This guide tells you everything you ever wanted to know about Singapore Math: is it spiral or mastery? Do I need the Home Instructor’s Guide? What makes Singapore Math different from other homeschool math programs?

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This time of year marks the halfway point in our academic calendar, and it’s when I take stock of our curriculum and educational plan, making changes based on what’s working and what isn’t. Since I’m planning for a sensitive, headstrong , sensory-seeking, asynchronous six-year-old who taught herself to write at age two, and who currently reads and comprehends well beyond middle school level, I’m always, always, adjusting. Not pushing, but adjusting; adjusting, and following her lead. Just because I love a book or a method, doesn’t mean it will be the best choice for her. And many times, I’ve purchased curricula in advance, only to find that she’d already outgrown the content by the time I planned to use it. Flexibility is key.

But no matter how objective I am about what’s working and what’s not, I can honestly say that Singapore Math always makes the cut. I receive messages nearly every week from inquisitive parents who wish to test the Singapore waters, but are apprehensive for one reason or another. In fact, I’d venture to say that of all the curriculum we use, Singapore Math piques the largest amount of curiosity — and is victim to the largest amount of misinformation.

Here are the questions I am asked most often.

Why Singapore Math, in particular?

The approach Singapore takes in teaching math concepts is more in line with the type of mathematics instruction students receive in the non-US countries where math scores are higher than US student math scores.  The plain truth is that the way mathematics and arithmetic have been taught in the United States for years hasn’t actually worked out that well. Each of us, of course, has had a different educational experience, and while some personally feel their math educational suited them well, I hear over and over from people who feel rather strongly about having been insufficiently equipped by American math instruction. In either case, the rankings don’t lie. [1] The most recent (2015) global rankings of students across the seventy-two countries reveal that in math, American students rank 35th out of 72. Thirty-fifth! That’s far below even the global average, and is sadly even worse then the 2012 results (28th out of 72). Vietnam, Lithuania, Malta, and Latvia — just to name  a few — are all doing a better job teaching math than the United States. Do you know which country ranks first in math scores? That’s right, Singapore.

“But it’s not the way I was taught!” or, “I’m not any good at math!”

Based on the global math scores quoted above, I’d venture to say that “the way it’s always been done” might actually be doing American students a disservice.  This is not meant to be a controversial statement. When global test scores in math clearly show American students lagging behind their same-age peers, the data suggests room for improvement. A recent report from the National Numeracy organization in the United Kingdom asserts the following:

“Negative attitudes, rather than a lack of innate talent, are at the root of our numeracy crisis. In order for people individually – and the country as a whole – to improve and in turn benefit from raised levels of numeracy, our attitudes have to change. It is culturally acceptable in the UK to be negative about maths, in a way that we don’t talk about other life skills. We hear ‘I can’t do maths’ so often it doesn’t seem a strange thing to say (Kowsun, 2008). Maths is seen as the remit of ‘mad scientists’, ‘nerdy’ boys, and the socially inept (Epstein et al, 2010). We talk about maths as though it is a genetic gift possessed only by a rare few, and inaccessible to the general public.” [2]

When we look at mathematics and arithmetic as subjects only some people have the capacity to understand, we do everyone a disservice. I’m often equally fascinated and disheartened by the muscle thrown behind pre-literacy efforts, while any similar push for pre-numeracy skills is seen as hothousing, or rejected as developmentally inappropriate. We simply don’t have the same kind of reverence for opening up the world of 123s as we do for opening up the world of ABCs. Maybe, just maybe, we’re conditioning our kids early to feel like math is inapproachable, difficult, and “only for math people”.

Can you achieve the same results as students in Singapore, just with the Singapore Math curriculum?

This is a big question to tackle. I suggest the answer lies in cultural attitudes toward mathematics and arithmetic. (Mathematics and arithmetic are not the same thing, by the way. According to the Oxford Dictionary, the term “mathematics” refers to “the branch of science concerned with number, quantity, and space” , while “arithmetic” is “the use of numbers in counting and calculation”.)

In the West we tend — not as an absolute, but as a tendency — to view a math brain as something you either have, or you don’t. Not so in Singapore. Cambridge Assessment’s Director of Research is quoted in the Financial Times as saying, “It [Singapore’s approach to math] is a different approach to ability — really, a major overhaul of the way in which children are viewed…A switch from an ability-based model of individualized learning, to a model [which says that] all children are capable of anything, depending on how it is presented to them and the effort which they put into learning it.” (emphasis mine) [3]

Is Singapore Math is only suited for kids who are good in math?

Certainly there are different learning styles and different personalities. But, to unilaterally say that the Singapore math methodology is only good for “kids who are already good in math”, is to ignore not only the very real difference in cultural attitudes toward math and beliefs about children’s math ability, but also the fundamental differences between typical math instruction in the United States and typical math instruction in Singapore.

What makes Singapore Math different? Is the Home Instructor’s Guide really necessary?

Yes. The Home Instructor’s Guide contains the bulk of the Singapore Math program. Beginning with Level 1A, it would be difficult to teach the program in a truly Singapore-method way without it. In fact, if I were to assemble a Singapore Math curriculum on a tight budget, I would omit the textbook before I ever omitted the Home Instructor’s Guide. The fact is, without the strategies in the Home Instructor’s Guide, you will inevitably teach math the same way you learned. The Home Instructor’s Guide gives you easy-to-understand, practical, and usable access to the “concrete, pictorial, abstract” method. This is necessary not because elementary math is hard, but because this is the method which sets Singapore Math apart from other math programs.

Unless you happen to have prior experience teaching the Singapore Math method, I do not believe the student workbook and textbook by themselves are adequate to teach the Singapore method.

The Home Instructor’s Guide contains games, tips, and suggestions to explain abstract concepts in concrete ways. Singapore Math never expects the student to simply accept a math rule and begin carrying it out, without a logical buildup and explanation. I have sometimes heard detractors of this program argue that Singapore Math students will end up deficient in math facts, because of the program’s focus on the why and how behind mathematical concepts. In actuality, students end up  proficient in both arithmetic (calculations) and mathematics (theory), because Singapore Math understands that these two go hand in hand. For each kind of math problem or concept, the Home Instructor’s Guide teaches several strategies and approaches. I especially like this, since different approaches will be hits for different kids at different times. And by being exposed to several ways to tackle each kind of problem, the student gains a deeper understanding of each problem, and learns how to solve problems most efficiently. This means that when a student is working through pages of math facts in the workbook, he or she is not just rewriting memorized facts, but is actually practicing mathematical thinking and learning how to employ different problem-solving strategies. And the fascinating thing I’ve observed is that through working this way, the student memorizes math facts without even realizing it.

In beginning addition instruction, for example, the student is required to memorize facts through 20. Rather than being given a stack of flash cards and timed tests, the student is instead given physical objects to sort and count. As the student is engaging in tactile ways through moving counters/manipulative, the student is being taught strategies, such as memorizing doubles (this allows him/her to know all doubles and all doubles plus one), counting up by 1, 2 or 3, and training his/her brain to spot the combination of numbers equaling ten in any given set of numbers. When a student becomes stuck, he or she is prompted to count up, look for doubles, or look for a ten.

If a student still hasn’t grasped memorization at the end of this process, the Home Instructor’s Guide encourages the student to pause and work through mental math exercises, provided in the back of the guide, before moving on to the next unit. But for the most part, as the student goes through this process — progressing through the concrete, pictorial, and abstract stages — the student finds he/she is suddenly capable of doing addition entirely mentally! Mental arithmetic ability is achieved through building a thorough understanding of mathematics.

Each step in Singapore Math methodology truly builds on the previous step. Yet, without a big picture perspective of what this approach is trying to accomplish, detractors often look at just these strategies and argue that this sort of math is adding too many steps and doesn’t have enough memorization. But when the program is taken as a whole — Home Instructor’s Guide, textbook, and workbook — students gain a rich understanding of mathematical reasoning while at the same time engaging in problem solving, and committing math facts to memory. Each time I happen to question why a certain strategy is presented in the curriculum, a few more pages or chapters later I see exactly why the concept was tackled in that way.  It all ends up fitting together. And the curriculum never leaves you guessing how deeply you should cover a concept before moving on, because the Home Instructor’s Guide gives helpful insight along the lines of “this concept will be covered in detail later; this is just an introduction”, or, “stop now and review these facts, as the student will need to know this for the next concept.”

I wholeheartedly endorse the Home Instructor’s Guide as a means to implement the Singapore Math method.

Is Singapore Math spiral or mastery?

Whenever this question is posted on discussion boards, it seems about half the people argue that it’s spiral, and the other half argue that it’s mastery. Actually, Singapore math is neither spiral nor mastery. According to the publishers themselves, “The Singapore Math^® curriculum does not conform strictly to any of the above approaches. The strong point of Primary Mathematics is its clear and multi-pronged presentation of concepts. There is an effective mix of drill, word problems and mental calculation instruction connected to all important concepts.” [4]

In the sections of the curriculum which learn toward mastery, users of only the workbook and textbook might think there is not enough substance to adequately master the material. However, users of the Home Instructor’s Guide will see that for each simple-looking problem in the student books, there is a wealth of teaching in the Home Instructor’s Guide on the mathematical reasoning, problem solving, and abstract thought behind each type of problem, as explained above.

Is Singapore Math Common Core?

Yes, and no. There are three different, separate versions of Singapore Math [2], and each is very clearly named: the U.S. Edition, the Standards Edition, and the Common Core Edition. Only the Common Core version is aligned to Common Core standards.

Which edition of Singapore Math is best?

Generally, when people refer to “Singapore Math”, they mean “Primary Mathematics” from publisher Marshall Cavendish. Throughout this post, this is what I mean, as well. There are other publishers who use the term “Singapore Math” as well, such as the Frank Schaffer practice books often spotted at Costco, but those aren’t the same as the original Singapore Math Primary Mathematics curriculum discussed in this post.

If you’re sold on the Singapore Math methodology, you can’t go wrong with any Singapore Math edition from Marshall Cavendish –the U.S. Edition, the Standards Edition, or the Common Core Edition. (Obviously, if you have strong feelings about the Common Core edition of Primary Math aligning with Common Core standards, you’ll want to avoid that one.)

We use the Standards Edition. All the textbooks are full-color, unlike the U.S. Edition (not a deal breaker, but a really nice perk if you happen to have a very young math aficionado.) And in my opinion, the Standards Edition it has the very best, most thorough teacher’s component. This chart from Marshall Cavendish explains the differences between the U.S. Edition, the Standards Edition, and the Common Core Edition of Singapore Math.

There are so many books for each level of Primary Mathematics. Which ones do I need?

For a complete Primary Mathematics curriculum, you’ll need the Home Instructor’s Guide, textbook, workbook, and Mathlink cubes. One full year of math instruction will require a minimum of six books: A and B level Home Instructor’s Guide, A and B level textbook and A and B level workbook. The Home Instructor’s Guide serves as the planner and teaching guide for each lesson, after which the student is assigned a few workbook pages and a few textbook pages. Because Singapore is neither spiral nor mastery but a combination of the two, there actually aren’t that many problems assigned each day, so textbook and workbook together isn’t an overload of material. We do not currently do the separate supplementary Singapore Math practice books containing challenging word problems, tests, or intensive practice at this point, although they are available. At the end of the post, I list the additional math resources we currently utilize.

(For kindergarten, all you really need are Earlybird Kindergarten Textbooks A and B. More on that below.)

What are the grade equivalents to Singapore levels?

Before Singapore Math redid their website, they used to have a section stating that Singapore level B of one grade is equivalent to the first semester of the following grade (1B and 2A make up a typical second grade year, 2B and 3A are equivalent to third grade from another publisher, and so on). Once the website was revamped, that page disappeared. Now, the homeschooling planning section links to Singapore Math assessment/placement tests, and advise students start with an assessment two grade levels below their current math level.

What about middle school and high school (secondary-level) Singapore Math?

Primary Mathematics is available through Level 6B, then secondary-level Singapore math curriculum is available for levels 6, 7, and 8. (Why don’t the Singapore math levels and United States grade-level equivalents line up exactly?)

It is worthwhile to note that New Elementary Mathematics version (available in levels 7-8 or 1-2) is considered by the publishers themselves to be more rigorous than the Dimensions Math edition (available in levels 6-8). However, according to the Singapore Math website,  “A student who has completed either of these should be prepared for second year algebra or geometry at the high school level.  An advanced homeschooled student could potentially do a college level intermediate algebra or pre-calculus text.” [5]

What books do you recommend if I want to begin Singapore Math in preschool or kindergarten?

We used — and loved — Earlybird Kindergarten Math, Standards Edition. For both the A and B levels, a Teacher’s Guide, textbook, and activity book is available, as well as additional storybook readers. While I’m a huge proponent of the Home Instructor’s Guides for Primary Mathematics 1A and up, I actually found that for Earlybird, just Textbook A and Textbook B themselves provided a fun and comprehensive kindergarten math education. Unlike the Primary Mathematics textbooks which contain no teacher’s segment, Earlybird textbooks do include separate teacher’s notes at the bottom of each page, which guide the parent through each lesson.

The first book, A, doesn’t deal as much with actual numerals as it does with mathematical reasoning, and learning to express why sets of items are “different from” or “similar to” each other. This emphasis on why, focus on pictorial representation, and lack of writing makes Earlybird A a thorough yet developmentally-appropriate first introduction to mathematics and critical thinking. I would say the curriculum could be undertaken as early as four years old — or even an older three-year-old in the case of a precocious child.

Since the program starts out slowly, some fail to see the need for Earlybird A. However, by the end of Earlybird B, though, the practical foundation laid by the seemingly slow exercises in Earlybird A become very clear. We did lots more than one page/day during the easy units, and slowed down a bit for the more challenging units. Earlybird A and B are a terrific foundation for Primary Mathematics.

The whole kindergarten course is extremely simple and open-and-go. For A, the only manipulatives I used were shapes cut out of construction paper, although wooden or plastic tangrams would have been more practical and durable. Once you begin Earlybird B, I would recommend purchasing some physical counters (like the recommended Mathlink cubes as manipulatives.  You’ll want to have counters anyway as you go on to 1A and beyond, as they are an integral part of the program.

Singapore Math suggests additional manipulatives as well, should you wish to invest in more hands-on math materials.

Besides Singapore, what other resources do you use for elementary math?

• Basher Books, like Math, and Algebra & Geometry
• Khan Academy Math (there’s an app for that!)
• Shanghai Maths Project practice books (The answer keys are included in the back of the books)
• Hands-on Math Wrap-Ups for tactile learning
• Dragon Box apps, like Algebra 5+ for teaching linear equations to young children
• Library books, like these 100+ kid-approved books about math
• An old scientific calculator, for exploration and self-led learning
• A math reference book, such as Math to Know

If you have additional questions, please leave them in the comments and I’ll do my best to answer! [Edited to add: This is post is not in any way sponsored by Singapore Math or Marshall Cavendish. We just truly love this curriculum!]

This post has been linked to  iHomeschool Network’s Our Homeschool: What’s Working and What’s Not. Click the image below to read other #ihsnet bloggers’ mid-year curriculum reviews!

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