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Exploring Singapore Math: Methodology & Curriculum Guide

Ever wondered what makes Singapore Math so special?  Well, get ready for a journey into its world! Are you facing a math meltdown with your child? Or are you a teacher in need of new tricks to spice up your math lessons? Fear not! This guide is your lifeline. We’ll unravel the mysteries of Singapore Math using simple language. From understanding its unique method to choosing the perfect curriculum, we’ve got your back. So, let’s dive into the fascinating world of Singapore Math together and make learning a blast!

Understanding Singapore Math: A Holistic Approach to Mathematical Learning

Singapore Math isn’t just about numbers and equations; it’s a revolutionary approach to teaching and learning mathematics. So, what exactly is Singapore Math, and why is it gaining global recognition?

The Essence of Singapore Math

Singapore Math encompasses a unique blend of methodologies aimed at fostering deep conceptual understanding and problem-solving skills among students. Unlike traditional rote memorization, Singapore Math adopts a concrete-to-pictorial-to-abstract(CPA) approach, guiding students through a journey of discovery rather than mere repetition.

1. Concrete Learning: Laying the Foundation

At the heart of Singapore Math lies the concept of concrete learning. Students are introduced to mathematical concepts using tangible, hands-on manipulatives such as blocks, cubes, and geometric shapes. This tactile experience helps solidify their understanding of abstract mathematical ideas by grounding them in real-world contexts.

For example, instead of simply memorizing multiplication tables, students might use physical objects to explore the concept of multiplication, grasping the fundamental principles through direct manipulation and exploration.

2. Pictorial Learning: Visualizing Mathematics

Once students have grasped the concepts concretely, they move on to the pictorial stage. Here, abstract mathematical ideas are represented visually through diagrams, illustrations, and model drawings. These visual representations serve as powerful tools for students to visualize and solve complex mathematical problems.

For instance, when learning about fractions, students might use bar models or fraction circles to represent and compare different fractions, making abstract concepts more accessible and intuitive.

3. Abstract Learning: Transitioning to Symbolic Representation

Finally, students transition to the abstract stage, where mathematical concepts are represented symbolically using numbers, symbols, and mathematical notation. By this stage, students have developed a solid foundation of understanding through concrete and pictorial experiences, enabling them to tackle abstract mathematical problems with confidence.

For example, after mastering the concept of addition using concrete objects and visual models, students can seamlessly transition to solving addition problems using mathematical symbols and equations.

Why Singapore Math Works

The success of Singapore Math can be attributed to its emphasis on conceptual understanding, problem-solving, and critical thinking skills. By guiding students through a structured progression from concrete experiences to abstract concepts, Singapore Math equips them with a deep and lasting understanding of mathematics.

Moreover, Singapore Math’s focus on mastery learning ensures that students build a strong foundation of mathematical skills and concepts before progressing to more advanced topics. This approach not only fosters academic success but also cultivates a genuine love for mathematics among students.

Exploring the Pros and Cons of Singapore Math

Singapore Math has garnered widespread acclaim for its innovative approach to mathematics education. However, like any educational methodology, it comes with its own set of advantages and disadvantages. Let’s delve into the pros and cons of Singapore Math to gain a comprehensive understanding of its efficacy and limitations.

Pros of Singapore Math:

• Clear and Coherent Curriculum: The Singapore Math curriculum is well-structured and cohesive, with a clear progression of topics from one grade level to the next. This consistency facilitates smooth transitions for students and provides educators with a roadmap for effective instruction.
• Engaging and Interactive Lessons: The use of hands-on manipulatives, visual models, and problem-solving activities makes Singapore Math lessons engaging and interactive for students. This active participation enhances student motivation and deepens their understanding of mathematical concepts.
• Emphasis on Conceptual Understanding: One of the primary strengths of Singapore Math is its focus on deep conceptual understanding rather than rote memorization. By using concrete manipulatives and visual representations, students develop a solid foundation of mathematical concepts that enables them to tackle complex problems with ease.
• Mastery Learning: Singapore Math promotes mastery learning, allowing students to progress at their own pace and ensuring that they achieve a thorough understanding of each mathematical concept before moving on to the next. This approach fosters long-term retention and application of mathematical skills.
• International Recognition: Singapore Math has consistently produced high achievers in international assessments such as the Trends in International Mathematics and Science Study (TIMSS). Its success on a global scale has cemented its reputation as a leading mathematics education approach.

Cons of Singapore Math:

• Requirement for Teacher Training: Implementing Singapore Math effectively requires teachers to undergo comprehensive training to familiarize themselves with the curriculum and instructional strategies. This can be a significant investment of time and resources for schools and educators.
• Limited Focus on Applied Mathematics: While Singapore Math excels in developing strong foundational skills and problem-solving abilities, some critics argue that it places less emphasis on real-world applications of mathematics. This narrow focus may not fully prepare students for practical situations outside the classroom.
• Consumable Materials: The use of manipulatives and workbooks in Singapore Math often involves consumable materials that need to be replenished regularly. This recurring expense can be a financial burden for schools and families, particularly those with limited resources.
• Potentially Challenging for Some Students: The rigorous and accelerated pace of Singapore Math may pose challenges for students who require additional support or have different learning styles. Educators must differentiate instruction to meet the diverse needs of all learners.
• Alignment with Local Standards: While Singapore Math is renowned for its effectiveness internationally, educators in some regions may encounter challenges aligning it with local educational standards and requirements. Flexibility and adaptation may be necessary to ensure alignment with specific curriculum frameworks.

Exploring the Singapore Math Curriculums: A Comprehensive Overview

Singapore Math offers a diverse range of curriculums tailored to different educational settings and grade levels, each with its own unique features and instructional approaches. Let’s take a closer look at some of the prominent Singapore Math curriculums and their key components.

Primary Mathematics:

Primary Mathematics is one of the flagship Singapore Math curriculums, widely used in the United States and Canada. It comprises four editions, each designed to cater to specific educational standards and requirements.

• U.S. Edition: This edition closely mirrors the original Singapore Math program but incorporates U.S. measurements and currency to align with American educational standards.
• Standards Edition: Developed to meet the 2006 Mathematics Content Standards for California Public Schools, the Standards Edition includes additional topics such as probability, data analysis, negative numbers, and coordinate graphing.
• Common Core Edition: Aligned with the Common Core State Standards, this edition features minor adjustments to the scope and sequence, with updated teacher guides to include student materials.
• 2022 Edition: Representing a significant departure from previous editions, the 2022 Edition introduces entirely new content and structure, reflecting current classroom practices in Singapore and offering enhanced differentiation opportunities.

Dimensions Math:

Geared toward PK-5 grades, Dimensions Math serves as Singapore’s flagship program, renowned for its comprehensive, rigorous, and visually appealing design. Comprising four main components—textbooks, workbooks, teacher’s guides, and tests—Dimensions Math follows the Singapore Math approach, emphasizing the Concrete-Pictorial-Abstract (CPA) progression and mastery of essential mathematical concepts.

Math in Focus:

Math in Focus, the U.S. version of Singapore’s mathematics program My Pals are Here!, is distributed through Houghton Mifflin Harcourt and covers grades K to 8. The curriculum underwent a significant revision in 2020, incorporating printed materials and online resources to support both schools and homeschool students.

Dimensions Math Beyond Grade 5:

For middle school years (grades 6-8), Dimensions Math offers a comprehensive curriculum that integrates pre-algebra, algebra, geometry, trigonometry, and advanced math topics. This rigorous series continues the Singapore Math approach, focusing on problem-solving and mathematical reasoning skills.

Choosing the Right Singapore Math Curriculum: A Guide for Educators and Parents

Selecting the appropriate Singapore Math curriculum is crucial for optimizing student learning outcomes and ensuring alignment with educational objectives. Here’s a comprehensive guide to help educators and parents navigate the process effectively.

• Understand Your Educational Objectives: Before choosing a Singapore Math curriculum, it’s essential to clarify your educational objectives and priorities. Consider factors such as curriculum alignment with educational standards, instructional approach, and desired learning outcomes for students.
• Assess Student Needs: Take into account the diverse needs and learning styles of your students when selecting a Singapore Math curriculum. Conduct thorough assessments to identify students’ strengths, weaknesses, and areas for improvement, and choose a curriculum that caters to their individual learning needs.
• Review Curriculum Components: Evaluate the components of each Singapore Math curriculum, including textbooks, workbooks, teacher’s guides, and supplementary materials. Consider factors such as clarity of content, instructional support, and alignment with instructional objectives.
• Consider Curriculum Flexibility: Opt for a Singapore Math curriculum that offers flexibility to accommodate diverse teaching styles and classroom settings. Look for curricular resources that allow for customization and adaptation to meet the unique needs of your students.
• Assess Resource Availability: Take stock of available resources, including teacher training, manipulatives, and technology infrastructure, before selecting a Singapore Math curriculum. Ensure that you have the necessary resources and support systems in place to effectively implement the chosen curriculum.
• Seek Community Insights: Tap into online communities, professional networks, and educator forums to gather insights and recommendations from peers who have experience with different Singapore Math curriculums. Learn from their experiences and consider their feedback when making your decision.

Discover the WuKong Math!

WuKong Math Course isn’t just another math class—it’s a dynamic journey designed to spark excitement for math while honing critical thinking skills. Here’s why their course, inspired by Singapore Math, is in a league of its own:

Revolutionize your child’s math education with WuKong Advanced Course!

What Sets Their Course Apart:

• Flexible Sessions: With sessions running 60 to 90 minutes once a week, their course effortlessly fits into any busy schedule.
• Personalized Attention: Classes are small, ranging from 1 to 28 students, ensuring every learner receives the attention and interaction they need.
• For All Ages: Perfect for kids aged 6 to 18, their course offers a comprehensive learning experience suitable for all skill levels.

Exciting Features of the Course:

• Aligned Curriculum: Their syllabus aligns with school standards and international competitions, following the principles of Singapore Math and setting students up for success in exams and contests.
• Interactive Learning: Dive into math with captivating story themes and vibrant animations that make learning not just effective, but enjoyable too.
• Tailored Practice: Handpicked practice problems offer real-world applications, empowering students to master concepts and sharpen their problem-solving skills.
• Innovative Teaching: Through the “6A teaching method,” blending inquiry-based learning with top-notch teaching expertise, inspired by the principles of Singapore Math, students gain a profound understanding and passion for math.

FAQs about Singapore Math:

Q1. what is the history behind singapore math’s success.

Singapore Math’s success can be traced back to Singapore’s decision in the early 1980s to develop its own math curriculum. This shift led to a remarkable ascent in international rankings, with Singaporean students consistently excelling in assessments like TIMSS, showcasing the effectiveness of their unique approach.

Q2. Why prioritize problem-solving in Singapore Math?

Problem-solving is prioritized in Singapore Math because it encourages critical thinking, creativity, and a deeper understanding of mathematical concepts. By focusing on problem-solving, students develop the skills necessary to tackle real-world challenges and excel in mathematics.

Q3. Is Singapore Math suitable for all learners?

Yes, Singapore Math is designed to cater to diverse learners. Its emphasis on understanding mathematical concepts through visual representations and hands-on activities makes it accessible and effective for students with varying learning styles and abilities.

In this article, we explored the world of Singapore Math, a method that makes learning math fun and effective. We learned about its unique approach, emphasizing understanding over memorization, and how it prepares students for success in exams and real-life situations. We also discovered the Wukong Math Advanced Course, inspired by Singapore Math, offering interactive lessons and personalized attention to help students excel. Whether your child needs extra support or is looking to challenge themselves further, enrolling in the Wukong Math Advanced Course can be the key to unlocking their mathematical potential and building a strong foundation for the future.

Delvair holds a degree in Physics from the Federal University of Maranhão, Brazil. With over six years of experience, she specializes in teaching mathematics, with a particular emphasis on Math Kangaroo competitions. She firmly believes that education is the cornerstone of society’s future. Additionally, she holds the conviction that every child can learn given the right environment and guidance. In her spare time, she enjoys singing and tending to her plants.

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Delvair holds a degree in Physics from the Federal University of Maranhão, Brazil. With over six years of experience, she specializes in teaching mathematics, with a particular emphasis on Math Kangaroo competitions. She firmly believes that education is the cornerstone of society's future. Additionally, she holds the conviction that every child can learn given the right environment and guidance. In her spare time, she enjoys singing and tending to her plants.

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What Is Singapore Mathematics?

Why the singapore mathematics method., the history of singapore mathematics.

​Before the 1980s, Singapore imported its math textbooks from other countries and its students were ranked in the lower half of countries in mathematics. In the beginning of 1980, Singapore started developing its own primary and secondary textbooks, The Curriculum Development Institute of Singapore published its first math program in 1982. In 1995, Singapore’s students were ranked first in the Trends in International Mathematics and Science Study (TIMSS). Since then, Singapore’s students have been consistently ranked among the top.

​ THE SINGAPORE MATHEMATICS FRAMEWORK

​SOURCE: WWW.MOE.EDU.SG

​The Singapore Mathematics framework was developed on the basis that mathematical problem solving is central to learning math. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems. The development of mathematical problem solving ability is dependent on five inter-related components, namely, Concepts, Skills, Processes, Attitudes and Metacognition.

​CONCEPTS/ CONCRETE LEARNING

​Mathematical concepts covers numerical, algebraic, geometrical, statistical, probabilistic and analytical concepts. Students would be given a variety of learning experiences to enable them to develop a good understanding of mathematical concepts and their connections and applications. Concrete materials (manipulatives) such as cubes, blocks, place value mats, geometric figures and practical work are used as part of the learning experience.

​The Singapore Mathematics method in elementary grades uses the concrete to pictorial to abstract learning approach to encourage active thinking, understanding and communication of mathematical concepts and problem solving. Singapore Mathematics also emphasizes mental math and model drawing. This approach helps students transition better to more complex mathematical problems and algebra.

​Singapore Mathematics emphasizes the “why” before the “how”. At the concrete stage our center uses manipulatives such as cubes, blocks, place value mats and geometric figures to model each mathematical concept.

​PICTORIAL LEARNING APPROACH

​At this stage, the concrete model is transformed into a pictorial level. This may involve model drawing, drawing circles, dots or number bonds.

​Model drawing is an excellent approach solving word problems. Model drawing is versatile can be used for first grade addition problems or 5th grade pre-algebra. Not only can this be used as a visual aid, but a teacher can use the same model to extend learning and ask questions such as: What is the ratio of the amount of money Kathy’s has to the amount of money Lucy has? or Howmuch more money does Kathy have than Lucy?

ABSTRACT LEARNING APPROACH

​At this stage, the teacher models mathematical concepts at a symbolic level using numbers, notations and math symbols. Students are encouraged to reflect on mathematical attributes and relationships.

​Mathematical skills include procedural skills in numerical calculation, algebraic manipulation, spatial visualization, data analysis, measurement and estimation.

Understanding underlying mathematical principles is emphasized before developing students to be competent in mathematical skills.

​ Mathematical processes refer to process skills and includes reasoning, communication and connections, thinking skills and heuristics, application and modelling.

​Being able to use mathematical language to express mathematical ideas and arguments clearly and logically helps students sharpen their mathematical thinking. Students should be able to make linkages between mathematics and everyday life and other subjects.

​Singapore Mathematics encourages students to use thinking skills and heuristics to solve mathematical problems. Under the framework, heuristics are grouped in four categories according to how they are used.

​1) To give a representation (e.g. draw a diagram or use equations)

2) To make a calculated guess (e.g. look for patterns or make suppositions)

3) To go through the process (e.g. work the problem backwards)

4) To simplify or restate the problem.

​Application and modelling play an important role in developing understanding and competence in mathematics. In mathematical modelling, students learn to use a variety of data representations and apply appropriate methods and tools to solve real-world problems.

​Singapore Mathematics makes math fun. meaningful and relevant to foster positive attitudes towards mathematics.

​METACOGNITON

​Metacognition or “thinking about thinking”, refers to the one’s awareness and ability to control the thinking process and selection and use of strategies to solve mathematical problems. By providing students with the metacognitive experience, students are empowered to develop their own problem solving skills.

​Some activities used to encourage metacognition awareness include:

1) Encouraging students to think aloud during the problem solving process.

2) Encouraging students to find and discuss alternative methods of solving a mathematical problem and check to see if the answer is appropriate and reasonable.

3) Exposing students to general problem solving and thinking skills and heuristics and apply it to problem solving.

Singapore Mathematics In the News

Singapore mathematics in the us, kenliworth, il (district 38) adopts singapore mathematics, jeff and mackenzie bezos use singapore mathematics to teach their kids mathematics., in surprise move, seattle schools approve ‘singapore math’.

Singapore Math

Looking for Singapore Math help? We have a collection of video lessons, examples and solutions, activities and worksheets that are based on Singapore Math or Maths.

Related Pages Word Problems Solved The Singapore Math Way 2-Step Word Problems And Bar Models Singapore Mental Math Strategies Math Games Math Worksheets

We will look at:

• What is Singapore Math or Maths?
• Using Singapore Math to solve word problems.
• Singapore Math from Grade 1 to Grade 6 (Videos and Worksheets).

What Is Singapore Math?

Introduction to Singapore Math Part 1. What are the benefits and strategies of Singapore Math? What are number bonds?

How To Use Model Drawing?

Introduction to Singapore Math Part 2.

Examples: (1) Carla and Jerome kept track of the miles they ran over the weekend. Carla ran three times as far as Jerome. If Carla ran 6 miles, how far did Jerome run?

(2) Mrs. Walsh made 300 cookies. She sold 3/4 of them and gave 1/3 of the remainder to her neighbor. How many cookies were left?

Helping Parents Explain Singapore Math - Word Problems 1

Demo for parents and educators on how to use “thinking blocks” (block diagrams) to help even young children - 1st grade, 2nd grade - understand, model and solve word problems.

Examples: (1) David has 45 marbles. His sister gave him 32 more. How many marbles does he have altogether?

(2) Caleb wants to buy a scooter that costs $63. He saved $38 so far. How much more money does Caleb need?

Helping Parents Explain Singapore Math - Word Problems 2

Part 2: 2-Step Word Problems.

Examples: (1) Anna is riding in a bike-a-thon. She rode 49 miles in the morning, stopped for a lunch break, then rode another 37 miles in the afternoon. Anna was then only 62 miles from the finish line. How long was Anna’s bike ride?

(2) Kierka bought a juice for 55 cents, a breakfast bar for 27 cents and a package of gum. She spent $1.22 altogether. How much did the package of gum cost?

Solve Word Problems Using Singapore Math: By Topics

These lessons and videos show how to use the block models (tape diagrams or bar models) in the Singapore Math method of solving word problems. The blocks can assist the students in visualizing, modeling and solving the word problems without using algebra.

Addition Word Problems (1-step word problems) Addition Word Problems (2-step word problems) Subtraction Word Problems (1-step word problems) Subtraction Word Problems (2-step word problems) Addition & Subtraction Word Problems (2 or 3 steps) Addition & Subtraction Word Problems (2 or 3 amounts) Multiplication Word Problems (1-step word problems) Multiplication Word Problems (2-step word problems) Multiplication Word Problems (comparing 2 or 3 amounts) Division Word Problems (1-step word problems) Division Word Problems (2-step word problems) Mixed Operations Word Problems (3-steps) Solving Challenging Word Problems (mixed operations) Fraction Word Problems (introductory) Fraction Word Problems (intermediate) Fraction Word Problems (difficult) Decimal Word Problems (1-step word problems) Decimal Word Problems (2-step word problems) Decimal Word Problems (difficult) Percent Word Problems Ratio Word Problems Algebraic Reasoning Problem Sums

Solve Word Problems Using Singapore Math: By Grades

2nd Grade Word Problems: 1-step Addition, Subtraction, Multiplication & Division Word Problems: Time, Fraction Word Problems: Model Drawing, Addition Model

3rd Grade Word Problems (2-step Addition & Subtraction) 3rd Grade Word Problems (2-step Multiplication & Division) Grade 3 Basic Word Problems 2-Step Word Problems and Bar Models Grade 3 Solving Word Problems using Bar Models Grade 3 More Word Problems: Multiplication, Mass, Time 4th Grade Word Problems (3-step Mixed Operations) 4th Grade Word Problems: time, weight, volume, measures

5th Grade Word Problems (Ratios & Proportions) 5th Grade Word Problems (Percent) Ratio (Equivalent Ratios, Simplify) Data Analysis (Average) Measurements (Triangles, Cubes & Cuboids) Grade 5 Word Problems Fraction Word Problems Whole Numbers Word Problems 1 - 4 Whole Numbers Word Problems 5 - 8 Whole Numbers Word Problems 9 - 12 Whole Numbers Word Problems 13 -16 Whole Numbers Word Problems 17 - 20 Whole Numbers Word Problems 21 - 23 Ratio & Proportion Word Problems Percent Word Problems 1 - 4 Fraction, Discount, Prices, Tax. Percent Word Problems 5 - 8 Banking Principles, Measurement (length), Convert Percent to Fraction. Decimal Word Problems 1 - 4 Subtraction of two decimals and unit conversion, Measurement using decimals to explain unit conversion. Decimal Word Problems 5 - 8 Multiplying decimals by 10s and rounding off decimals, Word problems involving decimals, fractions and measurement, Compare decimals involving measurement (volume). Decimal Word Problems 9 - 11 A measurement (area) word problem involving decimals, Word problems involving measurement (mass) and unit conversion.

6th Grade Word Problems (Ratios & Fractions) 6th Grade Word Problems (Ratios & Proportions) 6th Grade Word Problems (Percent) 6th Grade Word Problems (Average Speed) Elementary and Intermediate Word Problems Advanced Word Problems Grade 6 Word Problems 1 - 4 Simplifying Algebraic Expressions, Average Speed, Circles, Triangles and 4-sided figures. Grade 6 Word Problems 5 - 11 Venn Diagrams, More Challenging Word Problems, Heuristic Approach to Problem Solving. Data Analysis Read, make and interpret pie charts, Solve 1-step word problems using information presented in a pie chart. Grade 6 Geometry Volume of Cubes and Cuboids word problems.

7th Grade Word Problems (Ratios & Proportions) 7th Grade Word Problems (Fractions & Percent)

Worksheets And Questions For Grade 1 Singapore Math (Primary 1)

Number Bonds Numbers To 10 Making number bonds with cubes, Learn Number Bonds in Song, What Makes 10? Number Bonds - Addition within 10 Number Bonds - Subtraction within 10

Fact Families or Family of Number Sentences Making A Family Of Number Sentences, Fact Families.

Place Value: Numbers to 20 Place Value: Give the digit in the tens or ones place Place Value: Give the place value of the digit

Addition using number bonds Adding by Making 10, Adding Tens and Ones, Add a Two-Digit Number and One-Digit Number, Adding by grouping tens. Worksheets To Practice Addition 2-digit number + 1-digit number (no regrouping) 2-digit number + 1-digit number (with regrouping)

Subtraction using number bonds Subtract Ones, Subtract a One-Digit Number from a Two-Digit Number, Subtract Tens, Subtract Tens and Ones. Worksheets To Practice Subtraction 2-digit number − 1-digit number (no regrouping) 2-digit number − 1-digit number (with regrouping)

Adding and Subtracting Multiples of 10 Adding a Multiple of 10 to a Two-Digit Number, Subtract a Multiple of 10 from a Two-Digit Number. Word Problems for addition and subtraction

Worksheets & Questions For Grade 2 Singapore Math (Primary 2)

Numbers: Tens & Ones, Two-Digit Number Words, Place Values Worksheets to practice 2-digit number words Mental Math Strategies Add/Subtract Ones Add subtract tens

Worksheets & Questions For Grade 3 Singapore Math (Primary 3)

Place Values Read & write up to 10,000, Relate each 4-digit number to its place value, Compare & order numbers within 10,000, Number patterns with place values. Worksheets To Practice Place Values Give the digit in the thousands, hundreds, tens or ones place Give the place value of a specified digit

Adding 4-digit numbers Subtracting 4-digit numbers Worksheets To Practice Addition 4 digit numbers + 2-digit numbers 4 digit numbers + 3-digit numbers 4 digit numbers + 4-digit numbers Worksheets To Practice Subtraction 4 digit numbers − 2-digit numbers 4 digit numbers − 3-digit numbers

Worksheets & Questions For Grade 4 Singapore Math (Primary 4)

Fractions Types of Fractions, Improper Fractions & Mixed Numbers, Simplifying Fractions & GCF, Comparing Unlike Fractions & LCM, Subtracting Related Fractions. Worksheets on Fractions Equivalent Fractions, Comparing Fractions, LCM, Adding & Subtracting Fractions. Shape & Area Which shape cannot tessellate? Areas of Figures,Decimals.

Worksheets & Questions For Grade 5 Singapore Math (Primary 5)

Whole Numbers Place Values of Whole Numbers, Writing Whole Numbers from Figures to Words, Writing Whole Numbers from Words to Figures or Numerals. Comparison & Approximation Comparison, Ordering & Patterns in Whole Numbers, Approximation & Estimation, Whole Numbers. Basic Operations Multiplying Whole Numbers by 10s, 100s & 1000s, Dividing Whole Numbers by 10s, 100s & 1000s, Operations on Whole Numbers, Order of Operations.

Add & Subtract Fractions Add fractions (adding unlike fractions), Subtract fractions (subtracting unlike fractions), Add mixed fractions or mixed numbers, Subtract mixed numbers or mixed fractions. Multiplying & Dividing Fractions Multiplying fractions, Multiplying a mixed number (mixed fraction) & a whole number, Dividing a proper fraction by a whole number, Concept of fraction as division.

Decimals Fractions & decimals, Multiplying Decimals by 10s, 100s & 1000s, Dividing Decimal Numbers by 10s, 100s & 1000s, Rounding off Decimals, Approximation & Estimation of Decimals. Multiply Decimals by 10s, 100s & 1000s Divide Decimals by 10s, 100s & 1000s

Percent Introduction to Percent, Percent & Fraction, Percent & Decimal.

Geometry Angles, angles on a straight line Angles at a point Vertically opposite angles Isosceles triangle, equilateral triangle & right-angled triangle Sum of angles of a triangle Drawing different types of triangle Find unknown angles in a four-sided figure Drawing parallelograms, rhombus & trapeziums

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What Is Singapore Math?

• History of Singapore Math
• Singapore Math Curriculum
• Singapore Math in Action
• Pros and Cons

Frequently Asked Questions

The Singapoe Math method was developed by Singapore's Ministry of Math Education and it is taught in public schools in Singapore. This method follows three steps, moving from hands-on math to picture models, to abstract mathematical equations. It's proven to be quite an effective way to learn math and many American homeschooling families have adopted it.

The framework of Singapore Math is developed around the idea that learning to problem-solve and develop mathematical thinking are the key factors to being successful in math. Without a solid foundational base, students won’t have anything to draw on when it comes to increasingly complicated math learning.

This doesn’t mean, however, that the skills elementary students learn are simplistic. Rather, the view is that when teaching a concept or a skill, it’s essential to spend as much time as needed for students to master the skill. That way, you’re not moving on to the next concept with the thought that earlier skills can always be retaught if necessary. Teachers can simply revisit instead, opening up more instructional time.

The CPA Approach

The method uses a three-step learning model, which consistently introduces concepts in a progression. It moves from the concrete to pictorial representation and then on to the more abstract (Concrete, Pictorial, Abstract or CPA). Students learn not only to know how to do something but also why it works.

History of Singapore Math 

What is referred to as Singapore Math in other countries is, for Singapore, simply math. The program, developed under the supervision of the Singaporean Minister of Education, was introduced as the Primary Mathematics Series in 1982.

In 1998, Jeff and Dawn Thomas realized that the math program they brought back from Singapore and used to supplement their own child’s schoolwork could be helpful to schools and homeschoolers across the nation. As the program began garnering attention, the couple incorporated under the name Singaporemath.com Inc. and marketed their books under Singapore Math, a registered trademark.

In the U.S., Singapore Math first gained popularity among homeschoolers and small private schools. Singapore is consistently a top country in Trends in International Mathematics and Science Study (TIMSS), revealing Singapore’s fourth-graders and eighth-graders as the leading math performers in the world. Of note, Singapore remains the top-performing country as of the 2019 TIMSS.

Singapore Math Curriculum 

With so much interest in the method, in 2007, U.S. educational publisher Houghton Mifflin Harcourt teamed up with the leading academic publisher in Singapore to publish and distribute a math series called "Math in Focus: The Singapore Approach." This series and the Thomas' "Dimensions Math" and "Primary Mathematics" are the only curriculum packages available to United States educators and parents for teaching the Singapore math method.

The Singapore curriculum comes with a textbook, workbook, and teacher’s or home instructor’s guides. The textbooks present new concepts, the workbooks offer practice to solidify the concepts, and the guides provide lesson plans and instructions for using the books.

Singapore Math in Action 

A typical third-grade math instruction might go something like this: "Today we’re going to learn about long division." Students watch while the teacher demonstrates the steps and actions necessary to solve a long division problem.

Singapore Math instruction looks different. Instead of watching a demonstration of a new math concept and then doing similar problems to reinforce the idea, students are tasked with mastering the theory at the onset.

For instance, with the long division example, a parent or teacher might say, "I have some pennies I want to put in some jars." The instructor then places baggies of pennies and jars on the table. They then clarify, "I have 17 pennies I want to share equally in 5 jars." First, students must figure out how that might work and then share their ideas about what sharing equally means and how they approached the problem.

Singapore Math Pros and Cons

Singapore Math’s unique focus on building problem-solving skills aligns with the Common Core State Standards. While some people see this as a benefit, others find it more detrimental.

Some find Singapore Math confusing for children to learn as part of a Common Core Standards framework and find that it unnecessarily complicates the teaching of mathematical principles to young children.

Singapore Math is popular with homeschoolers, private schools, and public schools alike—and for good reason. Research into the pedagogy of countries whose students excel in math, like Singapore and Japan, has found these countries’ use of diagrams in teaching math can provide a valuable bridge between early and advanced learning stages and encourage intuitive problem-solving skills.

Some benefits of Singapore Math include the following:

• It asks for students to build meaning to learn concepts and skills instead of rote memorization of rules and formulas.
• It aligns with the Common Core State Standards Initiative.
• It covers fewer topics in a year but in an in-depth way that ensures students have a foundation to move forward without needing to relearn concepts.
• Textbooks and workbooks are simple to read with clear and concise graphics.
• Textbooks are sequential, building on previously learned concepts and skills, which offers learning acceleration without additional work.

Despite the number of pros to Singapore Math and some research suggesting that it is superior to traditional U.S. textbooks, some schools find that the method is not easy to implement. 

Some drawbacks of Singapore Math include the following:

• It aligns with the Common Core State Standards (yes, this can be a pro and a con, depending on whom you ask).
• It may not work well for a nomadic student population. Many students move in and out of school districts, which isn’t a big problem when the math programs are similar. However, since Singapore Math is sequential and doesn’t re-teach concepts or skills, using the program could potentially set these students up for failure whether they’re moving into or out of a district using it.
• It has less of a focus on applied mathematics than traditional U.S. math textbooks. For instance, Everyday Mathematics, a curriculum developed by the University of Chicago, which came out around the same time as Singapore Math, emphasizes data analysis using real-life, multiple-step math problems. On the other hand, Singapore Math’s approach is more conceptual and ideological.
• It requires extensive and ongoing teacher training, which is neither financially nor practically feasible in some school districts and not always practical for homeschooled children.
• Supplies are consumable and must be re-ordered for every classroom every year, which can put a financial burden on already strained school budgets and homeschoolers alike.

How do you teach Singapore Math?

Teaching Singapore Math follows a Concrete, Pictorial, Abstract (CPA) approach that helps students understand math by building on existing knowledge. In the concrete phase, you will encourage students to interact with physical objects to work out problems. In the pictorial step, you will help students mentally connect their objects and visual representation. In the abstract phase, you will guide students to use numbers and math symbols.

How is Singapore Math different?

Singapore Math differs from other math curriculums in its approach. Instead of rote memorization and drilling concepts through similar problems, Singapore Math teaches students how to mathematically think so that they can rely on the theory and build on concepts.

How can I help my child with Singapore Math?

Remember that Singapore Math utilizes a progressive learning process that includes helping kids understand the concrete, the pictorial, and the abstract. If you are your child’s teacher, be sure to utilize the teacher’s guides, which offer lesson plans and instructions. Whether you are homeschooling or supporting a child who attends public or private school from home, you may find online communities, like Singapore Math’s Facebook group, helpful.

How do I know what level to start at in Singapore Math?

Singapore Math’s grades align with U.S. schools. Even so, it may be helpful to have your child take Singapore Math’s placement test.

What grades does Singapore Math cover?

Singapore Math is for students in pre-K through 8th grade.

What comes after Singapore Math?

Since Singapore Math teaches students critical mathematical thinking skills, students can transition to nearly any math curriculum after Singapore Math.

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Singapore School Mathematics Curriculum

• First Online: 07 April 2022

Cite this chapter

• Lu Pien Cheng 21 &
• Kai Kow Joseph Yeo 21  

Part of the book series: Education in the Asia-Pacific Region: Issues, Concerns and Prospects ((EDAP,volume 66))

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In Singapore, education is regarded as an investment instead of a social service. Singapore’s Education System has evolved over time and so have school mathematics curricula in Singapore. Mathematics education in Singapore schools in the twenty-first century is still going through a period of change. Mathematics is a compulsory subject up to Grade 10 in Singapore schools. The present-day School Mathematics Curriculum is based on a pentagonal framework with mathematical problem solving as its central focus. In this chapter, we review the developments of Singapore school mathematics curriculum for the past sixty years and describe some of the important features of the intended, attained and implemented aspects of the mathematics curriculum in Singapore. The implementation of the 2019 secondary mathematics syllabus and the 2020 primary mathematics syllabus began in 2020 and 2021, respectively. This chapter also examines the implications and issues related to the implementation of these two syllabuses.

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Cheng, L.P., Yeo, K.K.J. (2022). Singapore School Mathematics Curriculum. In: Lee, YJ. (eds) Education in Singapore. Education in the Asia-Pacific Region: Issues, Concerns and Prospects, vol 66. Springer, Singapore. https://doi.org/10.1007/978-981-16-9982-5_22

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