How to Study Maths for the HSC!

Illawarra Tutoring
31/10/2023

As you brace yourself for the rigours of the Higher School Certificate (HSC), you might feel a mix of excitement and anxiety, particularly when it comes to subjects like advanced mathematics. Excelling in advanced maths is not just about understanding complex formulas or memorising theorems; it's about developing a deep comprehension and appreciation for the beauty of mathematical concepts and their applications.

Whether you're tackling Standard, Advanced, Extension 1 or Extension 2 mathematics, the following strategies—rooted in educational research—will guide you in maximising your study effectiveness and boosting your performance.

Embrace Active Learning

Ditch passive reading; embrace active problem-solving. Maths is not a spectator sport, and research has continually proven that students who actively engage with the material fare much better. When you tackle problems head-on, you encounter a variety of scenarios that deepen your understanding.

Another facet of active learning involves teaching others. If you can explain a concept to a classmate—or even an imaginary audience—it reinforces your own understanding and retention of the topic.

The Magic of Spaced Repetition

You've probably heard the old adage, "Don't cram!" There's solid evidence behind it. Spaced repetition is a technique where you review study material at increasing intervals over time. This method takes advantage of the psychological spacing effect to help your brain better encode and recall information.

Interleaved Practice

When you study, resist the temptation to work on one type of problem until you've mastered it before moving on to the next. Instead, mix up different types of problems. This strategy, known as interleaved practice, can improve your ability to transfer skills learned in one context to another—a critical factor in solving complex mathematical problems.

The Art of Self-Explanation

As you work through problems, articulate each step and decision aloud or in writing. This self-explanation technique doesn't just keep you focused; it helps clarify your thinking and exposes any gaps in your understanding.

Cultivate a Growth Mindset

Your beliefs about learning and intelligence can affect your motivation and success. Carol Dweck's research on mindset reveals that students who see their intelligence as a quality they can develop (a growth mindset) tend to outperform those who view their intelligence as fixed. So, embrace challenges, persist in the face of setbacks, and see effort as the path to mastery.

Visualise to Memorise

Advanced mathematics is full of abstract concepts that are often easier to understand with the help of visual aids. Use diagrams, graphs, and drawings to create mental images of the problems you're trying to solve. Visual aids are not just study aids; they're thinking tools.

Real-world Applications

Mathematics is not just about numbers and equations; it's the language of the universe. Applying mathematical concepts to real-world situations not only makes them easier to grasp but also demonstrates their practical value. When studying, always ask yourself, "How can I apply this concept to real life?"

Seek and Utilise Feedback

Feedback is an integral part of the learning process. Regularly seek out feedback on your problem sets from teachers or study peers. Learn from your errors by understanding where you went wrong and how to correct it. This approach leads to improved performance and helps prevent future mistakes.

Mnemonic Devices

Mnemonic devices can be a lifesaver, especially when it comes to remembering formulas or properties. Create acronyms, phrases, or even songs to help jog your memory during exams.

The Importance of Chunking and Structure

Advanced mathematics can seem overwhelming. By breaking down the subject matter into smaller segments, or "chunks," you can make the learning process more digestible. Understanding how these chunks fit into the broader structure of mathematical theory can also help you see the "big picture" and make connections between different areas of study.

Consistent Practice

There is no substitute for practice. Like learning an instrument or a language, the more you practice maths, the more fluent you become. Regular practice not only reinforces what you’ve learned but also increases your speed and accuracy.

Develop Healthy Study Habits

Your brain is part of your body, and like any other part of your body, it functions best when well-cared-for. Regular breaks, sufficient sleep, a balanced diet, and effective stress management are not just good life advice; they're good study advice.

Collaborate with Study Groups

Working in study groups can provide multiple perspectives on difficult problems, offer moral support, and keep you accountable. Just ensure that the group remains focused on the goal of studying and that sessions are structured and productive.

In Conclusion

As you prepare for the HSC, remember that studying for advanced maths is more of a marathon than a sprint. It requires planning, dedication, and smart strategies. By incorporating the research-backed methods outlined above, you'll not only enhance your mathematical prowess but also enjoy the journey of learning.

Remember, these strategies are a starting point. Tailor them to fit your learning style and study preferences, and don't be afraid to try new approaches. Your HSC journey is unique, and finding the most effective way to study is part of the challenge.

By far, the most effective way to learn these strategies is with the help of a private tutor. Contact us today to get started.