A distinctive trait of Singapore’s math curriculum is the use of model drawing. Since the 1980s, students have been equipped with the skills to solve mathematical problems through the use of rectangular bars. This method is part of the CPA methodology – concrete, pictorial, abstract – a fundamental learning theory behind Singapore’s math curriculum according to Marshall Cavendish Education.

The model drawing method offers several benefits and can be particularly effective for certain types of problems.  

Model drawing with its use of visualisation helps young learners map out complicated problems. Abstract mathematical concepts can be broken down into nifty graphical representations, allowing learners to grasp relationships between quantities with much more ease. To illustrate, think about how fractions in its numerical form are in essence a theoretical concept, when students are able to utilise model drawing to break down the concept into bars, they are able to turn that theory into an easy to digest form. 

Math in Focus Model Drawing 2

Students can visualise the process of arriving at a solution by breaking problems down into smaller, more manageable parts. A mathematical problem can be slowly broken down through model drawing. For example, if a problem involves finding the total cost of several items, students can start by representing each item separately and then combining their costs step by step. Not only does this foster problem-solving skills and encourages students to think critically about the structure of a problem, it facilitates sequential thinking, breaking down a complex problem into parts. 

As a more analytical concept, MOE mathematics educators have noticed the modelling method is not easily understood by many students. Some students also struggle with scaling when drawing models especially if they neglect to use a ruler. As another option, some students may find algebra a better alternative, this is where rectangular bars are replaced into variable expressions in algebraic notations. 

And schools do encourage the switch, at the Primary 6 level, the particular skill set in modelling is transferred into their ability to start using algebra. This transition into algebra is to allow for students to be even more precise when it comes to representing mathematical relationships one where model drawing cannot offer. Furthemore, in an article for Forbes, Mathematician John Ewing postulates that skills learnt in algebra carry over to real life application, it isn’t just ‘facts and procedures’ its ‘thinking and understanding’ he emphasises.  

Symbolic representation 

Math in Focus Model Drawing

Algebraic notation allows for concise and precise representation of mathematical relationships. Mathematical ideas can be worked with more easily when they are represented in this symbolic manner, especially in contexts where precision and clarity are essential. Model drawing, while helpful for visualising problems (as seen from the Fig taken from Math in Focus), may not always offer the same level of clarity or precision.

Complexity 

According to the California Mathematics Framework, “In algebra, students learn to reason symbolically, and the complexity and types of equations and problems that they are able to solve increase dramatically as a consequence.”  Algebra is designed for dealing with complex mathematical relationships and equations. Complex problems may require increasingly intricate diagrams, which can make model drawing difficult.

Efficiency

Visual models tend to become laborious for students, especially as the difficulty level of questions go up. Once a student manages to master algebra techniques, they will be able to solve mathematical problems much easier and much more efficiently. 

Serves as a foundation 

Higher level mathematics and even science topics depend on the techniques learned in foundational algebra. Professor of mathematics at the University of Maryland College Park, Denny Gulick, emphasises the importance of algebra as it is a prerequisite for practically all college-level and more advanced mathematics courses. 

The transition into algebra may prove tough for some students, especially outside of the school text. However, it is important to motivate your child to start engaging in the use of algebra more frequently when solving problems. So, both methods do offer certain benefits, and your child may find one easier than the other, but it is important to hone the differing skills and slowly build up the mathematical foundation for more complex and tougher problems in the future. 

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