Math in Focus®: Singapore Math® by Marshall Cavendish®: Research Foundations
At a glance
What is Singapore Math®?

Math in Focus®: Singapore Math® by Marshall Cavendish®, for Grades K–8, is the U.S. edition of Singapore’s most widely used curriculum, bringing Singapore’s effective approach to mathematics to U.S. classrooms.

Singapore Math® emphasizes problem solving and positive attitudes toward mathematics, while focusing on student development of skills, concepts, processes, and metacognition. Students are encouraged to reflect on their thinking and learn how to self-regulate so that they can apply these skills to varied problem-solving activities. The Singapore Ministry of Education uses a pentagon with problem solving in the center to represent its curriculum framework.

This framework aligns with a strong base of foundational research and has also been proven to produce exceptional results both internationally and within the United States. 

Singapore Mathematics Framework

From the Singapore Ministry of Education

“Singapore Math’s resounding success can be traced to its unique pedagogy which helps students master the concrete, pictorial, and abstract. What we have learned from Singapore has enabled us to form a program that has been proven to improve math scores wherever it is implemented.” —Marshall Cavendish, Singapore
Foundational Research

Singapore Math® is built upon key research-based principles

Problem Solving

Principles From Research
“Problem solving is a fundamental part of mathematics—and everyday life. The ability to solve problems is both a goal of mathematics—and a tool within mathematics. As such, problem solving should be integrated into all mathematical learning situations.” —National Council of Teachers of Mathematics, 2000

Turning Principles into Success With Math in Focus
Problem solving is at the heart of the Singapore Math® curriculum. Each chapter contains numerous embedded problem-solving situations so that students learn to flexibly apply their mathematical knowledge. Additionally, Put On Your Thinking Cap! problems require students to extend the concepts they have learned to non-routine situations to demonstrate mastery.

Conceptual Understanding

Principles From Research
“This concrete to pictorial to abstract approach benefits all students but has been shown to be particularly effective with students who have mathematics difficulties, mainly because it moves gradually from actual objects through pictures and then to symbols.” —Jordan, Miller, & Mercer, 1998

Turning Principles into Success With Math in Focus
Singapore Math® emphasizes a concrete-pictorial-abstract pedagogy. Students are first introduced to concepts with concrete manipulatives, which allow them to experience and understand the math they are learning. They then learn to visually represent concepts using models, including number bonds and bar models. Finally, once students have a strong understanding of the concept, they move to the abstract stage where they use symbols, such as numbers and equations, to represent mathematical situations.

Visualization/Representation

Principles From Research
“For students to understand such mathematical formalisms, we must help them connect these formalisms with other forms of knowledge, including everyday experience, concrete examples, and visual representations. Such connections form a conceptual framework that holds mathematical knowledge together and facilitates its retrieval and application.” —Donovan & Bransford, 2005, p. 364

Turning Principles into Success With Math in Focus
“Many students who have difficulty grasping abstract mathematical concepts would benefit from visual representations of mathematical ideas. As part of this approach, the Singapore illustrations demonstrate how to graphically decompose, represent, and solve complicated multi-step problems.” —Ginsburg, et al., 2005, p. xii.

Math in Focus teaches students several consistent visual models they can use to make sense of mathematical relationships and solve problems. They include bar models, place-value charts, number bonds, array models, and more. Each model is fully integrated into the program and carried across grade levels, allowing students to build upon them and understand increasingly complex concepts.

Differentiated Instruction

Principles From Research
“Differentiated instruction is an instructional process that has excellent potential to positively impact learning by offering teachers a means to provide instruction to a range of students in today’s classroom situations.” —Hall, Strangman, & Meyer, 2003

Turning Principles into Success With Math in Focus
Math in Focus supports mathematical instruction at a variety of levels to target all learners, from struggling to gifted. Teachers have access to online and print resources including Reteach, Extra Practice, and Enrichment. Students also benefit from colorful, engaging online Interactivities. Additional support is included in the Teacher’s Edition to further differentiate instruction and ensure success for all learners.

International Results

Strong research-based foundations lead to exceptional international results

Data from international studies has shown that the United States has been surpassed in its mathematics performance. Meanwhile, Singapore’s students have consistently been top performers in international assessments. This is evidenced in Singapore’s consistent top performance on the TIMSS and PISA™ studies.

Trends in International Math and Science Study (TIMSS)
Since the Trends in International Math and Science Study (TIMSS) began in 1995, Singapore has consistently ranked at the top. In the latest TIMSS report, Singapore ranked first among the top 15 nations, outperforming the United States by 65 points (Provsanik et al., 2016).

OECD Programme for International Student Assessment (PISA)
In 2012, Singapore participated in the PISA study, which assesses 15-year-olds in industrialized countries. Singapore was a top-performing nation in math, and while Singapore students scored significantly above the international average, the United States scored below the average, ranking #36 out of 66. (OECD, 2014)

Common Core Connection

Singapore’s international success paves the way for the Common Core Standards

“Overall, the Common Core State Standards (CCSS) are well aligned to Singapore’s Mathematics Syllabus. Policymakers can be assured that in adopting the CCSS, they will be setting learning expectations for students that are similar to those set by Singapore in terms of rigor, coherence and focus.” —Achieve (achieve.org/CCSSandSingapore) 

Because of its consistent success in achieving exceptional student achievement and its foundation on key research-based principles, Singapore Math® was one of the key models for the Common Core State Standards. According to Achieve, an independent, nonprofit educational foundation.

Principles from the Common Core “For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country.” —Common Core State Standards, corestandards.org

Turning Principles into Success with Math in Focus One of the key high-performing countries that the creators of the Common Core State Standards looked at was Singapore, whose mathematics curriculum truly embodies the notion of focused and coherent. Through multi-day lessons and minimal repetition from year to year, students learn concepts in depth to mastery.

Principles from the Common Core “The composite standards [of Hong Kong, Korea, and Singapore] have a number of features that can inform an international benchmarking process for the development of K–6 mathematics standards in the U.S. First, the composite standards concentrate the early learning of mathematics on the number, measurement, and geometry strands with less emphasis on data analysis and little exposure to algebra.” —Common Core State Standards, corestandards.org

The key ideas in the Common Core State Standards parallel the Singapore Mathematics Framework.

Turning Principles into Success with Math in Focus Math in Focus emphasizes number and operations in every grade. The textbook is divided into two books, roughly a semester each. Book A focuses on number and operations while Book B focuses on geometry and measurement, where number concepts are practiced, connected, and applied.

Principles from the Common Core “One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.” —Common Core State Standards, corestandards.org

Turning Principles into Success with Math in Focus The Singapore Mathematics Framework and pedagogy emphasize deep understanding, which is demonstrated through consistent opportunities to explain why mathematical concepts work. This is modeled for students throughout Math in Focus with thought bubbles, which display pictures of students expressing their understanding. Students then have the opportunity to justify their own understanding through activities such as Math Journals.

References

Achieve (2010). Comparing the Common Core State Standards and Singapore’s mathematics syllabus. Washington, DC: Author. Retrieved from http://achieve.org/CCSSandSingapore

Donovan, S. & Bransford, J. (2005). How students learn: mathematics in the classroom. Washington, DC: National Research Council. 364.

Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). What the United States can learn from Singapore’s world-class mathematics system (and what Singapore can learn from the United States): An exploratory study. Washington, DC: American Institutes for Research

Hall, T., Strangman, N., & Meyer, A. (2003). Differentiated instruction and implications for UDL implementation. National Center on Accessing the General Curriculum. Retrieved January 15, 2009 from http://www.k8accesscenter.org/... nstruction.asp

Jordan, L., Miller, M., & Mercer, C. (1998). The effects of concrete to semi-concrete to abstract instruction in acquisition and retention of fraction concepts and skills. Learning Disabilities: A Multidisciplinary Journal, 9, 115–122.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Author.

Provasnik, S., Malley, L., Stephens, M., Landeros, K., Perkins, R., and Tang, J.H. (2016). Highlights From TIMSS and TIMSS Advanced 2015: Mathematics and Science Achievement of U.S. Students in Grades 4 and 8 and in Advanced Courses at the End of High School in an International Context (NCES 2017-002). U.S. Department of Education, National Center for Education Statistics. Washington, DC. Retrieved from http://nces.ed.gov/pubsearch.

OECD (2014). PISA 2012 Results in focus: What 15-year-olds know and what they can do with what they know. Paris, France: Author. Retrieved from http://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf