Singapore Math is a method of teaching mathematics developed in Singapore in 1982. Since then, it has been used in schools around the world, including the United States. Rather than teaching procedures straight away, Singapore Math emphasizes fostering an understanding of concepts first. It uses both a practical and visual approach to teaching, emphasizing a strong sense of numbers and problem-solving.
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How to teach Singapore math
1. Learn the Singapore Math Framework
Before you can teach Singapore Math effectively, you need to understand not only how it works, but also the philosophy behind its development. Singapore Math is probably not like the math education you grew up with, so it may take some getting used to. This general philosophy can be explained better by referring to the Singapore Math framework, which is comprised of five components: Concepts, Skills, Processes, Attitudes, and Metacognition. These 5 components are key to developing math problem solving skills.
- Concepts refer to numerical, algebraic, geometric, statistical, probabilistic, and analytic concepts.
- Skills relate to numerical computation, algebraic manipulation, spatial visualization, data analysis, measurement, use of mathematical tools, and estimation.
- Attitudes relate to beliefs, interest, esteem, trust, and perseverance.
- Metacognition refers to the monitoring of one’s thinking and the self-regulation of learning.
2. Understand the math concepts
Students must learn each of these mathematical concepts—numerical, algebraic, geometric, statistical, probabilistic, and analytical—as individual ideas, but more importantly, they must learn how they are connected. Students need to be given a selection of materials and examples to understand these concepts and how they are all connected. They must also be able to apply these concepts when actively solving math problems to be more confident with their math skills.
3. Develop the math skills
Students must learn a variety of mathematical skills including: numerical computation, algebraic manipulation, spatial visualization, data analysis, measurement, use of mathematical tools, and estimation. They need these skills to learn and apply the math concepts they are being taught. However, the key to Singapore Math is not to overemphasize the “how” and not to overemphasize the “why”. It is important for students to understand why a math principle works, not just how a math problem can be solved.
4. Understand the mathematical processes
Mathematical processes, sometimes referred to as knowledge skills, include skills such as: reasoning, communication and connections, reasoning skills and heuristics, and application and modeling. All of this knowledge is needed and used to better understand a math problem and the process used to solve it.
Reasoning – Analysis of a particular mathematical problem and the ability to articulate the reasoning behind the analysis. Students learn these skills by applying the same reasoning to different math problems in different contexts.
Communication – is the language of mathematics. A student must be able to understand the mathematical language of a problem and express concepts, ideas, and arguments in the same language.
Connections – Mathematical integration involves linking mathematical concepts. It is also the ability to relate mathematical ideas to non-mathematical subjects and the real world. Being able to make these connections allows the student to actually understand what is being taught in the context of their daily life.
Reasoning Skills – are skills that can help students think way through a math problem, may include: classifying, comparing, sequencing, analyzing parts or wholes, identifying patterns and relationships, induction, deduction, and spatial visualization.
Heuristics – are similar to reasoning skills and are divided into four categories: the ability to provide a representation of the problem (e.g. chart, list, etc.); the ability to make a calculated guess; the ability to work through the process in different ways; and the ability to change the problem to better understand it.
Application – means using the mathematical problem-solving skills that a student develops for various reasons, including everyday problems and situations.
Mathematical Modeling – is able to apply representations of data to a specific problem and then determine which methods and tools to use to solve the problem.
5. Shape math settings
For some reason, math always gets a bad rap in school. However, this reputation does not necessarily develop because mathematics is difficult. It develops partly because math can be boring. What kid wants to spend hours learning their class schedules? Mathematical attitudes is the concept of making math fun and exciting so that a child’s experience of learning math is positive.
In addition to fun and exciting attitudes, mathematics attitude also refers to a student’s ability to apply a learned mathematical concept, method, or tool they have learned to their actual everyday life. This type of application occurs when a student understands why a concept works and what other situations that concept can be applied to.
6. Provide a metacognitive experience
Metacognition is a strange concept – it refers to being able to think about how you think and being able to proactively manage that thinking. It is used to better teach students problem-solving skills without overwhelming them. Some ways metacognition is used to teach Singapore math are:
Teaching general (non-mathematical) problem-solving and thinking skills and demonstrating how these skills can be used to solve problems (both mathematical and non-mathematical).
When students think a problem out loud, their minds focus only on the problem at hand.
In order to solve problems for students, the student must plan how to solve the problem and then evaluate how they solved the problem.
Have students solve the same problem using more than one method or concept.
Allow students to work together to solve a problem by discussing different methods that could be used.
7. Apply the approach gradually
Singapore Math does not try to teach a student all concepts and methods at once. Instead, these concepts are introduced gradually over a period of time. First, a student is taught a concrete concept that is very specific, such as manipulating numbers by counting. The student is then taught the concept using pictures instead of actual numbers. Finally, the student is taught the concept using an abstract approach, where one number often represents something else.
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