# Singapore Mathematics Model

Updated: May 22, 2020

Many education systems have been looking to Singapore for inspiration in revamping their mathematical studies for K-12 education (7 to 16 years old) after Singapore’s performance in the PISA and TIMSS. Singapore’s success in various Mathematics competition boils down to the enabling of various factors, one factor has always been the highlight which every country looks to: Singapore Model Method in Problem Solving.

Singapore ranked highly in PISA.

As a Mathematics educator in Singapore, I have witnessed successes of Singapore Model Method. Singapore Model Method builds on the **Concrete-Pictorial-Abstract (CPA) concept**.

**Concrete **– where students first learn about Mathematics through concrete objects / learning kits / manipulatives where students are able to use their five senses to learn simple Mathematical concepts.

**Pictorial **– where they will be guided to pictures and diagrams where teacher will guide students along using the board. Using models is part of the pictorial approach where students draw various models to represent what would have been objects and manipulatives.

Example of using Singapore Model Method as a pictorial method to solve word problem.

Taken from __PSLE Prep Programme__.

**Abstract **– consists of using units and alphabets (e.g. algebra) to represent and or replace the model drawing that they are familiar to.

The systematic flow of Concrete-Pictorial-Abstract concept is to provide ample scaffolds for students to learn problem solving skills through the lens of Mathematics. Therefore, Singapore Model Method can be seen to be the **bridge and scaffold between objects/manipulatives to the algebraic method**.

Another example of using Pictorial aspect to simplify Abstract problems. Taken from __PSLE Prep Programme__.

The Singapore Model Method seems to be the antidote for young students and students struggling to understand the algebraic method. Parents and teachers in elementary schools worldwide may also be very excited to learn how it works and how to implement in their schools. Many have also signed up for courses or invited speakers or trainers to share how to implement for their students. However, the implementation of model drawing in your context requires certain prerequisites.

Although the Singapore Model Method is indeed useful in scaffolding students to the more abstract algebraic method, there are several fundamentals that both parents and teachers need to recognise and work on before or while embarking on the journey of Singapore Model Method in their schools to their own students.

Firstly, **Numeracy and Arithmetic** is the foundation of all Mathematics. Student needs to be proficient in basic operations such as addition, subtraction, multiplication and division before being able to manipulate models and draw accurate and precise models. I am not referring to high level mental sums but be able to comprehend simple sentences and translating it to mathematical statements. Without basic mastery in Numeracy and Arithmetic, students will struggle to follow simple word problems and translating it into model drawings. Hence, this is an important aspect parents and teachers need to bear in mind while transiting to basic model drawing.

Example of Application of Arithmetic and Numeracy in Solving Word Problems Using Model Method.

Taken from __PSLE Prep Programme__.

Next, students need to be well versed in **Fractions, Decimals, Percentages and Ratios**. Many word problems either test the concepts singly or infuse a combination of these concepts together. Therefore, it is not only important to master these concepts as singular well, students also need to be able to convert them interchangeably. This is essential in intermediate and advanced model drawing and therefore important for students to master this interchangeability before moving on to advanced model drawing. Basic model drawing can also be used to represent the interchangeability of these fractions, decimals, percentages and ratios. Hence, it is important for parents and teachers to practise with students this core concept before moving on to model drawing.

Example of a Word Problem Involving Fraction and Percentage. Using Singapore Model Method to solve complicated word problems.

Taken from __PSLE Prep Programme__.

In the __next__ article, I will be sharing more on the principles of model drawing and how it helps students in comprehending the question and scaffolding students to the algebraic method.

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