Math Curriculum Showdown – Two Popular Math Methods, But Which One is Right for You?
If you’re a homeschooling parent looking for an effective way to teach math, chances are good you know how important picking the right math curriculum can be.
The right math method has to fit with an overall schooling strategy and goals, but even more importantly has to teach math in a way that fits with how a child learns best, preventing them from becoming overly anxious, bored, or frustrated by math.
It also has to help them develop the solid math skills and knowledge that can help them find success in school and let them pursue a STEM career if they so choose.
Saxon Math and Singapore Math are two very well-known methods for teaching math that have long track records of effectiveness and promoting achievement.
They are not only popular with homeschools, but have even been adopted by independent and private schools around the country as an alternative to standard state math curricula.
As with anything related to education, especially homeschool education, there are a lot of different opinions out there and some…spirited debate around these programs. This can sometimes confuse, and even intimidate, those new to homeschooling math.
To help out, we decided to compare Saxon Math and Singapore Math so that parents can make an informed decision on which to use for their child.
How Long Have Saxon Math and Singapore Math Been Around?
Both Saxon Math and Singapore Math have been around, in some form, since the early 1980s, which means that they are both fairly well-established math curricula with pretty long track records behind them.
Interestingly, and perhaps very relatably to many parents, despite their differences both programs were created in response to a changing educational and social environment, and the general dissatisfaction their creators had with math results among students at the time.
A Brief History of Saxon Math
Saxon Math was developed in the US by John Saxon in 1981 as a response to perceived deficiencies in reform mathematics, which was gaining momentum among educators at the time.
With the new push to team-based projects and creative explorations in math, Saxon felt that students would be better served by an approach that breaks concepts down and offers lots of drill and practice for students to gain fluency.
Starting off publishing on his own, Saxon’s back to basics approach to math soon found widespread support among those looking for a more foundational and rigorous math methods than they were finding in their kids schools, and Saxon Math eventually became something of a household name with homeschoolers and independent schools across the US.
A Brief History of Singapore Math
The Singapore math method was developed, as you might expect, in Singapore and released in 1982.
With Singapore going through a period of rapid economic development, the government decided it needed a new approach to math that could strengthen its students’ knowledge of math and improve their rather lackluster results in international math rankings.
As a result, the Curriculum Development Institute of Singapore developed an approach that emphasized problem solving and critical thinking skills over computation, and adopted it as the main curriculum for its primary schools.
Singapore schools soon shot to the top of international ranking, and in 1998 Singapore Math (the company) and Marshall Cavendish translated, adapted and subsequently introduced the curriculum to the US market, where it has found widespread success.
Saxon vs Singapore Math: Curriculum & Grade Levels
Both Saxon Math and Singapore Math are complete math curriculums, in that a complete grade level kit will provide everything parents need to teach all the various topics in math for a given grade (and sometimes more).
Where they differ is in the span of grades they cover.
Saxon Math is a K-12 program, covering everything from Kindergarden level math (telling time and dates, counting, basic skip counting and more) to high school level math, such as Algebra 1+2, Geometry and Calculus.
Singapore Math, on the other hand, is a pre-K-8 math program. It covers math from pre-Kindergarten to Grade 8.
While it does offer more work to help introduce math concepts in early childhood, it does not cover high school math (grades 9+). Students will then have to move onto other programs, such as Thinkwell, CTCMath, Math U See or, if they are strong in math, even Art of Problem Solving.
Saxon Math vs Singapore Math: How They Approach Math
Spiral vs Mastery Learning
Saxon Math uses a spiral approach to teaching math.
This means that topics and concepts are in constant rotation and continually reviewed.
As a child goes through a course, topics are introduced, taken to some depth, temporarily set aside as a new topic is introduced, and then repeatedly revisited over and over again throughout the course, each time going into a little more depth and complexity.
This approach tends to be able to cover more math topics in a year, tends to keep learning fresh with new material, ideally linking concepts together more naturally, and lets kids absorb the information in more manageable bite sizes, working on their skills over time, with almost constant review of older material to help reinforce learning.
But has been noted for its downsides, as well, such as:
- The rapid change of topics and constant review process isn’t necessarily ideal for all students
- It doesn’t offer kids as much of an opportunity to learn at their own pace, particularly if they like to explore concepts in depth
- The constant review and repetition of material can annoy, bore and frustrate some kids
In contrast to Saxon Math, Singapore Math is based more on a mastery approach to teaching math.
This essentially means that topics in math are explored more deeply and for longer periods of time, with kids needing to achieve a certain level of proficiency and understanding before moving on and introducing new topics.
Unlike the spiral approach, there is far less of an emphasis on review and repetition – once a topic has been mastered to a level of proficiency, students will not often review the material again at that level.
Increasingly popular since the 1990s, the mastery approach has been praised for:
- Providing a more solid, deep foundation in math concepts due to greater exploration of a topic
- Allowing kids to better work at their own pace, as they won’t move to a new topic until proficiency is reached
- Requiring less repetition in the long term, which can be boring to many students
The mastery approach does have its critiques, such as:
- Going deeper into one topic and then moving on can make it a little harder to see how math concepts interlink when students spend a long time learning them as a singular module
- Some students do best with a lot of review and drill in order to grasp concepts, and they can forget things, leading to gaps in knowledge in the long term
- Kids can get bored learning about the same topic over a longer period of time
Overall, though, both Spiral and Mastery have been shown to have good long term results if used as part of a carefully constructed curriculum and it really boils down to how students prefer to learn and under which method they learn best.
Approach to Teaching Math
Saxon Math’s teaching style is characterized by a process of incremental development and continual review.
Incremental development is a process where Saxon takes complex math concepts and topics and breaks them down into bite sized pieces for lessons.
It then introduces these pieces a little at a time, fitting a spiral approach, and lets math concepts build upon one another, with the overall idea being that skill and knowledge development are spread out over time, which ideally puts less of a strain on working memory at one time.
Saxon Math also implements a system of continual review. There is a heavy emphasis on practice questions, exercises and drill, and concepts and topics in math are constantly being reviewed and practiced.
In fact, in addition to teaching new material, each Saxon Math lesson reviews and practices previous concepts and skills, with specific sections that intentionally mix older topics with newly introduced ones in order to reinforce learning through practice and repetition over the year.
So what should I expect from Saxon Math?
In general, with Saxon Math, parents can expect a more traditional approach to teaching math, with lessons introduced through the textbooks, a good deal of learning and memorizing math facts and approaches, followed by a lot of exercises and practice to develop skill.
Singapore Math is known for its different approach to teaching math- the CPA process.
Recognizing that kids, especially younger ones, tend to have a hard time grasping abstract concepts in math, Singapore Math gradually eases them into it by introducing concepts in three stages: Concrete, Pictorial and Abstract.
In the Concrete stage, kids learn by doing, handling or otherwise experiencing physical objects as representations of math word problems.
Moving to the Pictorial stage, kids are encouraged to think and work through problems using drawings or other models of the problem.
Finally, at the Abstract stage, kids shift their thinking a bit more and begin to USE symbols, notation and written equations, which are abstract representations of real items.
In this way, mathematical concepts and word problems are brought from concrete, real world applications to abstract mathematical thought in a way that kids can better understand.
And because, as a mastery approach, it spends time diving deeply into each topic, it has the time to do so effectively.
This approach also inherently places a greater emphasis on logic, critical reasoning and problem solving, as well as manipulating numbers to find solutions.
In addition to the CPA process, Singapore Math is also a big believer in developing mental math skills.
While the textbooks still have quite a bit of pencil and paper computation, Singapore Math encourages the development of skills like rounding, estimation,adding tens and so on to help kids do math “in their head” and speed up calculations.
Ultimately, this is intended to give kids a stronger familiarity with numerical properties, helping with developing better numeracy, logical thinking and number sense that will help them in problem solving later on.
Finally, Singapore Math’s teaching style is well known for its use of visual representation when it comes to problem solving. Singapore Math gives kids a variety of visual tools, the most well known being bar models and number bonds, that they can use to understand and solve complex math problems in a more intuitive manner.
So what should I expect from Singapore Math?
Overall, with Singapore Math, parents can expect a much more hands-on approach to learning math. There is a stronger emphasis on developing the critical thinking and logic needed to think through problems in an efficient way.
There is more time spent getting comfortable with numbers, understanding the process behind the math and strengthening mathematical thinking in general, as well as developing the ability to easily manipulate numbers to find solutions to complex word problems.
Hands-on Learning and the Use of Manipulatives
Both Saxon Math and Singapore Math are known for their use of hands-on learning, particularly through manipulatives and activities.
In terms of using manipulatives (that is, physical objects like physical blocks and shapes) in math lessons, Singapore Math uses them far more often than Saxon Math.
Where Saxon Math mainly requires them for K-3 learning, Singapore Math is more of a believer in making math a tactile and visual experience (through the CPA process) and therefore uses extensive use of them throughout the K-8 math curriculum.
In terms of learning activities, both Saxon Math and Singapore Math make extensive use of them throughout each of their lessons, integrating in-lesson activities and explorations of concepts into their lesson plan structures.
Conceptual vs Computational Math Learning
One way in which Saxon Math and Singapore Math differ quite significantly is in how they balance the understanding of math concepts versus the ability to solve math problems.
That is, how each program emphasizes the how of math versus the why of math, an almost philosophical discussion.
Now, it’s important to note that any math program has to balance the how and the why of math, or kids wouldn’t understand what they’re doing or how to do it.
Obviously, as popular and successful math programs, Saxon and Singapore teach both concepts and computation skills, they just tend to emphasize one or the other.
Saxon Math, with its strong emphasis on repetition, drill, practice and assessment, does tend to focus more on developing computational skill.
Kids tend to learn, review and memorize math facts, learn and use strategies and algorithms and overall do lots and lots of math problems.
As a result, they tend to develop strong computational skills and math fluency, which can lead to better performance on standardized tests and school classes where computation is critical.
Singapore Math, while offering fairly challenging sets and practice, tends to work on developing a deeper understanding of math concepts and stronger numeracy skills, with less of an emphasis on memorizing formulas and algorithms.
Students are encouraged to think through problems, and approach word problems using critical reasoning and mathematical logic, which can lead to better performance in higher level math classes (where computation is less important) and when faced with unusual or unfamiliar problem sets.
What Do I Need to Buy?
Both Saxon Math and Singapore Math are primarily textbook driven curricula.
Although Saxon Math does have a bit of a different structure for K-3, typically, most grades complete sets will include:
|Singapore Math||Saxon Math|
|Textbook (Grade A/B)||Textbook|
|Workbook (Grade A/B)||Testing/worksheets Book|
|Teachers Guide (Grade A/B)||Solutions Manual|
|Solutions Guide (Grade A/B)||Powerup Book (Intermediate editions)|
Both programs are flexible in how you can buy their course materials. Parents can buy complete kits or you can buy books piecemeal, which is great if you want to keep the textbooks but get new consumable books for younger siblings, for example.
That said, Singapore Math is a bit unusual in that it splits each year into two (A +B) so there are more books overall, which means that there are more books you’ll have to buy, which means if you don’t buy a complete kit it can be more of an involved process.
Book Length and Style
Saxon Math Textbooks tend to be far longer, more in line with what you might expect from a traditional classroom textbook, due largely to its greater emphasis on revision and exercises.
Parents can expect hefty textbooks that are well into the hundreds of pages, with a good deal of sometimes lengthy text based explanations.
Singapore Math textbooks on the other hand, tend to be shorter, due to less revision and the lessened emphasis on rote practice examples, and are usually under 250 pages each.
They also are more visual, with a far greater amount of graphics and imagery, which tends to make them more appealing to visual learners and younger kids.
Look and feel
Both Saxon and Singapore Math generally use softcover books when it comes to homeschool editions, although Saxon’s high school textbooks and Intermediate textbooks do come in hardcover versions, especially those intended for classroom learning.
Overall however, Singapore Math softcovers can come spiral bound, which gives them a bit more of a quality feel to them compared to Saxon.
If you are a fan of more advanced, technologically driven learning, to be honest there is not a huge amount of digital options developed by either companies.
You won’t see too many app-driven, gamified online classrooms like you would with Beast Academy, Adventure Academy or Smartick, or the sort of adaptive and powerful K-12 online learning environments, as with IXL or Time4Learning.
That said, Singapore Math has begun offering digital videos and lessons, as well as digitizing some of its books for e-readers, but that’s about it as of writing.
In addition, if you do like these curricula and the way they teach, there is an assortment of third party companies who have begun to create more advanced learning support for these math methods, such as creating DVDs, online lessons and more.
How Easy is it to Get Started Teaching?
Overall, Saxon Math tends to be easier for parents to start teaching with.
Lessons tend to be a little more scripted, especially at the earlier levels, which makes planning and executing lessons a lot easier, and the way in which math is taught tends to be similar to more traditional math programs – most lessons involve reviewing math facts, learning a new concept and then doing practice exercises and in-lesson activities.
Further, Saxon Math tends to encourage independent learning as kids progress, meaning there is less of a requirement for supervised learning and parental involvement at the upper levels.
With Singapore Math, the way it teaches can be a significant departure from what many parents have experienced themselves.
The CPA approach, its unique visual tools and its greater emphasis on developing conceptual understanding, can be quite unfamiliar to parents just starting out.
As a result, parents may need to spend time familiarizing themselves with the material before starting to use it.
Although it does also encourage independent learning over time, compared with Saxon Math Singapore Math tends to require more parental involvement, with a greater amount of hands-on and exploratory activities in its lessons overall.
Common Core Alignment
While both Saxon Math and Singapore Math pre-date common core standards by a couple decades, both have begun making an effort to offer editions that align with Common Core.
Saxon Math’s newer Intermediate editions and their newer upper level editions tend to correlate with Common Core state standards, while Singapore Math has both a specific Common Core edition and a Dimensions edition that correspond with Common Core.
That said, recognizing that not all parents want to follow a Common Core curriculum, both Saxon Math and Singapore Math still offer non-aligned editions that parents can buy.
Academic Rigor and Enriched Math Learning
While both programs are more rigorous than what can be found in most public school math classes, with far more difficult exercises and engaging activities to challenge students, Singapore Math has a reputation for being a bit more rigorous.
Singapore Math places a stronger emphasis on developing math concepts, which means the exercises and problem sets tend to require far more critical thinking skills and logical reasoning than other programs, including Saxon for the most part.
While there are fewer exercises than Saxon, Singapore Math tends to require kids to sit down and spend time thinking about them more deeply, sometimes drawing things out or making use of mental calculations to help.
Despite being a mastery system, Singapore Math also tends to introduce concepts earlier than Saxon Math. While Saxon maps more or less to grade level, Singapore Math’s curriculum is usually a grade level higher than standard, meaning new parents are strongly advised to take its placement tests before starting.
Finally, for students who are talented in math and for whom the regular curriculum is not enough, Singapore Math also offers a variety of extra books with some extremely challenging puzzles and exercises designed for enrichment purposes, something that Saxon Math does not.
In terms of cost, neither Saxon Math nor Singapore Math are the cheapest math curriculua out there.
Both require quite a few books, and have consumables that will have to be replaced with if parents want to use them for subsequent children.
In terms of how they compare to each other, in general Saxon tends to be more expensive than Singapore Math.
Although it strongly depends on where and when you buy them, a complete grade level kit for Saxon Math will cost somewhere between $100-140, while a grade level kit from Singapore Math can often be found around $85.
|Saxon Math||Singapore Math|
|Introduced||1981||1982, 1998 in the US|
|Full Math Curriculum||✅||✅|
|Matches Typical Grade Level?||✅||❌ – Grade Level Above|
|Characterized by||Concepts broken down into bits and introduced slowly over a period, lots of practice and review||An approach that moves kids from concrete to abstract, a deeper understanding of math concepts, mental math skills and a visual-tactile approach|
|Emphasizes||A back to basics approach – Memorization of math facts and algorithms, practice, drill and developing computational fluency||Developing a stronger understanding of math concepts, mathematical thinking, critical reasoning, logic and multiple approaches to problem solving|
|Common Core Options||✅||✅|
|Non-Common Core Options||✅||✅|
|Easy to get Started Teaching||⭐⭐⭐⭐⭐||⭐⭐⭐⭐|
So, how do I decide between Saxon Math and Singapore Math?
As Saxon Math and Singapore Math are both highly respected and widely used programs, each of which have a lot of different features to consider, it can sometimes be hard for parents to figure out which might suit their needs best.
We believe that when deciding on any math program, parents should consider how their student learns best.
Whether they have a particular aptitude, prefer to learn through one or more of their senses, like to go slower, like to go faster, get bored easily…all these can have a significant impact on how they respond to a curriculum.
The chart below can help guide parents by considering some of their student’s typical behaviors and tendencies.
|My student||We Would Recommend|
|Enjoys understanding why things are the way they are, rather than just doing them||Singapore Math|
|Enjoys solving problems and seeing something get done rather than going over the why||Saxon Math|
|Develops their skills better when given lots of repetition and drill||Saxon Math|
|Hates jumping around from topic to topic and likes working on one thing at a time||Singapore Math|
|Hates drill, gets bored or frustrated with repetition, or picks up concepts quickly||Singapore Math|
|Prefers to go slower, and learn things in bits||Saxon Math|
|Enjoys learning by physically interacting and exploring and/or likes using visual aids||Singapore Math|
|Prefers visual explanations and using drawings to help solve word problems||Singapore Math|
|Prefers longer, text based explanations||Saxon Math|
Almost as important as the student’s preferences, homeschooling parents often have their own considerations and educational preferences. There’s a reason, after all, that they decided to homeschool.
If a program doesn’t fit the beliefs and preferences of that homeschool, they won’t be easily implemented and can cause significant frustration and disappointment in the long run both from parents and children.
As Saxon Math and Singapore Math both have features that can help or hinder them when it comes to fit.
The chart below, based on our own opinions, offers some things that parents might want to consider before choosing between Saxon Math or Singapore Math.
|I’m a parent and…||We Would Recommend|
|I’m teaching Grades 9+||Saxon Math|
|Time is a factor and I prefer a curriculum with less parental supervision requirements||Saxon Math|
|I like to teach things my way and not have to follow a scripted lesson as much||Singapore Math|
|I want my child to develop fast math solving skills, strong bank of math facts and to develop math automaticity…how to do math||Saxon Math|
|I prefer my child develop a deeper math understanding and stronger critical reasoning and mathematical thinking skills…why math is the way it is||Singapore Math|
|We would like to bring math into the physical world and explore math concepts physically||Singapore Math|
|We believe more in learning math facts, math strategies and doing drill||Saxon Math|
|We prefer to dive into concepts and learn about them to completion||Singapore Math|
|I like to keep learning fresh, with new concepts and new topics to introduce||Saxon Math|
|I want a more advanced or enriched math program for my child||Singapore Math|
|I’d like our program to go slower and gradually build up||Saxon Math|
|I don’t mind possibly learning a new way to teach math||Singapore Math|
|I’m a new homeschooler/we’re shifting into a new curriculum and we want to do it as easily as possible, with as much structure as possible||Saxon Math|
For More Information
If you’d like more information about either of these programs, we did full reviews of both curricula that go into some depth for each.
Read our in depth review of Saxon Math
Read our in depth review of Singapore Math
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.