For most, studying Math means just practicing through brute force until something just clicks in your head. The most fundamental part about studying is learning about how to navigate and make sense of the content that you are given. This is actually why most of us say ‘practice makes perfect’ – we do different variations of a certain type of question until we ‘get it.’ While practice does make perfect, sometimes it takes us a very long time to get there and the process can be despairing when we’re groping in the dark for understanding. Other times, we just keep trying and trying but every question is either a hit or miss.
But how do we ‘get it’? Math always seems to be a subject with a ridiculous learning curve.
‘Getting it’ is when we start to understand how each piece of information is used. We can read a question and we know we have to use this technique and formula just by the information given. And while this might seem self-explanatory, it shows how studying is ultimately split into two steps: understanding the content and applying such content.
Everything that you learn at school has its own specific purpose and way it will be used in an examination. Therefore, it is important to know what exactly you’re being tested on, and how you are being tested on it.
To study Math, there are two concrete, deliberate steps you can take the actively improve on how you study and learn math concepts in which I have split into building a math ‘foundation’ and math ‘vocabulary.’
Building a Math ‘Foundation’
Lots of people say ‘Oh I have a good/bad math foundation.’ But what does that actually mean? The best way to know and test if you have a good math ‘foundation’ is to view the A Level syllabus and learning objectives posted on SEAB. At the most basic and fundamental level, all examination questions are surrounded on testing those objectives.
Hence, building a Math ‘foundation’ is about practicing arithmetic and basic, fundamental questions. Having a good math foundation means you know the quadratic equation, ratio theorem and how to use the graphic calculator to sketch a circle. Having a strong foundation is the first step to tackle Math. Without which, it is almost to jump from here to a question that links many topics together or requires high level of interpretation.
The best way to build a Math foundation is to do the simplest questions that require the least interpretation to do. Find questions that outright ask, ‘if both A and B are independent, what is the probability that ….’ or how to add certain vectors together. These correspond with their learning objectives directly and will show you if you struggle with the concept itself, or its application.
For every topic of Math you learn, go through its respective learning objectives found in the SEAB link. You can use this as a way of how to create notes. Take each learning objective and explain what each is, means and how to understand it.
For example, for the learning objective: ‘vector and cartesian equations of lines and planes’, you can first write what a vector and cartesian equation of a line is, then how to understand the equation, and how to convert between vector and cartesian.
Building a Math ‘Vocabulary’
The second part to learning Math is knowing how to make that jump between understanding and applying. A good way to gain clarity when studying is while doing your tutorials and practice papers. Take note of how each question is aligned with the learning objectives. Write down how each LO is used and tested, and how the question gives you information to use the each piece of information you have learned.
Let’s use the topic of Vectors as an example. In the learning objectives, there is none that lists ‘finding the coordinates of a point that is reflected about a plane.’ Yet, when asked, we must apply two concepts. We need to know the coordinates of the point, the coordinates of the foot of the perpendicular, and apply ratio theorem to get the point reflected about the plane – all of which are listed in the learning objectives.
Learning Objective 3.1 and 3.3
- use of the ratio theorem in geometrical applications
- 3-D vector geometry: finding the foot of the perpendicular and distance from a point to a line or to a plane
So when you approach a question, break down each into steps that are based on learning objectives. This allows question types to be stripped down into steps, and more importantly, you understand what the use of what you learn is in the context of the examination.
The H2 Math syllabus also lists down common ways in which application is tested across topics.
Ensure you compile how you combine learning objectives together to tackle questions. At the very least, you should cover the learning objectives and the possible list of applications and contexts given by SEAB. This means that most of what you need to know is covered, and you will have a strong grasp of Math to apply to questions you have never seen before!
Compiling Your Knowledge
Of course, there are a thousand and one combinations of Math questions out there. Surely, you might think, it is impossible and impractical to study Math by doing this for every single question out there. However, this isn’t just a framework or process for you to study Math, but a way you can take Math notes and examine your process of thinking. Are you limiting yourself in solving a question because you don’t engage with other topics? Maybe instead of reflecting the graph first you often translate first without realising that reflecting afterwards will affect the overall equation.
This is a especially good way for those of you who are stuck with Math and can never seem to get out of the rut, or if you just can’t do a certain topic. Using those two steps, you can learn how to break down Math into its monomers, seeing how the basic learning objectives build up to give you what you need to solve complex questions.
With this article, I hope you have gained concrete ways to study Math. Go and study Math there.
Just for laughs:
The How to A Level series is meant to provide an in-depth analysis on how to study for particular subjects for A Levels, more than the generic ‘just study la!’ Read the first article on How to A Levels: Preliminary Idea Project Work here.