math_for_Teachers_Complete_Package_p/emftcp.htm) A Math professor friend taught a college class for future elementary school teachers from these books, last fall, and really liked them.

Just noticed on the website, there is *"The Essential Parents' Guide to Primary Maths",* written primarily for parents. "Parents can use this guide to learn and master various strategies to help their children solve challenging and non-routine mathematical problems encountered at the upper primary level."

Many Math professors, who have looked at the Singapore K-6 Math Books, are strong advocates of them because these books

1. Do an especially good job in training students in Basic Skills and

2. Do an especially good job in providing students with Conceptual Understanding and

3. Provide an especially good background in Arithmetic and Arithmetic word problems, for the learning of Algebraic calculations and for learning how to solve Algebraic word problems.

4. Do an especially good job in training students in non-trivial Arithmetic word problems; while American texts largely avoid non-trivial Arithmetic word problems.

Grade 5 or 6 students, trained in the Singapore math model-drawing approach to problems, will consider the following Tart and Triple Ratio Problems to be child's play.

*Tart Problem* . (From a 5th grade Singapore math textbook) "Mrs. Chen made some tarts. She sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make?" [From http://www.cbmsweb.org/NationalSummit/Plenary_Speakers/ma.htm]

*Triple Ratio Problem* . Three boys, Juan, Seth and Jared shared a number of stamps in the ratio 3 : 5 : 7. If Seth received 45 stamps, how many more stamps did Jared receive than Juan?

[ From page 25 of the U. S. Edition of the Singapore Primary Mathematics Workbook 5B (second term of Grade 5) ]

Challenge: Try the Tart and Triple Ratio Problems on Grade 7 or 8 students.

5. The main guideline for American textbooks, is "the two-page spread"; each lesson is restricted to two pages, whether it is understandable or not, often it is not. The main guideline for Singapore Math Books is that they be understandable by students; there is no two page restriction.

6. American math textbooks have so many math errors, that t he 1999 California Framework and Standards introduced a unique requirement: K-6 Math textbooks be free of math errors. This applies *only* to the California editions. Singapore math textbooks have few if any Math errors.

7. Being able to do Tart and Ratio Problem type problems is important for doing organized logical analysis in science and economics. Greatly increasing the percentage of Grade 5 students who can do this type of problem would be a worthy goal/challenge. And, it would enable middle school science teachers to considerably raise the level of arithmetic-based science lessons.

The Tart Problem, above is quite similar to the following Geese Problem. This Geese Problem was an SAT Math test problem; one that the SAT rated at the highest level of difficulty. [It was Question #25 of Section 4 of the May 2000 Math SAT; the SAT rated it as Level #5 on its scale of 1 to 5.] Students, trained on The Tart Problem in Grade 5, will consider This Geese Problem to be child's (Grade 5 level) play.

*Geese Problem.* (SAT Level 5) "A flock of geese on a pond were being observed continuously.

At 1:00 P.M., 1/5 of the geese flew away.

At 2:00 P.M., 1/8 of the geese that remained flew away.

At 3:00 P.M., 3 times as many geese as had flown away at 1:00 P.M. flew away,

leaving 28 geese on the pond.

At no other time did any geese arrive or fly away or die. How many geese were in the original flock?"

Singapore math textbooks provide teachers with a ready made coherent course/curriculum; it's one less important thing for a teacher to worry about.

The Singapore textbooks were written in English for Singapore children, for whom English is a second language.

John Hoven is a local expert on Singapore Math. He is giving presentations at MD schools.

John Hoven was co-president, Gifted and Talented Association of Montgomery County, MD

*Three drawbacks of Singapore math textbooks* :

(*) Currently, fully certified K-8 teachers, even those with "endorsements" as a "highly qualified" middle school math teacher, may not be required to know how to do the Tart and Triple Ratio Problems, above.

(^) This is ameliorated by the complete explanations in the textbooks themselves. The textbooks are written to be understandable by students, so they should also be understandable by teachers. (In contrast, in American textbooks, the not-always-complete explanations are split between the text and the teachers' manual). It is still wise to have serious staff development for the teachers.

(^) There is a college textbook, "Elementary Mathematics for Teachers", by Math professors Thomas Parker and Scott Baldridge, which is based on and provides instruction for teachers on the methods of Singapore math books. ( Scott Baldridge is a friend of J. Dancis )

(^) There are "Elementary Mathematics for Teachers" books, for use in conjunction with the Singapore Grades 3-6 Math Books, first half of year only.

(*) There are no answer books. When Singapore books were handed to the teachers at one school, the first question was: Where are the answer books? When informed, that there were none, the teaches rolled their eyes, which was interpreted as "Then why are we even considering using these books?" Two years later, these teachers were all in favor of the books.

(*) Singapore math textbooks omit the superficial data analysis and probability required for MD state exams. Supplementary material for test prep could by written and provided to teachers.

Middle school math teachers are *not* required to know how to do (never mind how to teach) the Triple Ratio Problem, above. The No Child Left Behind Act (NCLB) requires that middle school math teachers be "highly qualified" in math. The Maryland State Department of Education chose the Praxis II middle school math content exam, as a criteria for its official "endorsement" as a "highly qualified" middle school math teacher.

Two of the twelve sample multiple-choice items, for the Praxis II "middle school math" content exam for teachers [on the Web at ftp://ftp.ets.org/pub/tandl/0069.pdf)] are ratio questions; both are simple ratio questions. Neither of these two sample questions requires calculations as sophisticated as required by the Triple Ratio Problem, above.

*Excerpts* from an Associated Press article, Date: Sun, 14 May 2000

"The curriculum believes in the students' abilities," [Professor of Mathematics, Yoram] Sagher said of books approved by Singapore's Ministry of Education. "One of the effects of these books on all teachers is that they are much more courageous about giving harder problems to students."

Singapore's eighth-graders ranked No. 1 in math among 41 nations tested by the Third International Mathematics and Science Study, released in 1996. American eighth-graders came in 28th.

The Singaporean textbooks - written in English, the language of instruction there - are lightweight paperbacks filled with sample problems and step-by-step explanations that help students understand not only how to use a formula, but why.

Felicity Ross, a math teacher at Baltimore's Robert Poole Middle School, said U.S. textbooks tend to jump from topic to topic without helping students understand the basic concepts that connect all math problems.

The Singaporean texts, with their multistep word problems and emphasis on logic, develop skills that help children solve all types of problems - even those they've never tried, she said. "They're more confident problem-solvers in general," she said. "I definitely think the textbooks have something to do with it."

From my friend, retired community college math professor Herb Gross:

This year I taught in-service math courses to over 80 kindergarten and prekindergarten teachers in New Bedford, MA. As part of the course each of the teachers was given a copy of the Singapore math books for first grade and kindergarten. I wanted the teachers to have these books because they came the closest to teaching basic arithmetic in a way that was similar to what I was teaching. The teachers were under no obligation to use the books nor were they required to examine and evaluate them. The books were simply a gift. Unsolicited, over 50 teachers sent me messages telling me how much they liked the books and how helpful they were. Several wanted permission to make copies and use them in place of the books the school district was using.

These were teachers who, for the most part, had been previously intimidated by math. Their average score on the pretest was 36% [the teachers were not well versed in mathematics]. Their posttest average was 70%. In fact, that's one reason they were in the course and why Mass Insight Education offers the program. The point is that most elementary school teachers are not comfortable with mathematics and as a result they tend to teach math in the same mechanical way in which they were taught (One of the teachers commented that prior to our course all of her mathematical knowledge was faith based).

The Singapore model drawings make it almost impossible for students not to grasp what a fraction means and how to understand the arithmetic of fractions.

When the material is not being presented well by the teacher, the Singapore texts lend themselves better to self-study than most other textbook series I've been shown.

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Singapore Math is a distinctive Math Syllabus for Elementary School (Aged 7 to 12). The key characteristics of Singapore Math is that it promotes *visual learning through drawing models*, rather than using algebra which may not be well understood by elementary school students.

Using this method, students can actually understand the math, rather than just following procedures. Singapore Math is highly ranked and esteemed overseas, and used as alternative textbooks in countries like the United States. It is also a excellent syllabus for home school children.

This is the question that everyone must be asking “What is so good about Singapore Math?” To answer this question objectively, we have to trace the history of Maths back to the ancient Greeks. During the time of ancient Greeks, mathematicians like Euclid viewed Mathematics mainly as the study of Geometry. Everything in Math could be expressed in pictures or diagrams. However, later on as Mathematics progressed, the shift of emphasis went to Algebra. Mathematicians like Descartes started the revolution whereby almost every field in Mathematics could be expressed in algebraic equations, with no need to refer back to a picture or diagram.

There are pros and cons of Algebra versus Geometry, but for young children, it is clear that most kids are visual learners. That is where Singapore Math modelling method starts to shine. Singapore Math transforms a word problem into a geometry problem, where magnitudes of numbers are represented typically by a bar chart or model. This enables children to actually visualize the Math problem at hand, and solve the problem like a geometric puzzle, rather than a system of algebraic equations.

The power of Singapore Math can be seen through long Word Problems, typically worth 5 marks each. The wall of text can initially frighten the child, and the untrained student may not know how to start. However, the student who is trained in Singapore Math Technique will know how to start. The way to start is typically to draw a Singapore Math Model, which will be taught in the books recommended above.

*Example of a Real Life Singapore Math Question*

Q) Julia, Ken and Sass had $38 282 altogether. Julia had $1065 more than Ken and thrice as much as Sass. How much did Sass have?

[Taken from Primary 5 (Age 11) CHIJ CA1]

This is a typical question that the Singapore Math Technique is catered to. This is not the most difficult question definitely, the most difficult questions are from Primary 6 (Age 12) preliminary exam questions. Note that students from age 11 onwards have the help of calculators to help them to do arithmetic.

So how would we start? Starting the question is the hardest part in Singapore Math. As a tutor, I have observed that most students who get the starting part correct will be able to derive the correct answer. (Careless mistakes is another common problem for young kids, check out this post on How to reduce careless mistakes.)

First, we should draw a simple Model as such:

Hand drawn Singapore Math Model

After this, the solution should be clear to the Singapore Math-trained student. We need to add $1065+$38282=$39347, which represents 7 units. Then, $39347 divided by 7 is $5621, which is one unit. Thus, Sass has $5621.

Note that even though on hindsight our Singapore Math model is not to scale (1 unit is $5621 should look longer than $1065), the answer turned out correct. There is no way to know a priori how long a unit should look like, hence the important part is that Ken’s amount should NOT in anyway look like one unit otherwise there is a chance of misinterpretation. This is a very common mistake while drawing Singapore Math models.

Some students may no doubt find Singapore Math too easy or too difficult. If you are looking for more challenging Singapore Math questions, you may want to check out GEP Math or Math Olympiad, which is the epitome of Singapore Math. It is well known that the more challenging Singapore Math questions have a Math Olympiad flavor.

For precocious students, Singapore Math is an ideal way to teach very young children Math. As it is a very visual method, Singapore Math is very suitable for young kids. For starters, it is possible to use teaching tools such as Place Value Disks (140 Disks: 20 for each of 7 values), Singapore Math Manipulatives (Grades 3-6) to teach children the idea of place values like ones, tens, hundreds, and so on.

As a Singaporean student who has undergone the entire Singapore Math training from Primary to Tertiary level, I do know of some disadvantages of the Singapore Math method. However, the benefits severely outweigh the disadvantages. The downsides are that some questions with irregular numbers for example “Alice has 2.5 times the number of apples as Ben” are not easily drawn with models. However, the well-trained Singapore Math student will be able to deal with this and draw 5 units for Alice, and 2 units for Ben. Singapore Math is not a permanent learning solution, no one expects a university student learning quantum mechanics to still draw Singapore Math models to solve simple equations. However, as a bridge to algebra for young children, Singapore Math provides a really good foundation for kids to have a feel of Math. It is really empowering to able to intuitively understand a question and solve it for children, rather than be told to solve simultaneous equations mindlessly without understanding.

Despite the Singapore Math Model Method seeming like an alternative to Algebra, the truth is that they are not mutually exclusive. The most adept students at age 12 are able to use both Singapore Math Model Methods and Algebra, depending on which suits the situation better. Algebra can be a good last resort if the model is hard to draw. Books like the extremely popular Algebra Survival Guide Workbook: Thousands of Problems To Sharpen Skills and Enhance Understanding can serve to increase the algebra skills of children. Basically, at age 12 if a child can solve simultaneous equations in two variables, that is already a very very commendable achievement and that will enable him/her to solve Singapore Math problems with ease.

One of the most famous students the Singapore Math system has produced is probably Lim Jeck, an IMO (International Mathematical Olympiad) perfect scorer. He is a born and bred true Singaporean, and his achievements have made Singapore proud. (Getting an IMO Perfect Score 42/42 is arguably harder and rarer than getting an Olympic Games Gold Medal, since every Olympic Games will definitely have a Gold Medalist, but not every Math Olympiad each year has a Perfect Scorer.) Read more about Math Olympiad Books to understand the beauty and ingenuity of Math Olympiad questions.

This may be one concern that parents have. Yes, Singaporean students are often reported to lack creativity, but to be honest this has nothing to do with Singapore Math. Singapore Math, if anything, actually promotes creativity. The idea that Math is a boring subject where one simply follows algorithms to produce the answer is really not accurate. Using Singapore Math, each question can be solved in a variety of ways, especially the long word questions. That is why for Singapore Math, it is important to write down the working rather than just the answer. The working is the important part of the question since it enables the teacher to see whether the student is thinking correctly or is he just getting the answer due to chance. As a tutor, I often see students randomly adding, subtracting and dividing numbers and miraculously arriving at the right answer. Or otherwise, sometimes students literally make the proverb “Two wrongs make a right” true by making two mistakes that cancel each other out and arriving at the right answer. Parents teaching from Singapore Math books can look at the student’s working to check out if such a thing is happening.

Other than Singapore, many other countries are using Singapore Math Textbooks. The good thing is that Singapore uses the metric system (i.e. meters and kilograms, rather that the more archaic and less scientifically compatible feet and pounds). Countries using Singapore Math include the United States, Canada, United Kingdom, Israel, Philippines. Many parents also buy Singapore Math textbooks for supplementary home schooling. Singapore’s good performance at PISA has lead to greater usage of Singapore Math books in many nations.

The typical idea of Singapore Math is that it is for elementary school children only (i.e. from age 7 to 12). This is not really true. Although the Singapore education system from age 13 to 16 is based on the UK O Levels System, it is uniquely Singapore in the sense that the questions of Singapore O Levels are set independently by Singapore. It is a famous/infamous opinion that Singapore O Levels / A Levels are the hardest in the world, being more difficult than the UK or any of the British former colonies like Hong Kong. To learn more about Singapore Math after the elementary school level, check out Additional Maths 360 , a book by Singaporean authors. Additional Maths is a challenging version of Singapore Math for High School students (Grade 7 , Grade 8, Grade 9 or Grade 10). Students who have learned the Singapore syllabus may want to proceed on to the high school version of Singapore Math. I personally used an earlier version of this textbook for my studies some years ago.

Which is better: Singapore Math or Common Core? As a Singaporean, I am definitely more familiar with Singapore Math, but I also read news on Math and education very frequently and hence am acquainted with the Common Core in the USA.

Firstly, Singapore Math places much less restriction on the method of solving the questions. Although algebra may be slightly frowned upon, it is accepted and given full marks if the answer is correct. There is no restriction of forcing students to use “number bonds” to add 7+7 and things like that. Students can use mental arithmetic, traditional working or even counting with fingers if they wish.

Singapore Math uses the traditional method of subtracting using the traditional “Borrowing” Concept

No doubt the Common Core approach also has its merits, especially for very weak students. The step by step approach, although extremely tedious and convoluted, is great for beginners. However, for students who have already mastered subtraction, personally I feel they should be allowed to use any method. 🙂

Singapore Math usually does not incorporate the Abacus, but students can incorporate abacus training while doing Singapore Math questions. Despite abacus being viewed negatively by some as “rote learning” and hence not true math, for young kids the main problem they are facing are simple addition, subtraction, multiplication and sometimes division problems. Mastering the four operations is a necessary step towards mastering Singapore Math. Hence, students can supplement their training with Abacus training. A recommended Abacus to purchase is this high quality Abacus: Japan Japanese Standard Abacus Soroban Tomoe Four balls 23 figures . Abacus Mind Math Level 1 Workbook 1: (of 2) Excel at Mind Math with Soroban, a Japanese Abacus would be a good book for beginners starting to learn the abacus. As for concerns whether the abacus can be brought into the exam hall, parents can note that students who are proficient in abacus can utilize mental abacus techniques to perform calculations with an imaginary abacus. No physical abacus is used.

As a tutor with many years experience, I can safely say that yes, Singapore Math does actually work. Especially for weaker students, the model drawing aspect of Singapore Math enables students to start the question. I always advise students to start by drawing a model. The hardest part of a journey is always taking the first step. After taking the first step of drawing the model, many of the students will naturally see the way to proceed. It may sound magical but it is truly happening on a daily basis. Parents can purchase a comprehensive set of Singapore Math books like CARSON DELLOSA SINGAPORE MATH BUNDLE GR 7 (Set of 3) to start their Singapore Math journey.

For students who prefer the high-tech way of learning, yes, there are Singapore Math CD ROMs available for sale online. One of them is Math in Focus: Singapore Math: Teacher One Stop CD-ROM Course 1 . Rated very highly on Amazon, this CD is a good bargain. A CD Rom can actually hold more information than an encyclopedia! After viewing the Teacher CD-ROM, one can proceed to generate worksheets using the Math in Focus: Singapore Math: ExamView Assessment Generator Course 1 . Singapore Math does require some practice to perfect the Singapore Math techniques, so the Exam Generator will come in handy.

Technically speaking, Singapore Math is not a novel or new idea. Since the time of ancient Greeks, mathematicians have known the benefits of using diagrams to represent Math problems. Singapore Math is officially founded in 1981, where the Singapore Ministry of Education Curriculum Development board started to produce its own textbooks. Ever since then, other countries have started using Singapore Math textbooks as their curriculum.

There are a few famous Singapore Math Book authors that most students have heard of. One of them is Dr Yeap Ban Har (author of Every Child Can Do Math ). Dr Yeap teaches mathematics at the National Institute of Education in Singapore, which trains teachers. Hence, Dr Yeap can be said to be a teacher of teachers.

Another famous Singapore Math Book author is Dr Fong Ho Kheong (author of Math in Focus : The Singapore Approach Student Book, Grade 3A ). Dr Fong earned his PhD from King’s College London, specializing in Math Education. He is the author of many textbooks both locally in Singapore and in the USA.

Learning Singapore Math from the above two authors is really excellent, equivalent to learning a martial art from a true grandmaster. The above two authors can be said to be some of the leading proponents of true Singapore Math.

Since students learning Singapore Math are typically of a very young age, parental guidance is really important at this stage. Parents can read up more about Singapore Math on the internet, and try out some of the sample questions. Guidebooks like The Parent Connection for Singapore Math: Tools to Help Them Get It & Get Behind It will enable parents to understand what is going on in the Singapore Math curriculum. Parents should try to solve some of the Singapore Math questions on their own, it is motivational for children to know that their parents can solve the question too!

Motivation is a huge factor in learning, including Singapore Math. Sometimes it is possible to get caught up in other minor details where the main problem lies with the child’s motivation to learn. Like all other subjects, learning Singapore Math requires an open mind and a willingness to learn. Parents from the States can check out this book Motivate Your Child: A Christian Parent’s Guide to Raising Kids Who Do What They Need to Do Without Being Told to try to get your child motivated and hyped up about learning Singapore Math! Also check out even more motivational books here.

Also, all work and no play makes Jack a dull boy, there is nothing better than some Math games to let your child play and learn at the same time! Learning Resources Money Bags Board Game is a fun game that lets children practice the most useful skill in math — counting money and making change. This is surely one skill that all children and adults need to know!

Singapore Math books sometimes have many terms and vocabulary that sounds very intimidating. Mention “Singapore Math manipulative” and to be honest, the average Singaporean kid learning the true Singapore math will have no idea what that is. Same goes for “Singapore Math Number Bonds”, “Partial Quotient”, “Branching” and many other terminologies. The truth is, the names don’t matter much at all, it is much more important to know the Why and How, than the terms. That is why books like Why Before How: Singapore Math Computation Strategies, Grades 1-6 are good! However, if you are unsure of a certain Singapore Math term do post it in the comments, and we will try to research to find out what it means.

I will be writing more on the topic of Singapore Math (intending to make this page an encyclopedic reference on Singapore Math), and if you have any comments or questions do post them below! 🙂

We have compiled a list of *Top 5 Best selling and Top rated Singapore Math Books* on Amazon. This list is more targeted towards parents and students living outside Singapore, like in the United States. Students in Singapore are already breathing and living Singapore Math!

Hope this list will help you in finding the Best Singapore Math Books for your child. The reviews are from actual customers on Amazon. We also added a lot of comprehensive information about Singapore Math at the bottom of the post.

Note: This series also has other Grades other than Grade 2.

Amazon Review: This math practice book contains wonderful teaching strategies from the Singapore math program including number bonds and counting on. This would be a good book for homeschooling. We use it as an enrichment tool when we have a little extra time during vacations or on weekends.

I would recommend it to parents who would like to teach their struggling kids math, because it tells you how to teach these concepts.

Amazon Review: I really thought learning Singapore Math would be difficult, but I can really do this! Now I am comfortable teaching it.

Amazon Review: Get a complete math curriculum in one with this specially bundled package of Singapore Math learning. Singapore Math is one of the leading math programs in the world! Each grade-appropriate set includes level A and B of the Singapore Math Practice series, 70 Must-Know Word Problems, Mental Math, and Step-by-Step Problem Solving. So, jump start your math learning today!

Amazon Review: I’m not an expert. I have taught Singapore Maths to my son for four years and will start another soon. I use Singapore Maths curriculum as well as the Intensive Practice books. Not for the faint of heart! I read this book from cover to cover and found it to be informative and a very welcome refresher for me. I welcomed the tips and suggestions throughout. For example the suggestion of reading problems reflectively, which as a parent I sometimes assume my little guy does, but perhaps not. I highly recommend this book as an additional resource when teaching Singapore Maths. I wish I knew about it from the beginning.

Amazon Review: I am a Math Tutor and a huge fan of the Singapore books. This book is great to use for students who are looking for challenging enrichment problems. The strategies gone over in this book can also be applied in the classroom and on standardized tests for specialized high schools.

Written by Dr Yeap Ban Har, a famous co-inventor of the Singapore Math system. This book will be very useful to unleash every child’s hidden math potential.

This comprehensive book includes an Audio CD and Interactive Whiteboard. Rated highly at 4.6 stars, this book is a good buy if it is within your budget. It teaches a variety of topics like Number Lines, Fractions, Geometry, Measurement, all core topics of the Singapore Math Curriculum.

Singapore Math: Place Value Addition

Learn the importance of place values in math. In this addition series we will use place value disks & place value mat.

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