How to Study: Mathematics
Like any subject, studying for mathematics presents unique challenges. Rote memorising formulae and methods, while helpful, is not enough to ensure success in maths. Below we share some simple tips as to how best to study for maths.
1. Avoid cramming! Mathematics is a subject that rewards genuine understanding. Try to study regularly, completing set questions and corresponding exam questions as you go through topics. The work is divided for you to make it easier to master the content as it comes. Cramming is stressful and leads to lower retention rates come final exams. While many subjects require memorisation and recall of information, mathematics demands the application of the ideas you learn. They must be practiced. Although there are many set methods for solving math problems, each question is unique and often must be solved in a slightly different way to another problem. This is especially prevalent in more advanced mathematics.
2. Attempt a diverse range of problems. Studying regularly and studying effectively are very different things, but hand in hand will see you achieve your goals. Reading a textbook or notes to familiarise yourself with content, even if it is every day, will not properly equip you with the skills you need to correctly tackle more complex problems. This is not to say that reading notes isn't a good starting point for learning new content, but it cannot stand alone.
One of the largest challenges in maths is not applying methods you have learned but identifying which methods are best suited when faced with a problem. An example is a quadratic equation, which can be solved a number of ways. Through repeated exposure to quadratics, and experience in solving quadratics, students will be able to quickly identify which method is appropriate for a given problem.
3. Rework incorrect questions. Erasers aren’t for people who make mistakes, but for those who wish to correct them! You’re probably tired of hearing it, but the easiest way to ensure self-improvement is to learn from your mistakes. To do so, you must understand where you went wrong and what line of thinking brought you there in order to prevent it from reoccurring. Its also important to not give up on a problem too early- always attempt the question before checking the back of the textbook as this can result in a reliance on working backward from the answer.
If you are struggling, revise your notes and attempt a simpler version of the problem. If this doesn't help, you can speak to a peer, ask your teacher (or a tutor) for help, or seek online resources if you need an alternative explanation that resonates with you. We recommend Khan Academy (https://www.khanacademy.org/) and MathPays (https://www.youtube.com/user/mathspays/videos)/. Eddy Woo also has fantastic YouTube videos with worked solutions and explanations, particularly for more complex mathematics problems https://www.youtube.com/channel/UCq0EGvLTyy-LLT1oUSO_0FQ.
4. Focus on your weaknesses. It is very common to study for subjects you are already confident in because you tend to enjoy them more. However, it is crucial to acknowledge your weaknesses and focus on building them into your biggest strengths. Most maths exams cover multiple topics, and in our experience tutoring, we have found that many students tend to focus their study on the topics they enjoy most, and are best at. It is important to break this habit and to tackle weaknesses before refreshing easier content. We have found that a good way of doing this is by listing all topics in a test and rating them from 1-5 in terms of how comfortable you feel doing it. After this, organise your study to prioritise the tougher content, ensuring that when the test arrives you are comfortable with all topics.
5. Do practice exams. Once you are feeling confident in the topics in an exam, it's important to practice your skills under test conditions. As well as providing pressure to work fast and efficiently, exam conditions also prohibit checking answers, which means you must adapt and find ways to check your working. You’ll find that the more you familiarise yourself with exam-style questions, the more confident you become, the less time each problem takes you to solve, and the less stressful it all seems. The harder you work, the luckier you become — exam questions will begin to feel like they “suit you” when it is really just a result of expanding your mathematical toolbox.
Written by Sally Evans who completed Extension Mathematics in the HSC and is currently undertaking a Bachelor of Science and Advanced Medical Science at the University of Sydney where she continues to hone her love for maths. For tutoring with Sally or any of our other tutors please contact us at 0422991843 or at firstname.lastname@example.org.