Methodology of Singapore Math Part 1

Summary

The Singapore Mathematics curriculum is grounded in the CPA (Concrete, Pictorial, Abstract) approach, inspired by Jerome Bruner's theory of representation. This method introduces abstract mathematical concepts through tangible materials, then progresses to visual representations before abstract symbolism. Examples include teaching addition and subtraction with manipulatives, transitioning to pictorial models in textbooks, and finally to symbolic notation. Additionally, the curriculum incorporates the theory of variability to enhance understanding through diverse representations and problem-solving variations.

Takeaways

• 📚 Singapore Mathematics is grounded in learning theories taught at the National Institute of Education, Singapore.
• 🔢 The CPA approach (Concrete, Pictorial, Abstract) is a fundamental theory used in Singapore Mathematics, based on Jerome Bruner's theory of representation.
• 👶 Concrete materials are initially used to introduce abstract mathematical concepts to children, making learning more tangible.
• 🎨 Pictorial representations serve as a bridge between concrete materials and abstract concepts, aiding in the understanding of mathematical ideas.
• 📈 The transition from concrete to abstract is exemplified in the learning of addition and subtraction, where children progress from physical objects to symbolic notation.
• 🔄 The concept of place value is introduced early through base-ten materials, emphasizing the importance of understanding mathematical structures.
• 👀 Perceptual variability is utilized to make mathematical concepts clearer, such as using different materials to represent the number 21.
• 🔄 Mathematical variability is applied in Singapore's textbooks to present problems in various forms, promoting a deeper understanding of concepts.
• 📘 The Singapore textbook examples show a deliberate use of variability in illustrations to enhance learning, such as counting distinct versus overlapping objects.
• 🌟 The overall approach in Singapore Mathematics is to make abstract mathematical algorithms understandable through the use of concrete materials and varied representations.

Q & A

What is the CPA approach in Singapore Mathematics?

The CPA approach stands for Concrete, Pictorial, Abstract. It is a method where abstract mathematical concepts are first introduced using concrete materials that children can manipulate, then represented visually, and finally learned symbolically.

Who is the theorist behind the representation theory utilized in the CPA approach?

Jerome Bruner's theory on representation from the 1960s is the basis for the CPA approach, where abstract ideas are introduced via concrete materials.

Can you provide an example of how the CPA approach is used to teach addition?

In the script, an example is given where children learn to add 11 and 23 using concrete materials. They see that the sum is 34, represented by 31 tens and four ones, eventually learning to write it symbolically as 11 + 23 = 34.

How does the CPA approach handle subtraction in Singapore Mathematics?

An example given is subtracting 11 from 32, where children physically take away 1 ten and 1 one, leaving 21. For a more complex subtraction like 32 - 15, they learn to exchange one ten for 10 ones to make the operation easier, leading to the result of 17.

What is meant by perceptual variability in the context of Singapore Mathematics?

Perceptual variability refers to the use of different materials to represent the same mathematical concept, with some materials making the concept easier to perceive than others. This is based on Zan de's ideas and is used to introduce place values.

How does the Singapore Mathematics curriculum introduce place values using base ten materials?

The curriculum suggests introducing place values using base ten materials because it visually demonstrates that 1 ten is 10 times as much as 1 one, which is not as obvious with other materials where the sizes might be the same.

What is an example of mathematical variability in Singapore Mathematics textbooks?

An example from the kindergarten textbook involves counting objects. Counting separately drawn elephants is easier than counting overlapping lions, demonstrating variability in the way tasks are presented to enhance learning.

How does the theory of variability apply to tasks in Singapore Mathematics?

The theory of variability is applied by not merely repeating tasks but varying them. For instance, after counting separately drawn objects, students might count overlapping objects, providing a different challenge and reinforcing the concept.

What is the significance of using concrete materials in the CPA approach for teaching algorithms?

Using concrete materials allows children to understand abstract algorithms by providing a tangible way to interact with and visualize mathematical operations before moving on to abstract symbolic representation.

How does the Singapore Mathematics curriculum ensure that students transition from concrete to pictorial and abstract representations?

The curriculum is designed to gradually introduce students to pictorial representations after they are comfortable with concrete materials, and finally to abstract symbolic representation, ensuring a smooth and comprehensive understanding of mathematical concepts.