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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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: 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.
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 Age and Grade Level
Singapore Math is a full math curriculum aimed at students from pre-Kindergarten to Grade 8.
There are two series of math curricula that Singapore Math offers that cover different age ranges, Primary Math and Dimensions.
- Singapore Math Dimensions covers pre-Kindergarten to Grade 8
- Primary Math, taken from the traditional Singapore math program, covers grades K-5
As a homeschool math program, Singapore Math can be used outside this age range.
Given its hands-on nature and clear explanations, both precocious students and those needing remedial review can easily make use of the program, although the grade level is fairly prominently positioned on each textbook’s cover, which can be a little embarrassing for students who are a bit behind grade level.
One thing to note is that some editions of Singapore Math are not common core aligned and can move at their own pace.
Further, the program is a little more rigorous and teaches math a little bit differently than many other homeschool programs out there.
As a result, it can be a little tricky for parents and students switching into the program from another curriculum to figure out where exactly they should start.
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.
There are tests for each version of Singapore Math, which is nice, and they are pretty comprehensive, giving parents a good idea of the concepts and expectations at each grade level.
There are a little long, however, with the company recommending parents budget about an hour for each test.
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 typically made up of:
- Textbook
- Workbook (note: in the new Primary editions, the student textbooks and workbooks are unified into a single student book)
- 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
Conceptual Math
One of the more defining features of Singapore Math, and what made the Singapore math curriculum such a game changer, is its focus on conceptual understanding of math, i.e. teaching kids the why of math, not just how to calculate a solution.
Singapore Math spends time explaining to students why math functions and algorithms work, as well as the logic and reasoning behind them.
This is intended to help kids develop a deeper understanding of what they’re doing, rather than relying on rote memorization and procedures.
There is also a greater focus on problem solving and word problems, and an overall greater emphasis on helping students think about problems more deeply and to explore alternative strategies for finding solutions.
Both of these qualities in Singapore Math can help students in formulating strategies and solving unfamiliar or tricky math problems later in their careers.
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.
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.
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.
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.
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.
Based on the original Singapore method, the Primary series brought into and adapted to the US market (and eventually to common core standards), and cover grades K-5.
Overall, there are a few editions for sale:
Singapore Primary Mathematics 2022 Edition – the newest edition in the Primary line up, this edition of Singapore Math was completely updated and redesigned, aligning with common core standards.
In addition to the classic CTA model, it remodeled its lessons around the Readiness-Engagement-Mastery process, a model where students are assessed on how ready they are to learn new concepts before introducing new ones.
This edition also consolidates the student textbooks and workbooks into a single consumable, introduces new opportunities for topical and comprehensive review, and provides greater help with differentiating lessons for students of different capabilities.
A more in-depth review of Primary Mathematics 2022 Edition can be found here.
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 its own curriculum 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.
Expanded grade levels
Unlike the Primary series, which is centered around K-5 learning, the Dimensions series introduces preschool learning with its Pre-K books and extends learning into middle school with grades 6, 7 and 8.
Accordingly, the series is broken into two separate lines:
- Dimensions Pre-K – 5
- Dimensions 6-8
New Lesson Format: Think, Learn, Do, Activities & Workbook
As well as some 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.
After that, the lesson moves on to more formal learning, working through the concept in the Singapore CPA approach.
Next kids do various exercises to get some practice, under supervision, and the learning is then reinforced with optional, supplemental activities.
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.
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.
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).
Singapore Math Pros and Cons
Pros
Rigorous math program with strong history of success
Singapore Math is a fairly rigorous program, diving into math concepts in a fair amount of depth and having a good amount of challenging problem solving exercises and word problems.
Very hands-on and multisensory
A key component of Singapore Math, the program makes ample use of manipulatives and hands-on activities to help students grasp abstract material, making it quite multisensory.
Explains abstract topics and concepts clearly and visually
Singapore Math does a pretty good job at explaining math concepts with diagrams, visuals and drawings, and does provide enough text for parents and students to really discuss the math material in some depth.
The curriculum’s emphasis on hands-on explorations, manipulatives and activities are also quite effective at helping students grasp abstract concepts and helping transition them to their mathematical representations.
The company also offers videos that can also help explain concepts in a more audio-visual manner, with concise demonstrations of concepts and problem sets.
Dives deeply into its topics
Singapore Math is a mastery program, so it spends a considerable amount of time exploring math concepts in depth, with plenty of supplements for more review and enrichment, and makes sure (especially with the newer editions) that students understand what they are doing before moving on.
Promotes a deeper understanding of math concepts
A cornerstone of the Singapore method, Singapore Math spends more time teaching math concepts and helping students understand what they’re doing compared to traditional math programs.
Rather than focus on the rote mechanics of math, it spends a considerable amount of time exploring the why of math, as well as encouraging students to think more creatively in solving problems.
Lots of supplemental materials to help adjust and personalize learning
In addition to the main workbooks, Singapore Math also offers supplementary books that can help with reviewing and drilling concepts, as well as enrichment books that offer students more challenging and complex math problems to hone their skills further.
Cons
It teaches math a little differently, can take time for some parents to get used to it
Singapore Math can be a significant departure from math programs for some parents, particularly those who grew up learning math in a more conventional, procedural, spiral method, and there can be a bit of a learning curve when first starting out.
Not as much drill and math fact memorization as some other programs
Singapore Math has done a lot in recent years to add more opportunities for review and practice for students who need it, integrating it into their updated curricula and offering more review and practice supplements.
That said, it is still largely more focused on developing a deep, conceptual understanding of math and so there isn’t as much drill and memorization involved with the program as some other, procedural spiral programs out there, which parents may prefer.
Who is Singapore Math Ideal For?
Parents and students looking for a rigorous, but still approachable, K-8 math program
Singapore Math is a fairly rigorous math program.
It works on developing a strong conceptual understanding of math, some of its versions introduce topics ahead of grade level, and it has a stronger focus on fostering strong critical thinking and logic skills than many other computational programs out there.
Students who enjoy delving into math topics
As a mastery program, students in Singapore Math will spend considerably more time delving into individual topics than they might under a spiral program.
As a result, it can be a good choice for students who like to dive into a topic and who get frustrated by programs that jump from topic to topic and circle back later.
Parents and students interested in understanding a deeper understanding of math
With its emphasis on conceptual math learning, students who study with Singapore Math will work on developing a more solid understanding of math concepts, in particular by exploring the reasoning and logic behind what they’re doing, rather than just learning how to do it.
Hands-on learners and those looking for a multisensory approach to math
Singapore Math involves a good deal of manipulatives work and other hands-on activities and explorations that make the curriculum a little more multisensory than some others, and can be a great choice for more tactile learners.
Who is Singapore Math Not Ideal For
Parents and students looking for a computational, drill and math fact program
Some parents prefer a more traditional, math fact and memorization-heavy curriculum that is perhaps more similar to what they learned.
With its more conceptual approach to teaching math, these parents may not really appreciate or be as comfortable with Singapore Math.
Parents looking for an independent, self-study math program for their kids
While it does encourage independent learning at higher grade levels, Singapore Math is still largely parent-led.
As a result, it may not be the best choice for those with extremely busy schedules or who prefer a more self-study approach.
Students who get bored studying a single topic at a time
Not every child is a fan of mastery learning and spending a fair amount of time on a single topic.
Such students may prefer a spiral approach, where topics are broken down into bits, and lessons teach a little of each at a time before revisiting them in the future at greater depth.
Price
Note: Prices correct as of writing, prices are in USD.
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 A | Semester B | |
| Price | From $60 | From $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 Sets | Essential 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.
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.