US schools adopt ‘Singapore maths’ to improve student performance

Imagine you’re a character in a maths problem. You have three platters, but two cakes. All three platters need to have the same amount of cake. How would you split it?

Without even saying the word “divide”, a group of about 20 teachers from private schools spanning the US states of Pennsylvania, Maryland and Virginia stacked cubes and folded notecards to find solutions. The answer? Two-thirds of a cake per platter. But the problem doesn’t end there.

During this training in “Singapore maths” – teaching methods and curriculums developed in Singapore, which has consistently led the world in student maths performance – Math Champions founder Cassy Turner then asked the teachers to explain why they did what they did before moving on to the next question.

A kindergarten to grade 12 girls’ school in Owings Mills, Maryland, recently hosted a two-day public workshop on Singapore maths. The Garrison Forest School is expanding the curriculum through eighth grade this year after seeing success with the teaching method in its lower school over the past two years.

Other Maryland schools – private, charter and public – have also incorporated the teaching style into their curriculums in the hopes of emulating Singapore’s three decades of success.

Singapore maths was developed by the Southeast Asian country’s Ministry of Education decades ago. It’s a teaching style that avoids rote memorisation and focuses on a slower learning approach to teach mathematical concepts, allowing students to understand them in greater detail.

At the kindergarten level, that means not introducing the plus or minus symbols until the end of the year, said Susan Resnick, a US-Singapore maths textbook consultant. Instead, students can spend their time telling stories with numbers to decode the relationship between them. For example, after looking at a picture, a student might say, “There are four boys in the picture and one girl. Four and one make five”.

Research has found that students learn maths best when mixing in physical objects like counting chips and blocks with drawings and in-depth discussion, said Pat Campbell, a retired professor from the University of Maryland’s Centre for Mathematics Education. Singapore maths teaches concepts beginning with concrete materials, then progresses to pictures and then brings students to abstract symbols like the plus or minus sign.

Older children’s class discussions go over three or four different methods the students used to solve a problem, always ending on the one closest to the day’s goal, Turner said.

Campbell said that Singapore maths’ portrayal of numerical relationships was particularly ‘clever’, especially in how it used drawn bars to help students visualise relationships.

On international measures of maths performance, Singapore has consistently been a top scorer since the mid-1990s. Seeing those high scores spurred American textbook publishers to localise Singaporean maths materials for US classrooms, according to Campbell.

But at the core of Singapore maths was problem-solving, Resnick said.

“Where we grew up, maybe thinking that calculation was the goal of mathematics … they teach calculation as a support to get to problem-solving,” she said.

Singapore teaches students starting with attitudes and thought processes, Resnick explained to the teachers, whereas American maths education usually gets bogged down in the skills and concepts.

Campbell said that while a conceptual understanding of maths was not unique to Singapore maths, it was “something that people in math education had been espousing for many years, but it required professional development on the part of teachers”.

Contrast Singapore maths with what Campbell called “a show-and-tell model” of maths instruction “where somebody shows you how to solve a problem, and you practice doing it over and over and over again, with a reliance on memory”.

“We actually know that doesn’t work very well if you look at the product of kids’ achievement,” she said.

By fourth grade, Turner said, kids know if they like maths or not, and were more aware of their peers and can get embarrassed by their answers.

“They won’t ask questions, they won’t raise their hand, and so they fall further and further behind,” she said. But Singapore maths can make the subject students’ third favourite behind physical education class, and lunch, Turner said.

At Garrison, all three divisions previously used a different textbook programme. Extending Singapore maths through middle school means students only have to transition to upper school maths, said Sydney Carter, the middle school’s dean and a sixth-grade maths teacher.

Strategies, like drawing bar models that students learn early on, can be used to support more advanced concepts like ratios, Carter said. “That helps them feel like, ‘Oh, I can access this sort of.’”

That confidence is translating to results for Garrison’s students. Most students, from kindergarten to grade 5, showed more than a year’s worth of growth in maths on Measures of Academic Progress assessments taken last school year, according to Shannon Schmidt, director of Garrison’s Boyce Centre for Learning and Thriving.

The 2022 Programme for International Student Assessment (PISA), which tests 15-year-olds, showed “some 41 per cent of students in Singapore were top performers in mathematics”. The United States had 7 per cent of the top performers in maths.

Even taking top performers out of the equation, Singaporean students still had an edge over their American counterparts: 92 per cent of Singaporean students attained at least Level 2 proficiency in mathematics; the US had 66 per cent reaching at least Level 2.

The trend holds for younger students too. In the 2023 Trends in International Mathematics and Science Study, which tests fourth- and eighth-graders in those subjects, Singapore had international top scores for both grades, while the US had around-average scores at both levels.

But Singaporean students are also highly creative. On the 2022 PISA creative thinking assessment, 58 per cent of 15-year-olds were considered top performers on the evaluation, more than 30 percentage points above the average for the 38 countries in the Organisation for Economic Co-operation and Development. The US did not participate in the creativity assessment.

Maths instruction isn’t the only difference between the two countries’ education systems, though. Singapore has a national maths curriculum. The government produces the educational materials. All teachers across the country teach the same maths concepts the same way, Campbell said.

In the US, by contrast, student-teachers rarely get intensive instruction on how to teach maths. Throughout her experience training teachers across the country, Resnick said it was typical for student-teachers without advanced degrees in maths to get one class in maths education and four or five in reading.

“We don’t teach our elementary teachers how to teach mathematics. We just don’t, and that’s why it’s necessary for people to have outside … professional development around the teaching method,” Resnick said.

Additionally, US, state and local jurisdictions, as well as individual teachers, have far greater control over curriculum and teaching methods than they do in Singapore, Campbell said.

Although some maths curriculums in Maryland do emphasise the concrete models and strategy discussions, Campbell said the professional development teachers receive and the instructional models they use vary.

Howard and Montgomery counties support students’ conceptual understanding of maths, she said. Howard County had the state’s highest percentage of students proficient in maths for the 2023-2024 school year, as measured by scores from the state’s assessment programme: 41.1 per cent. Montgomery County came in fourth with 33.4 per cent.

The state adopted new maths standards recently. The update follows Maryland’s adoption of Common Core Standards in 2010 and the updated College and Career Readiness Standards in 2013 and 2014.

All school districts were required to align their curriculum to the College and Career Readiness maths standards, Cherie Duvall-Jones, spokesperson for the Maryland State Department of Education, said when asked if a public school district could use a Singapore maths curriculum.

“If you really want to address student achievement across schools, you need to have the school as the unit of change. All the teachers have to be essentially in the same approach to teaching mathematics,” Campbell said.

“Everybody can be good at maths. It’s a matter of how you’re taught.”