Is Singapore math a spiral curriculum?

By Wenxi Lee, mathematician, PhD in math education, and the only Singapore math expert from Singapore building parent courses.

Yes. Singapore math is a spiral curriculum. It's also a mastery curriculum, and it's built to be both at once, not one instead of the other. That surprises a lot of parents, because Singapore's approach is often described in the U.S. as "mastery based," as if that rules out spiral. It doesn't. A spiral curriculum introduces a topic early and revisits it at increasing levels of difficulty across multiple years, rather than teaching it once and moving on. Singapore uses a specific version of this called a vertical spiral, where topics build on each other in deeply connected layers instead of spreading thin across many loosely related ones. It's one of the three core methods, alongside the Concrete-Pictorial-Abstract approach and bar modeling, that defines how Singapore teaches math.

Watch the spiral curriculum explained.

Singapore math is a spiral curriculum, and a mastery curriculum

This is the most common misconception parents run into when researching Singapore math, so let's settle it first. Singapore is not "a mastery curriculum instead of a spiral curriculum." It's both. Singapore's Ministry of Education is explicit about using the spiral approach in its curriculum design. This isn't a marketing claim. It's built into the scope and sequence, grade after grade, and it's been that way since long before "Singapore math" was ever a term used in the U.S.

The confusion has a real source, though. When Americans picture a "spiral curriculum," they're usually picturing something that looks nothing like Singapore's version. That's the next thing to untangle.

Two kinds of spiral, and they're not the same

DRAFT IMAGEHorizontal spiral diagram showing topics touched on repeatedly across a wide surface area with shallow connections between them.

A horizontal spiral looks like this. Topics get touched on repeatedly across a wide surface area, but the connections between them stay shallow and often tangled.

DRAFT IMAGEVertical spiral diagram showing each new topic building directly on a deep, connected foundation.

A vertical spiral, Singapore's approach, looks like this instead. Each new topic builds directly on top of a deep, well-connected foundation, so the knowledge structure gets stronger and more interconnected over time instead of just wider.

Both diagrams come from Wenxi's book, The Secrets to Singapore's World-Class Math Curriculum, where she breaks down Singapore's full curriculum framework in more depth.

Most Americans' mental model of a "spiral curriculum" comes from horizontal-style programs, the kind that jump from topic to topic day by day for repeated exposure. That's a legitimate design choice, but it's not what Singapore does, and it's exactly why so many people wrongly assume Singapore skips the spiral altogether in favor of mastery.

What this looks like in practice

Singapore's curriculum introduces addition and subtraction at the start of the school year. But the topic doesn't disappear once the unit ends, students keep adding and subtracting all year, woven into new topics like money and measurement, so the skill keeps compounding instead of going dormant until it's reviewed again next year.

The same progression repeats across every strand of the curriculum. Addition within 10, then within 20, then within 100, then within 1,000, then within 10,000, each stage building on mastery of the last rather than starting over. (For how this pacing interacts with the Concrete-Pictorial-Abstract approach, see How Singapore math uses the CPA approach.)

Singapore math is also a mastery curriculum

Here's the second half of the misconception. Spiral and mastery get treated as two competing categories in a lot of homeschool curriculum comparisons, as if picking one rules out the other. Singapore's curriculum is both. It's a vertical spiral, and it's mastery based, with review built into the spiral at regular intervals.

Mastery learning is actually a separate framework, developed by educational psychologist Benjamin Bloom, and it's about how a topic gets taught and assessed within a grade level, not how topics are sequenced across grade levels. Singapore does both at once, which is exactly why the "pick spiral or pick mastery" framing parents keep running into doesn't hold up.

Why this matters for choosing a curriculum

If you're comparing Singapore math to a program like Saxon Math, which also markets itself as spiraling, the label alone won't tell you much. The real question is whether new material builds directly on deep, connected prior mastery (vertical), or whether the curriculum is cycling back through a wide set of loosely related topics for repeated exposure (horizontal). Those two approaches produce very different long-term knowledge structures, even when both curricula use the word "spiral" to describe themselves. (For how this fits into Singapore's overall framework, see What is Singapore math?)

Frequently asked questions

Written by Wenxi Lee. Wenxi Lee is the founder of Singapore Math Circle. She grew up in Singapore and went through 12 years of the curriculum that helped Singapore rank #1 in the world. She is a trained mathematician from Washington University in St. Louis and holds a PhD in math education from the University of Illinois at Chicago.