Key Math Concepts For Secondary School Students

The Singapore math curriculum is considered one of the best in the world, prioritising deeper understanding of key topics – with our students placing high in international rankings.

Still, the difficulty of the math curriculum in question is not to be lightly dismissed. If anything, the reality of the difficulties that Singapore math students face has become something of a societal norm. The challenging national examination questions, the fast-paced rigour of school curriculum, and the stressful competitiveness among parents and students alike have been covered across countless news articles and documentaries.

So, it might be odd to hear that there is only a singular central focus of the entire math curriculum – the development of mathematical problem solving competency.

Of course, problem solving is a broad umbrella term, encompassing the components that enable students to do so. As defined by MOE, the five components are concepts, skills, processes, metacognition and attitudes.

What Is a Math Concept? 

The first of the five main components of Singapore’s math curriculum, math concepts can be said to be the building blocks of math. Much like what the atom is to chemistry, math concepts consist of properties, relationships, operations and algorithms – the essential foundations for solving math problems. As with most things in an organic world, these math concepts are organised into strands for categorisation – but are very much intertwined. 

A common critique of the Singapore education system is an overreliance on rote learning – excessive memorisation through repetition. In a day and age where information is so readily accessible, such an approach fails to prepare students for future job prospects in an uncertain world of technological disruptions.

Developing problem-solving skills are all the more important for students to remain relevant and competitive in such an ever-changing world. However, as mentioned earlier, to practice problem-solving is not akin to that for more mundane skills, but rather is more multi-faceted. 

Singapore’s shift away from traditional exam questions towards application ones does not render the knowledge of math concepts obsolete. Rather, it demands our students to do better than just ‘know’ their math concepts – and truly understand them, how they work, why they work, so that they can apply them in the right contexts. 

Commonly Used Terms for Math Concepts

Math concepts consist of properties, relationships, operations and algorithms – which mostly require use of notations that are the basis of the mathematics language. These notations can often be categorised and given terms for easier reference. These commonly used terms allow for greater ease when discussing and understanding the math concepts at hand.

Math Definition Coefficient 

Coefficient is a fundamental term used commonly within math concepts under the strand of Algebra. Coefficients are the constants written beside variables, to indicate the corresponding number the variable is multiplied to. 

While it may seem trivial to have a slightly shorter way to indicate the multiple of a variable, the strand of Algebra includes math concepts that deal with multiple instances of variables to different powers – most notably, those regarding quadratic expressions. Coefficients allow us a more elegant way to express algebraic terms, so that workings do not become overly long and messy, and end up affecting thought processes or lead to careless mistakes.

In functions and graphs, coefficients play an important role in determining the shape of said graphs. Similarly, they also show up in more math concepts under the strand of calculus.

Math Definition of Expression

Expression is a term commonly confused with the term equations. Equations are used to indicate the equivalence of two or more expressions. You may think of an expression as a statement in mathematical notation, consisting of at least two numbers or variables, and an operation.

Algebraic Expressions are used commonly to translate real-world situations into mathematical notation; hence, learning to form algebraic expressions based on question stems is a key step in learning to tackle application questions. Additionally, they can be formed to notate patterns and relationships between variables, and form the basis that allows us to solve complicated algebraic problems.

Basic Secondary Math Concepts 

In the secondary school math curriculum, math concepts are organised into the strands of numbers, algebra, geometry, probability and statistics, and calculus (for Additional Mathematics). For Elementary Mathematics, the concepts are streamlined into the following 3 content strands:

NUMBER AND ALGEBRA 

While often hard to visualise, Number and Algebra is perhaps the most relevant to everyday life. It equips us with the knowledge needed to transform many real-world problems into mathematical models. Algebra enables us to express unknown or changing variables in math. Many problems in the real-world arise from a lack of information – after all, everything humankind knows about the world has to be discovered for ourselves. 

Algebra, as a mathematical tool, allows us to solve for these missing bits of information based on extrapolation from known relationships. In a world where change is the only constant, finding and expressing the relationship between variables allows for simplicity in carrying out future calculations. 

Aside from math concepts under equations and inequalities or functions and graphs, Number and Algebra also encompasses math concepts under set notation and matrices – for the visualising and processing of complex data – and indices. In our organic world, linear scales of many various measurements do not produce meaningful data – rather corresponding to logarithmic scales for things like sound (decibel), earthquakes (the Richter scale), and acidity (pH). Most common of all, indices are used in compound interest rates in major banks all around the world – meaning an understanding of indices is crucial for financial literacy.

As the world grows, so does the importance of staying competitive in a fast-paced world – and that means efficiency. Nowadays, many traditional jobs have implemented computerised systems to speed up work processes – many of which employ some use of algebra to deal with varying or unknown values. 

GEOMETRY AND MEASUREMENT

While easier to visualise, Geometry and Measurement can often be more niche – after all, most of us don’t look at the Singapore Flyer and go, “huh, I wonder what the volume of a cabin is”. 

Nonetheless, the math concepts in it – across congruence and similarity, properties of circles, trigonometry and vectors – can allow us a better appreciation and awareness of the world we live in. After all, even if not entering a field such as engineering or architecture, spatial awareness and orientation are still quiet everyday parts of our lives. It can help us make better decisions in the little moments, like deciding whether to buy two medium pizzas or one large, or bigger moments, like when buying an apartment and figuring out floor plans.

After all, much like how you wouldn’t want to mistake a ⅓ pound burger for being smaller than a quarter pounder, you’d probably not want to be the person that thinks walking around the length and breadth of a triangle rather than its hypotenuse is shorter.

STATISTICS AND PROBABILITY 

In a complex world, our human desire to make sense of the world around us – and benefit from it – is realised by us simplifying such real-world problems into mathematical models. However, when these problems involve humans, we have to consider a key distinction that sets humans apart from other organisms and things. As humans, we possess the ability to make critical decisions and choices, and affect our outcomes. To simplify problems that involve multiple possible outcomes into mathematical models, we can no longer purely rely on algebraic expressions and equations – rather, we turn to statistics and probability.

Under the Secondary School syllabus, the math concepts under this strand fall under Data Handling and Analysis, and Probability. Math concepts under the former enable us to make sense of data gathered in research and surveys, to compare and interpret them in such a way to make more informed decisions. As for the latter, they equip us with the knowledge needed to determine the likelihood of specific combinations of mutually exclusive and independent events – allowing us to choose the better decision in such scenarios.