## Why Additional Mathematics is Important?

By: Debbie Wong, Founder and Teacher, Debbie’s Learning Cove

**What is Additional Mathematics?**

Additional Mathematics (A Math) is an O-level subject. Students who choose to study A Math begin learning it in the third year of secondary school (Sec 3) and take the O-level examination at the end of the fourth year (Sec 4). **Additional Mathematics** is a two-year course with a defined scope and syllabus.

The A Math curriculum has three main strands: Algebra, Geometry and Trigonometry, and Calculus. The syllabus equips students with a strong foundation in algebraic manipulation skills, mathematical processes, reasoning skills, and concept application. The O-level A Math examination consists of two written papers.

**A Math versus E Math**

O-level Mathematics, commonly referred to as ‘E Math’, is a compulsory subject for all students. E Math provides students with fundamental mathematical knowledge and skills. Its content is divided into three main strands: Number and Algebra, Geometry and Measurement, and Statistics and Probability. The focus of E Math is to equip students with the math skills needed for everyday situations. For example, students learn how to read and draw graphs, calculate income tax and bank interest, and compute averages and standard deviations. The** O-level Math examination **also consists of two written papers.

A Math is a separate subject that students can choose to take in addition to E Math. Since E Math is compulsory, a student who takes A Math will have two math subjects: E Math and A Math, each with its own syllabus and examinations.

**Why is A Math Important?**

The main reason A Math is important is that it adequately prepares students for A-Level H2 Mathematics. A Math serves as a foundation for H2 Math in junior college (JC). Not taking A Math can deprive students of the necessary foundation for H2 Math in JC.

Many parents do not realise that the third year of secondary school (Sec 3) is a crucial juncture where pathways are created towards either the science or arts streams. These pathways eventually lead to either science-based or arts and humanities courses at university. Not taking A Math can mean closing the door to science, engineering, and computing courses in university. A Math is a foundation subject required for **JC H2 Math**, and H2 Math is a core subject for science stream courses in JC. After A-levels, science stream students typically progress to considering science, engineering, and computing courses at universities. Many of these university courses require H2 Math as a prerequisite, so learning A Math in secondary school is essential.

A student who does not take A Math misses out on topics such as Logarithms, Trigonometric Identities, Differentiation, and Integration. These topics are not covered in the E Math syllabus but are considered fundamental knowledge for H2 Math in JC. While it is not impossible for a student without A Math to take H2 Math in JC, the learning gap can be daunting.

If you are a parent of a lower secondary child reading this, it is highly recommended that your child takes A Math in the upper secondary years. Not taking A Math can make it difficult for your child to pursue a career as a scientist, computer scientist, engineer, or doctor in the future.

**Why Students Find A Math Difficult**

Transitioning from lower secondary math to A Math in Sec 3, students experience a significant jump in the complexity of concepts. Math suddenly becomes more abstract. For example, one of the first theorems students learn in A Math is the **Remainder Theorem**. This theorem is a shortcut that enables one to find the remainder when a polynomial is divided by a linear expression. To understand this theorem, students must first grasp why it works and then apply it correctly to different questions. This can be challenging for a 15-year-old who was previously dealing with straightforward math. Many students struggle to understand it and resort to memorising it without comprehension. Some students do not even realise the theorem exists, leading to poor test outcomes.

Doing well in A Math also requires skills that students only begin to develop when they start learning A Math. I often teach students that to survive many deductive questions, they must have a ‘template mindset’. For example, if the equation f(x) = 0 has a solution x = 4, then the equation f(2x) = 0 has a solution where 2x = 4, and hence x = 2 is a solution. Students need to ‘see’ that the unknown x can be replaced whenever necessary. This is one of the skills students must acquire and know when to use.

Moreover, A Math problems often require many lines of the solution, and the work is procedural. For example, there are three steps involved in solving a trigonometric equation. Students must be familiar with these steps and work through the solution systematically. Such lengthy methods were not required in lower secondary math, where questions were short and straightforward. Consequently, students find A Math more demanding in terms of time and effort.

After roughly one semester of **A Math** learning, many students become more accustomed to its demands and rise to the occasion. However, some still struggle with the subject due to a weak foundation in lower secondary math or not learning the subject well in school.

Student feedback on A Math can vary greatly. Those who grasp the subject well find it enjoyable and sometimes easier than E Math. Those who do not understand what they are supposed to know often find A Math the hardest subject and lack confidence in securing a passing grade.

**How A Math is Made Easy at Debbie’s Learning Cove**

Students who understand A Math concepts and know how to apply them are the ones who find A Math easy. At Debbie’s Learning Cove, we make this happen through expert guidance, instruction, and top-quality resources.

First and foremost, students must be taught the subject well. With two decades of teaching experience, I know how students should think about math to excel. During my lessons, I train students to think mathematically. Using a topical approach, I help them understand how each concept came about, make connections to their prior knowledge, and extend from there. I teach for understanding, using various strategies honed over decades of teaching. I then instruct students on the procedures for solving specific problem types and how to analyse exam-type questions to apply the correct techniques and procedures. I also highlight common errors and misconceptions to avoid, helping students gain a more concrete understanding of A Math concepts. My core objective is to ensure every child understands the concepts and sees the light of each topic. During lessons, questions flow freely to ensure every child is learning and progressing.

Students are provided with a complete set of notes and practice materials for every A Math topic. These notes serve as clear references for students and help reduce their revision time. Every key A Math concept is stated and explained concisely. Practice questions reinforce the concepts learned and strengthen application skills. During practice sessions, I provide guidance and encouragement to help students build a positive self-image of their math abilities. Confidence, I strongly believe, is the key to unlocking one’s math potential.

Students at Debbie’s Learning Cove consistently provide positive feedback about the clear teaching and helpful notes they receive. Results speak for themselves: most students consistently score distinctions in A Math tests and exams. As a teacher, I feel immensely happy when I observe a child who started off lost and helpless in early Sec 3 maturing in his mathematical thinking ability and independently solving A Math problems with speed and accuracy. This child is a success story of Debbie’s Learning Cove **A Math tuition** and is ready to face higher math learning beyond the O-levels.