Understanding the Concept of Singapore Math
Imagine you're a character in a math problem. You have three platters, but only two cakes. All three platters need to have the same amount of cake. How would you split it? This simple question is an example of how Singapore math encourages students to think critically and visualize mathematical relationships. Without even saying the word "divide," a group of about 20 teachers from private schools in Pennsylvania, Maryland, and Virginia used cubes and notecards to find solutions. The answer was two-thirds of a cake per platter. But this is just the beginning of a deeper exploration into how Singapore math approaches teaching mathematics.
During a training session on "Singapore math," which is known for its effectiveness in improving student performance, Math Champions founder Cassy Turner asked the teachers to explain their reasoning before moving on to the next question. This method emphasizes understanding over rote memorization and fosters a deeper connection with mathematical concepts.
The Expansion of Singapore Math in Schools
Owings Mills K-12 girls' school, Garrison Forest School, hosted a two-day public workshop on this teaching style last week. After seeing success with Singapore math in their lower school over the past two years, Garrison is now expanding the curriculum through eighth grade this year. Other Maryland schools, including private, charter, and public institutions, have also incorporated this approach into their curricula, hoping to replicate Singapore's decades of success.
Singapore math was developed by the country's Ministry of Education and focuses on a slower learning approach that allows students to understand mathematical concepts in greater detail. At the kindergarten level, for instance, students are introduced to the plus or minus symbols only at the end of the year. Instead, they spend 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.”
Teaching Methods and Student Engagement
Research has shown that students learn best when they mix physical objects like counting chips and blocks with drawings and in-depth discussions. Singapore math teaches concepts starting with concrete materials, then progresses to pictures, and finally introduces abstract symbols like the plus or minus sign. Older children engage in class discussions that explore three or four different methods students used to solve a problem, always ending on the one closest to the day’s goal.
The use of drawn bars to visualize numerical relationships is particularly clever in Singapore math. This method helps students see connections and understand complex problems more easily. Memorization doesn’t work well in this system; instead, the focus is on problem-solving. American textbook publishers have localized Singaporean math materials for U.S. classrooms, but the core of Singapore math is problem-solving, not just calculation.
Addressing Challenges in American Math Education
In the U.S., math education often gets bogged down in skills and concepts, while Singapore math starts with attitudes and thought processes. Developing a conceptual understanding of math from the ground up is something that people in math education have advocated for many years, but it requires professional development for teachers.
Contrast this with what Campbell called “a show-and-tell model” of math instruction where someone shows you how to solve a problem and you practice doing it over and over again, relying on memory. This approach doesn’t work well if you look at the product of kids’ achievement.
Encouraging a Love for Math
By fourth grade, kids know if they like math or not. They’re more aware of their peers and can get embarrassed by their answers. They won’t ask questions or raise their hands, and so they fall further and further behind. But Singapore math can make the subject students’ third favorite, behind P.E. and lunch.
At Garrison, all three divisions previously used a different textbook program. Extending Singapore math through middle school means students only have to transition to upper school math. Strategies like drawing bar models help students feel like they can access more advanced concepts like ratios.
Results and International Comparisons
The results for Garrison’s students are impressive. The majority of K-5 students showed more than a year’s worth of growth in math on Measures of Academic Progress assessments taken last school year. Internationally, Singapore consistently ranks high in math performance. On the 2022 Programme for International Student Assessment (PISA), 41% of students in Singapore were top performers in mathematics, compared to 7% in the United States.
Even taking top performers out of the equation, Singaporean students still had an edge: 92% attained at least Level 2 proficiency in mathematics, compared to 66% in the U.S. This trend holds for younger students too. On the 2023 Trends in International Mathematics and Science Study, Singapore had international top scores for both fourth- and eighth-graders, while the U.S. had around average scores.
A Broader Educational Context
The difference in math instruction isn’t the only difference between the two countries’ education systems. Singapore has a national math curriculum, with the government producing educational materials and ensuring all teachers teach the same math concepts the same way. In the U.S., student-teachers rarely get intensive instruction on how to teach math. Throughout her experience training teachers across the country, Resnick said it’s typical for student-teachers without advanced degrees in math to get one class in math education and four or five in reading.
Additionally, U.S. state and local jurisdictions, as well as individual teachers, have far greater control over curriculum and teaching methods than they do in Singapore. While some math curricula in Maryland emphasize concrete models and strategy discussions, the professional development teachers receive and the instructional models they use vary.
Conclusion
All school districts are required to align their curriculum to the College and Career Readiness math standards. However, as Campbell said, “Everybody can be good at math. It’s a matter of how you’re taught.”