What is the methodology behind Singapore Maths?
Some of the key components to the methodology are as follows:
1. The CPA ApproachÂ (to understand concepts)
This means Concrete âž› Pictorial âž› Abstract .Â This approach enables students to encounter Mathematics in a meaningful way and translate mathematical concepts from the concrete to the abstract.Â This approach allows students to understand mathematical concepts before learning "rules" or formulaic expressions.Â
Students first encounter the mathematical concepts through the use of visual and concrete manipulatives. Students then move on to the pictorial stage in which pictures are used to model problems. When students are familiar with ideas taught, they progress to a more advanced or abstract stage in which only numbers, notation and symbols are used.
2. Model-drawingÂ (to visualise, see connections and solve problems)
Model-drawing transforms words into recognisable pictures for young minds.
Model-drawing is an ingenious problem-solving strategy were students are taught to visualise and construct bar models to help them make sense of word problems.Â The model-drawing method requires pupils to understand the mathematical concepts underlying the word problems and equips them with a strong conceptual foundation in Mathematics to solve even the most challenging problems.Â The model-drawing technique not only provides a powerful method for solving problems, but also serves to develop algebra.Â Symbolic representation of problems, the mainstay of algebra, emerges as a logical extension of the model-drawing technique.
Â This helps to visualise, see connections, solve problems
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3. Teaching to MasteryÂ (for deep understanding)
Each topic is covered in detail and taught to mastery.Â Immediately after new concepts are taught, students are engaged with a variety of mathematically rich problems.Â This ensures that the focus is on the students' deep understanding of each topic.Â The Singapore Maths approach is geared towards producing mathematical thinkers, and it does this by walking students through all the component parts of a problem before presenting them with the whole problem to solve.
4. Spiral ProgressionÂ (to build a strong mathematical foundation)
Topics covered previously are reviewed at higher grades and at increasing levels of difficulty.Â The introduction of new concepts is built upon the mathematical concepts students have learnt previously.Â Spiral progression also allows for a review of important mathematical concepts while expanding on that foundation, ensuring a coherent and focused programme.
5. MetacogntionÂ (to promote logical thinking, reflection and communication)
Metacognition refers to the ability to monitor one's own thought process.Â Teaching students to be conscious of the strategies they use to accomplish a task encourages pupils to think of alternative means of solving problems and promote logical thinking.