Singapore Math Review

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If you’re looking for a hands on, mastery learning approach to teaching math that also fosters a deeper understanding of math concepts and stronger problem solving skills, the Singapore Method might be what you’re looking for. 

And with affordable and high quality learning books and manipulatives, and an excellent reputation, Singapore Math might be the best way to go about teaching it.

What We Like

Based on renowned and effective Singapore math method
Rigorous and thorough math curriculum that has been shown to lead to significant improvement and achievement
Well made, well thought out books filled with activities
Manipulatives are offered to use with hands on activities, are well made and durable
Books and material are competitively priced
Books are filled with visuals, have a clean look and are easy to follow and use
Lots of available supplements for both gifted kids and those needing extra practice
Methodology gradually moves math from real, concrete things to abstract equations and symbols
Supports multiple learning styles, emphasizes hands on learning
Mastery method encourages deeper, critical thinking approach to math teaching
Many different editions to suit different needs and curriculum requirements
Flexibility in buying material – can buy bundles or individual books and associated material

But watch out for

Parents and teachers need to familiarize themselves with the teaching method
Not as much repetition and drill, some kids do benefit from this
Introduces math concepts earlier than traditional curricula, parents switching in should do a placement test

What is Singapore Math?

Singapore Math, Inc is a provider of a wide variety of books and resources for parents looking to teach their children math using the popular Singapore Method.

Founded in 1998, the company was the first to introduce and adapt textbooks featuring the Singapore math method to the United States. 

Singapore Math currently publishes and sells several editions covering pre-Kindergarten to Grade 8 mathematics, as well as producing a variety of physical manipulatives, and has recently begun venturing into the digital world with various assessments and video lectures.

Singapore math method vs Singapore Math

So what are we talking about here?

When people talk about Singapore math it can get a little confusing, so we’ll try and clarify.

The Singapore math method is a pedagogical approach, or way of teaching math to kids that was developed in Singapore in the early 1980s. It is, itself, unrelated to any company, service or product. 

Singapore Math, on the other hand, is a registered trademark of Singapore Math Inc (and Marshall Cavendish Education Pte. Ltd). It is a line of educational textbooks, videos and other material designed to help teach the Singapore math method to kids in the US, 

It was the first such program to adapt the method to the US, and is the most popular and well known Singapore math method product line in the US. When parents and teachers talk about Singapore Math, they’re generally talking about Singapore Math’s product line.

This review discusses and examines the Singapore Math books, curriculum and materials, rather than the overall way of teaching math.

Singapore Math Method: Some Background

In the early 1980s, driven by a desire to advance their technology sector and economy, Singapore decided to redesign its approach to teaching mathematics at the elementary school level, shifting from a traditional, abstract and computational method of teaching math to one focused more on problem solving and critical thinking.

In 1982, they released the first edition of the Primary Mathematics Series, which was then adopted by Singapore’s Ministry of Education as the primary math teaching method for Singapore public schools.

With time Singapore saw dramatic improvement in its standing in terms of international achievement, and has consistently ranked at or near the top of international primary school math rankings ever since.

How Singapore Math Works

As we mentioned, Singapore Math is a math program developed by Singapore Math Inc that adheres to the Singapore Approach for teaching math. 

The program covers Pre-Kindergarten to Grade 8 math, and each grade is made up of:

  • Textbook
  • Workbook 
  • And teachers guide/home instructor’s guide

That said, it’s important to note that each grade is separated into two semesters (A and B),  so parents do have to purchase two complete sets of books, which is something to keep in mind and budget for. 

Teaching is taught primarily in textbook/practice book format, where parents and students work through lessons together and then students complete related exercises in the workbook, as you might expect.

In addition to the textbooks and workbooks, Singapore math also offers a lot of hands-on activities sprinkled throughout the lessons. 

Designed to make math concepts more concrete and real for kids, Singapore math also offers a variety of manipulatives that go with their books, such as blocks, dice, chips, clock faces, containers, scales and more.

Singapore Math Digital Learning Options

Singapore Math has recently begun offering digital products, as well as its traditional physical books, which they call their At Home program. 

There are video lectures and explanations taught by a professional teacher and generally follow the various chapters of the textbook, and act as a audio/visual supplement to their textbooks learning, rather than a replacement. 

These videos are short, usually between 5 and 20 minutes long, and cover the various topics from each grade, and all told each grade has several hours worth of material to watch.

The videos themselves are very straightforward. While you won’t find a lot of animation or music to keep kids entertained, they do an excellent job at explaining concepts in a clear and concise way, with a lot of visual demonstrations. 

Overall, we feel these videos can be a particularly helpful resource for homeschoolers who aren’t all that familiar with or comfortable teaching math to their kids, and especially for families that are shifting to Singapore Math from another curriculum, as the Singapore method can take some time to get used to.

On the downside, unlike some other programs out there, there is currently no app or digital learning environment offered by Singapore Math at the moment. 

While it does make some sense, as Singapore Math does involve a lot of hands-on activities, this does mean that parents won’t have immediate access to more modern home teaching tools like progress tracking, adaptive question banks, online quizzes and games that can really help keep things organized and fun for kids. 

Singapore Math: Pedagogical Features 

Mastery Approach

Singapore Math takes a mastery approach to teaching math, as prescribed by the Singapore Method. 

Essentially, this means that students go deeper into each individual topics, taking time to develop a certain level of knowledge, skill and competence (or mastery) before moving on to the next concept.

As kids are expected to be far more comfortable with numbers and math concepts, as well as the thought process behind the math, Singapore Math’s texts and problem sets place a greater emphasis on thinking through and problem solving and manipulating the numbers to find solutions. 

This is as opposed to a traditional spiral approach, with its more mechanical, process-driven approach to problem solving and where math topics are taught to a certain level before moving on to new concepts, reintroducing topics and going progressively deeper later on. 

From Concrete to Pictorial to Abstract: The CPA Learning Process

Recognizing that, from a developmental point of view, kids in elementary school aren’t all that good at abstract thinking yet, in Singapore Math concepts are introduced in three stages – Concrete, Pictorial and Abstract.

This approach progressively takes kids from hands-on understanding of math concepts all the way to being able to understand and work with written symbols and equations. 

Concrete stage – At this stage, kids are expected to learn by doing, touching, creating, handling or otherwise experiencing physical objects. Exercises in the textbook may ask parents to add and subtract actual flowers or pennies to represent a word problem, for example. 

Picture of singapore math hands-on activity

Pictorial stage – Moving a step more towards abstraction, kids are encouraged to through problems using drawings or other models (such as representative blocks), rather than the items themselves.

Abstract stage – Finally, kids shift their thinking to symbols, notation and written equations, which are abstract representation of real items. For example, “4 pennies and 6 pennies makes 10 pennies” is now represented as just 4 + 6 = 10.

It’s important to note that this process is not totally linear. While the process is designed to move towards abstraction, weaning kids off the need for hands-on math, parents will find that Singapore Math books can and will move back and forth as needed or as to reinforce concepts. 

Developing Mental Math

In addition to the CPA process, Singapore Math is also known for its emphasis on helping kids get used to using mental math.

While the textbooks still have quite a bit of pencil and paper computation, Singapore Math does encourage the development of skills to help kids do math “in their head.” 

It teaches things like rounding, estimation and other strategies like adding by ones, adding tens and so on, which ultimately give kids stronger familiarity with numerical properties, help with computation and can help develop numeracy and number sense.

There are even supplemental books offered by the company dedicated to helping kids hone their mental math skills. 

Bar Modeling & Number Bonds

Two of the Singapore math method’s most well known tools for helping solve word problems are bar modeling and number bonds, and these are frequently found across Singapore Math textbooks. 

Bar Models

Bar Models are an intuitive way of understanding quantities and approaching word problems that involve parts and wholes. 

Photo of Singapore math bar model problem

They are a visual representation that uses a bar or squares to represent known and unknown quantities. Put simply, kids draw bars with one representing numbers given in the word problem set up and the other being the unknown quantity (how many X will they have?) and, in this way, are given a very visual way of working with a difference. 

Number Bonds 

Part of the pictorial stage, number bonds are an important way in which Singapore math helps develop number sense in kids. 

They are a visual representation of how numbers can join together or split apart. Essentially, the sum of two numbers is represented inside a circle with two lines branching out from it, each of which connects to a circle that contains a component number, the addends.

At first used to help teach addition and subtraction. Singapore Math eventually uses these to develop a more intuitive number sense that can help speed up more complex mental calculations.

Singapore Math Curriculum

Singapore Math’s overall curriculum has a reputation for being more rigorous than most traditional US curricula out there, and this reputation is well-deserved for the most part.

Singapore Math follows its own scope and sequence and tends to introduce concepts earlier and in more depth than other curricula, particularly when compared to common core state standards (which is why there is a specific edition for those following common core). 

Generally speaking, Singapore Math can be up to a grade level ahead of traditional curricula. For example, multiplication is actually introduced in the first grade and kids attain a stronger working skill set by the end of grade 2. 

This is great for parents of kids who want to see their kids develop a stronger and more advanced grounding in math compared to their peers, but it can mean that those switching into the program from another curriculum may have to play catch up. 

For that reason it is advisable for parents new to the method to have their kids take a specific placement test, which can help their kids find their place and determine what specific knowledge and skill gaps (if any) exist. 

Helpfully, Singapore Math offers free downloadable placement tests for every grade level. 

Another thing to consider is that both the Singapore Math curriculum and the way it is taught can be significantly different than what most parents are used to. Consequently, there can be something of a learning curve for homeschoolers and parents when it comes to properly using the program’s textbooks, workbooks and hands-on activities.

Parents may also need to budget more prep time for lessons, as the hands-on learning component and associated activities may be a bit more involved and time-consuming.

Singapore Math Editions

There are several different editions of Singapore Math that have been developed over the years.

All editions are based on the Singapore math method, and each have been configured in some way to fit the particular needs of certain parents and schools. 

Primary Mathematics 

The original Singapore Math curriculum, the Primary Mathematics series has been in circulation since around 1998.

Overall, there are three editions for sale: 

U.S. Edition, the original edition adapted and brought to the United States, when people talk about Singapore Math in the US, particularly homeschoolers, this is generally the one they’re referring to. 

Standards Edition – prior to common core, this edition was created to adapt the US Edition to California state standards, and it became popular for its comprehensive and easy to follow lesson plans. It also includes probability, data analysis, negative numbers, and coordinate graphing.

Common Core – After Common Core was introduced, an edition was created to adapt the US Edition to align with Common Core State Standards. It’s a little different than the US edition, with a different scope and sequence as well as different formats for the teachers guides, but can be quite helpful for those who want a Common Core Standards aligned math program.

Dimensions 

Recently, Singapore Math has updated its Primary curriculum with a newer, Common Core Standards aligned edition called Dimensions.

Overall it is quite similar to the Singapore Math Primary Mathematics that people have come to know and love, but there are some important differences.

New Lesson Format: Think, Learn, Do, Activities & Workbook 

Beyond some minor improvements in look and feel (more color printing), Singapore Math Dimensions has added a bit more lesson structure to the traditional Singapore Math curriculum.

Most lessons now follow a five stage format:

  • Think
  • Learn
  • Do
  • Activities
  • Workbook

Essentially, when approaching a new concept, kids and parents will work through real life problems, thinking about the concept in a more approachable way with hands-on activities. 

image from singapore math dimensions showing the think stage

After that, the lesson moves on to more formal learning, working through the concept in the Singapore CPA approach. 

image from singapore math dimensions showing the learn stage

Next kids do various exercises to get some practice, under supervision, and the learning is then reinforced with optional, supplemental activities.

image from singapore math dimensions showing the do stage

Finally kids work independently on exercises independently in their workbook.

This new lesson structure makes lessons a little more orderly and helps both parents and students in knowing what to expect. 

It also offers a lot more optional activities and practice for kids, which can help reinforce learned materials, something that was a major complaint from parents using the traditional Primary curriculum. 

It can also help homeschoolers in particular, as Dimensions generally provides far more detailed guidance on how to teach certain concepts to kids. 

However, all this does mean that lessons can be longer and more involved, requiring more lesson time and planning on the part of parents. 

This can be a drawback to parents who like to keep lessons short or more broken up, and the greater number of activities and exercises can be a little overwhelming to kids not used to it. 

Parents should also know that Dimension’s scope and sequence aligns more with Common Core Standards by default, which is something that not all parents are really looking for. 

Supplements

In addition to the main preK-Grade 8 textbooks and workbooks, Singapore Math also offers a number of supplementary books that parents can use to offer extra challenges and learning to students in case they want to take their learning to the next level. 

There are a variety of different books available for each grade, such as their extra practice and intensive practice series, which offer more practice material and their challenging word problems series which offer far more rigorous problem sets, which is perfect to help challenge gifted math students.

There are also books that help kids develop strong math skills, such as sprint (mental math) and process skills (logic and problem solving), which can be of particular benefit to kids switching into Singapore Math or who need a little more help.

Overall, Singapore Math’s supplements really increase the flexibility of the program. With them, parents can ramp the difficulty up and give gifted and advanced students more of a challenge, or give new and struggling students more focused practice in the skills they need to thrive.

Who is Singapore Math Designed for

Singapore Math offers math instruction for Pre K- Grade 8 students.

While it has a number of features that lend itself to achievement in math, and does go deeper into math concepts than other approaches, Singapore Math is a system that can be used by any student, from enriched to struggling students and everyone in between. 

It is, after all, based on a primary curriculum for all students in the Singapore public school system, a curriculum designed to be able to be mastered by the majority of students.

Given enough time and practice, we think pretty much any student can benefit from Singapore Math.

Students who aren’t very confident in math will appreciate the slower, deeper pace, the visual approach and the gradual introduction of abstract concepts, as well as the many opportunities to develop stronger and more fluid number sense through the main curriculum and various skill-developing supplements. 

Gifted students, on the other hand, may come to appreciate that there is less focus on repetition and a greater focus on critical thinking and the earlier application of knowledge to more unique and interesting problems. 

There are a variety of books, such as Challenging Word Problems series, that can really ramp up the challenge factor and keep gifted students from becoming bored.

Most of all kids who are kinesthetic or tactile learners can really benefit from the hands-on approach, as the various manipulatives offer a very hands on experience and the gradual shift from concrete to abstract concepts can really help play to their strengths. 

Singapore Math Curriculum: Look and Feel

In general, Singapore Math textbook feel fairly durable for a softcover book. They are also usually pretty short, usually anywhere from 80 to 190 pages each. 

The learning is very visual, with lots of pictures and diagrams to explain concepts and lots of large, easy to read print that gives it a clean, accessible design.

There is enough designated space for kids to write directly into the books, and there are generous amounts of questions, puzzles and problems to work through between textbooks and workbooks. 

That said, parents who have multiple kids coming up through elementary schools may wish to use a notebook and reuse these books later. 

The Dimensions teachers guide/home instruction and textbooks are in full color, while the Primary Mathematics Edition workbooks are in black and white. 

Manipulatives 

Designed to go with the Singapore Math textbook learning, there are a wide variety of physical objects (called manipulatives) that parents are encouraged to purchase and use in guided activities to provide a higher quality hands-on learning experience.

From Tangrams to help with spatial reasoning, to dice, to mathlink cubes, the manipulatives are usually made from high quality plastic (sometimes brass, wood or thick paper, as well) and feel quite durable. 

In fact, our testing child seemed to particularly enjoy using plastic geometric pieces and gave them a typical kid-testing, periodically dropping, building and even throwing them around without any damage (although obviously we wouldn’t recommend that). 

Price

Overall, Singapore Math’s pricing is fairly affordable for families – a complete year’s math curriculum (without manipulatives) costs less than $140, which makes it highly competitive with other well-known math programs.

The company does offer some flexibility in terms of purchasing.

While parents do need to buy textbooks, workbooks and a guide (as they work together), these can usually be bought as a bundle (subject to availability) or as individual books. This means that, with a little planning, parents on a budget can purchase what they need over time and that parents who need replacements can get them without having to spend a lot of money.

To give you an idea of pricing, we’ve included some of the pricing options below.

Note: Prices current as of writing and are in USD.

Singapore Math Primary Mathematics

Because the Primary Mathematics program for Singapore Math has a variety of possible editions, each of which are somewhat different in scope and sequence and contain different material, prices can be a little variable between editions and grades. 

Individual Books

Textbook (each semester)From $17.90
Workbook (each semester)From $16.90
Home Instructors Guides (each semester)From $19.00
Tests (each semester)From $13.00
Teachers Guides (each semester)From $25.00

Bundled Packages

Semester ASemester B
PriceFrom $60From $60
Textbook 
Workbook
Teachers Guide 

Singapore Math Dimensions

The pricing for Singapore Math Dimensions is a little more straightforward, being a single edition and curriculum, and (despite being a more updated version) is actually a little less expensive overall.

Bundled Packages

Complete SetsEssential Sets
Price$122$98
Textbook (A+B)
Workbook (A+B)
Teachers Guide (A+B)
Tests (A+B)

Individual Books

Textbook (each semester)$12.00
Workbook (each semester)$12.00
Teachers/Instructors Guides (each semester)$25.00
Tests (each semester)$12.00

Singapore Math At Home

Singapore Math At Home costs $85 per grade per student. 

However, keep in mind it only includes video tutorials, so you’ll need to buy the books separately.

How Singapore Math Compares to Traditional U.S. Math Curricula

Singapore Math is more advanced in terms of grade level than just about every other math program used in the U.S public school system.

There tends to be less repetition, and Singapore Math tends to introduce concepts and math standards at an earlier grade level, which means kids can end up more advanced in terms of math compared to their peers following other programs.

It is a mastery method, of course, which means it will teach each concept more thoroughly and sequentially than traditional programs, which follow a spiral approach and tend to revisit concepts in the future.

Of course, this means that if students miss a concept or simply jump into the program, they can have critical skill and knowledge gaps that impact their future performance since pervious material isn’t revisited as frequently.

In terms of how math is taught , Singapore Math focuses far more on the development of stronger logic and problem solving skills. 

Its textbooks and workbooks encourage kids to explore various approaches and develop an understanding of the meaning behind the math, i.e. why things are the way they are and why things work the way they do.

It also teaches a variety of techniques to encourage fluidity and number sense, such as actively promoting mental math. 

This is as opposed to the more mechanical, formulaic and computational approach taken by traditional programs, which is more focused on learning how to solve a problem efficiently and quickly, and tends to discourage mental calculations. 

Singapore Math also tends to take a more multisensory approach to teaching, teaching with manipulatives (kinesthetic) and through pictorial representations (visual), such as bar models and number bonds, before moving to abstractions like equations. 

Bottom Line:

If you’re looking for a hands on, mastery learning approach to teaching math that also fosters a deeper understanding of math concepts and stronger problem solving skills, the Singapore Method might be what you’re looking for. 

And with affordable and high quality learning books and manipulatives, and an excellent reputation, Singapore Math might be the best way to go about teaching it.

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About the Author

David Belenky is a freelance writer, former science and math tutor and a tech enthusiast. When he’s not writing about educational tech, he likes to chill out with his family and dog at home.