What is Singapore Math?

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Interest in Singapore Math is high because over the last three decades Singaporean students have consistently scored at the top in mathematics and science on international benchmarks such as TIMSS and PISA. These students are some of the best prepared in the world.

Their success is attributed to the high quality of the Singapore Math curriculum and strong teacher preparation programs. The learning process focuses on visualization in the context of problem-solving as opposed to mere memorization of facts.

What is the Singapore Math Method?

The Singapore Math method is founded on the constructivist research pioneered by Jerome Bruner in the United States in the 1960s. The Singapore Math pedagogy is based on the Concrete-Pictorial-Abstract Sequence. In this approach, students’ learning experiences are situated in a meaningful context that begins with explorations of concrete objects and virtual manipulatives and is followed by pictorial and abstract representations of these situations.

Mathematical concepts are abstract. Elementary school age children are entering the developmental phase where they can understand abstractions. It is important to create a bridge to understanding abstractions in a concrete and relevant context using common objects. Examples of common objects are apples, crayons, toy cars, etc. Examples of manipulatives include counters, connected cubes and others. The use of common objects and manipulatives corresponds to the concrete state. The pictures of these objects correspond to the pictorial representations of the objects. Subsequent calculations and equations correspond to the abstract stage.

The Singapore Math pedagogy for teaching math is based primarily on the five learning theories that were developed by leading European and American educators, mathematicians and psychologists of the 19th and 20th century: Jean Piaget, Jerome Bruner, Zoltan Diens, Lev Vigotsky, and Richard Skemp.

Jean Piaget, psychologist and educator, suggested that students should have ample learning time to accommodate new ideas. That’s why Singapore Math programs contain anchor tasks which are designed to be dealt with for a long time over the course of a unit. According to Piaget, children need to continually construct their understanding and then reconstruct prior ideas as they mature.

Jerome Bruner, an educator and a student of Jean Piaget, advocated for children to engage in concrete activities prior to moving to abstract learning. Bruner, believed that a student could learn almost anything, provided that instruction would go through appropriate stages. Each level in the instructional sequence should become more abstract.

Zoltan Diens, mathematician and educator, advocated that informal learning through exploration should take place before structured learning. He noticed that in trying to solve a problem, most people would engage in a random search for a solution. He called this stage “Free Play” and suggested that all learning should begin at this stage.

Lev Vigotsky, psychologist and educator, advocated cooperative learning in the zone of proximal development (ZPD). ZPD is the distance between a student’s independent problem-solving level and the potential level of problem solving under the guidance of an adult/expert.

Richard Skemp, mathematician and educator, suggested that it is important for students to develop a relational understanding of conceptual ideas. He believed that even elementary school children could create complex and complete conceptual frameworks and, as a result, they are capable of learning with deep understanding.

What is Bar Modeling?

Bar Modeling or model drawing is an ingenious problem-solving strategy built into the Singapore Math curriculum. Bar Modeling is a pictorial representation of mathematical quantities and their relationships. It helps students visualize abstract mathematical concepts to gain deeper understanding of the operations they need to use in order to solve word problems.

Bar Modeling improves student problem solving abilities because visual representations of word problems allow students to grasp them in their entirety (wholes) with minimum effort (law of Pragnanz). Bar Modeling allows students to organize textual information and then restructure it visually in a model. It helps students think holistically, gain insight and then solve the problem.

Bar Modeling is a term that was coined in the United States. The original term is the Model Method or Model Drawing that was developed in Singapore in the 1980s. Bar Models are also called Tape Diagrams or Strip Diagrams in the Common Core State Standards in Mathematics, New York State Modules, Eureka Math and some other elementary mathematics programs used in the United States.

The authentic Singapore Math curriculum is developed and tested in Singapore based on the curriculum approved by the Singapore Ministry of Education. The authentic program is focused on a few important topics and teaching problem-solving strategies in each grade. The small number of topics are explored in greater depth during the school year. Focusing on learning a few important topics in each grade reveals the main purpose of Singapore Math, which is to allow students to spend more time learning the most important concepts in elementary mathematics, deepen their understanding, and achieve mastery.

Due to its long-standing successful track record, interest in the Singapore Math curriculum has grown steadily over the last 10 years. Larger publishing houses began to notice the popularity of the Singapore Math curriculum and borrowed some elements of the program, such as model drawing and number bonds to incorporate into their programs. Some of these publishers even market their programs as Singapore Math. However, most of the programs that imitate the authentic curriculum lack the coherence and focus of the original materials from Singapore.

Junior Example

Advanced Example

Here's an example of how the concrete-pictorial-abstract approach would look in practice for teaching addition:
Concrete: The teacher gives the students a set of blocks and asks them to physically stack the blocks to show the concept of addition (for example, 2 blocks + 3 blocks = 5 blocks).
Pictorial: Next, the teacher provides students with a picture or a drawing showing two groups of objects (such as apples) and asks the students to count the total number of objects. The students then draw a similar picture to represent the sum (for example, 2 apples + 3 apples = 5 apples).
Abstract: Finally, the teacher introduces symbols (such as + and =) to represent the problem and solution (for example, 2 + 3 = 5). The students then practice solving problems using only symbols.
By following this approach, students are able to build a strong foundation for mathematical understanding and are better equipped to tackle more complex problems in the future.

Here's an example of how the concrete-pictorial-abstract approach could look for a more advanced topic, such as quadratic equations:
Concrete: The teacher gives the students a set of blocks and asks them to physically create a parabolic shape using the blocks to show the concept of a quadratic equation (for example, y = x^2).
Pictorial: Next, the teacher provides students with a graph of a quadratic equation (for example, y = x^2 + 4x + 4) and asks the students to analyze the graph. The students then use a ruler and a protractor to sketch a similar graph on their own paper.
Abstract: Finally, the teacher introduces the algebraic representation of the quadratic equation (for example, y = ax^2 + bx + c) and asks the students to solve for the coefficients (a, b, and c) given specific points on the graph. The students then practice solving for the coefficients using only symbols.
By following this approach, students are able to understand the abstract concepts of quadratic equations in a more concrete and visual way, making it easier for them to grasp the material and solve complex problems.

Placement Tests

Measures a student’s cumulative knowledge acquired in their prior grade level, uncover gaps, and establish learning goals.

Pre-Tests

A pre-test is given to assess the student’s level of readiness prior to teaching each new topic and unit. Gaps in student’s knowledge can be quickly filled with the lessons from the prior unit and grade.

Instructional videos

These fun, engaging and kid-friendly videos provide high quality Singapore Math instruction for each topic, unit and grade. They

Assisted practice exercises

The assisted practice exercises provide more visuals and guidance for students to acquire new concepts.

Games

Games motivate students to practice in a fun environment. They provide a lot of additional practice to reinforce development of procedural fluency

Benchmark practice exercises

The benchmark practice exercises enable on-level students to practice or reinforce concepts that they have already learned and develop procedural fluency

Intervention tests

The intervention tests allow teachers to diagnose whether students need simultaneous remediation of a number of skills.

Grade tests

The grade tests reveal students’ understanding of concepts learned throughout the grade level as well as abilities to apply that knowledge to solving non-routine and open-ended problems.

Why is the Skill Samurai Math Method so good? Is there any research?
There's a growing body of research that demonstrates the integration of Coding and Maths can boost student learning outcomes.

The MathCode Method is based on the Concrete-Pictorial-Abstract approach. A recent study found that the improvement of spatial sense ability (SSA) of students who received learning with the Concrete-Pictorial-Abstract (CPA) approach was significantly better compared to students who received conventional learning. (Putri, H. E., Rahayu, P., Muqodas, I., & Wahyudy, M. A. (2020). The Effect of Concrete-PictorialAbstract (CPA) in Improving Elementary School Students’ Spatial Sense Ability. Mimbar Sekolah Dasar, 7(1), 16-29. doi:http://dx.doi.org/10.17509/mimbar-sd.v7i1.19585.)

Mathematics and Coding: How Did Coding Facilitate Thinking? Calder, Nigel. (2022). The teachers involved in the project identified that the use of unplugged activities and coding language facilitated mathematical thinking in students. ScratchMaths has been shown to be an effective resource for developing coding and computational thinking in primary-aged children in the UK. (Calder, Nigel. (2022). Mathematics and Coding: How Did Coding Facilitate Thinking?)

The results showed that children with coding play experience had higher levels of computational thinking, self-regulation, and attention concentration. A positive correlation was found between computational thinking and attention concentration in children with coding play experience. The study concluded that coding play experience is an important factor in enhancing computational thinking in early childhood. (Kim, Mi-Jung & Pu, Sung-Sook. (2022). The effects of Self-regulation and Attention concentration on Computational Thinking according to Coding Play experience of children. Korean Association For Learner-Centered Curriculum And Instruction. 22. 571-588. 10.22251/jlcci.2022.22.12.571.)

Learning Math Through Coding and Learning Coding Through Math: Two Sides of the Same Coin. (Mamolo, Ami & Tepylo, Diane & Ruttenberg-Rozen, Robyn & Rodney, Sheree. (2023). Learning Math Through Coding and Learning Coding Through Math: Two Sides of the Same Coin. Canadian Journal of Science, Mathematics and Technology Education. 10.1007/s42330-022-00254-x.)
What if my child misses a class?
We've designed our classes to be family-friendly! Our goal is to be the most flexible in the industry.
The make-up class can be in the same week or following week.
Do you offer Sibling discounts?

Yes, siblings receive 10% off weekly memberships. Speak with your local
If my child misses a class, will they fall behind?

No.At Skill Samurai, your child will never fall behind. Our programs allow each child to work on their own courses/projects and focus areas at their own pace, ensuring a personalized and efficient learning experience.
Even if you miss a week or more, your child can easily pick up right where they left off. It's an educational approach that truly puts the child's needs first!
My child has a short attention span, is this program good for them?

Coding can be a great tool for kids with short attention spans, as it allows them to engage in a hands-on and interactive learning experience. Coding projects are often broken down into smaller, manageable steps, which can help to keep kids focused and on task. Additionally, the immediate feedback provided by the computer can help to maintain their interest and motivation. Through coding, kids can also develop their problem-solving and critical thinking skills, which can translate to improved attention and focus in other areas of their lives. Coding provides a sense of accomplishment as they see their ideas come to life through the projects they create, encouraging them to stay engaged and continue learning.

Combining Maths tuition with coding can help children fall back in love with Maths!
I have a busy schedule, how flexible is your timetable?

We get it, family schedules can be hectic. We've designed a world-class curriculum that is project based and self-paced. What does that mean? It means that your child can attend any scheduled class, any day. If you need to cancel at short notice, no problem, our booking system allows you to easily cancel, book and rebook. We've designed it especially for busy families.
What is your cancellation policy?
We understand needs and priorities change, and you may need to cancel classes. We do request that you give us a 30-day notice of intent to cancel. You may do that by sending us an email with the date that you would like to stop. However, we are not able to refund you for any classes that you have missed in the months before.
Our Camp cancellation policy is as follows.
30 days prior to the start of camp refund minus a $10 processing fee
14 days prior to the start of camp 75% refund.
7 days prior to the start of camp 50% refund.
Less than 7 days prior to the start of camp, no refund.
Our refund policy is strong because many of our summer programs sell out, and the closer that we get to the start of camp, the harder it is to find a replacement. In many cases, our owners have paid for staff, equipment, and software, and those funds are not refundable. Monthly memberships require 30 days cancellation.