The key to understanding mathematics
Singapore has consistently produced the best maths students in the world, but what is Singapore maths and why is it different?
Singapore maths is a developmentally designed curriculum for teaching maths concepts and problem solving. It is well respected and used in schools and as a home school curriculum worldwide. Unlike many curriculums that only use pictorial and abstract problems, Singapore maths uses a spiral approach and always begins with concrete models that children manipulate to discover what the numerals and the functions of maths represent.
Many academic studies have been conducted on the benefit of the Singapore maths curriculum that validate its methods over traditional maths instruction. Its focus on problem solving instead of computation has proven to be highly successful, in both classroom and homeschool settings. So how is Singapore maths different from other maths curriculums?
Discovery approach to problem solving
Although many maths curriculums recommend the concrete-pictorial-abstract progression, few adequately address the value of allowing students to discover multiple strategies to solve a problem. Teachers usually directly teach a single strategy and expect all students to use it, but by exploring many different problem-solving strategies, for example drawing a picture, children see mathematics as a challenging puzzle to solve instead of a rote memorisation of steps to follow. With Singapore maths, when a teacher introduces a problem, the students explore and discover different strategies that work. More importantly, before using a textbook or directly teaching a lesson, the teacher and the students discuss which problem-solving strategies were effective.
Journalling as part of the anchor task
In addition to the exploration and discovery of multiple problem-solving strategies at the beginning of a lesson, Singapore maths adds journalling as a step in the process to anchor the students. Discussion and journalling connect the student’s thought process to the problem and gives them the opportunity to write, read and discuss the vocabulary of mathematics. This extra step ensures that the vocabulary and process are both integrated into a student’s memory.
Although many different curriculums incorporate manipulatives to help children understand number concepts, without having the opportunity to reflect and discuss the activities that used the manipulative, the benefits of using them are minimal. Getting the right answer is not the goal of Singapore maths. Its purpose is to understand maths and be able to apply its principles to any problem-solving situation. Singapore maths is designed to encourage children to think deeply about maths and apply its principles to any problem, not just the one algorithm they see on a worksheet.
The value of dialogue
Mathematics has a vocabulary that is unique and often overlooked. It’s important to train students in the terminology of mathematics so communication is clear, and they are prepared for higher level mathematics. The teacher may be tempted to use simple words that they think are easier for students to understand, like “take away” instead of “subtract”. Using the vocabulary of mathematics is an integral part of Singapore maths.
In a traditional classroom, the teacher is the “sage on the stage”, talking to students. The delivery of knowledge is a one-way process. It is common for teachers and homeschool parents alike to complain that they don’t understand why a child did not learn a concept, because they knew they “taught” it. Singapore Maths understands that learning is not the same thing as listening to someone teaching. For children to learn, a two-way conversation needs to take place so that the brain integrates the vocabulary with the maths concepts. Meaning is tied to understanding. By asking “What do you think?” rather than telling the child how to solve a problem, a student benefits from going on their own problem-solving journey and exploring ideas. There are often many ways to solve a problem, and students are encouraged to try different methods and discover which one is most effective for them to use.
A balance of mastery and higher-order thinking to build confidence
Basic maths instruction emphasises the mastery of computation. Singapore maths uses computation as one component of the problem-solving process. It frames problem solving as an exploration, encouraging students to discover multiple ways to find a solution. Singapore maths uses higher-order thinking to combine mathematical reasoning and computation, which builds confidence in students. Students do not see maths as boring or difficult but an interesting challenge to overcome.
Learn more about Singapore maths
If you want to learn more about Singapore maths, and more particular aspects of it, spend some time watching Dr Yeap Ban Har’s videos. He is a renowned expert on Singapore maths.
You can also visit our Singapore Maths FAQs page.
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