We’ve all experienced the frustration: of pouring endless hours into a math topic, tackling practice questions, and slogging through past exam papers, only to feel like progress is an elusive mirage. If this struggle resonates with you, here’s the gist: there’s good news and there’s the less-than-stellar news. The good? This plight isn’t exclusive to you—it’s a rite of passage for many students. The not-so-great part? There’s no one-size-fits-all fix.
Just as fingerprints distinguish individuals, each student craves a unique strategy to fast-track improvement in math. In this article, I’ll delve into four unconventional nuggets of advice that have been game-changers for my students, propelling their math scores and deepening their comprehension.
Identifying the Heartbeat of the Topic
Every math topic revolves around a central crux, an identity and essence that it builds up from. Oftentimes, students and teachers briefly gloss over the underlying importance of a topic and delve right into formulas and equations. Here’s what I’ve discovered: once students uncover a topic’s true essence—grasping why it matters, how it connects to other subjects, and its real-world application—magic happens. They suddenly become much more proficient and adept in answering problems and taking on more difficult questions.
Let’s take calculus, notorious for spinning students’ heads with its complex equations. Once students grasp the fundamental essence behind calculus—its role in describing gradients and steepness—the once shaky foundation now becomes reinforced and we can build from there. You may be wondering ‘So how can we figure out the underlying core of a topic?’, a phenomenal question, glad you asked! Identifying this heartbeat behind a topic can be approached in two ways: immersing yourself in hours of research, hoping for clarity in complex explanations, or opting for a more manageable path. Seek guidance from those who’ve navigated these complexities already—teachers or tutors who can distil this intricate essence into digestible insights. It’s a more accessible route for students, tapping into the expertise of those who’ve travelled this educational terrain and have had success doing so.
Understanding the heartbeat of the topic is a superb technique for the students who struggle with the more applied problems, or find themselves getting lost in the algebra or geometry of questions. By capturing the deeper meaning behind mathematics, students ultimately become more responsive to complex explanations and concepts, further bolstering their mathematical prowess.
Another unconventional strategy to get better at math is to intertwine practice. By this, I mean that instead of practising each topic in isolation, you practice them together. For instance, instead of doing a set of algebra questions, then moving on to geometry, and then calculus, you could mix things up. You could try doing a few algebra questions, then some geometry, and then some calculus, and then come back to algebra again. This approach helps you to see the connections between different topics and how they relate to each other. It also helps you to reinforce concepts that you may have learned previously but may have forgotten. I’ve found through experience as a student and a tutor that when you get stuck on a problem or concept, it feels very difficult to move on from it. This is a natural reaction and delves deep into human psychology about filling in gaps and completing unfinished tasks. When you try to move on from a concept you haven’t finished, your brain will keep tinkering away at it and not give full attention to the new task at hand. By consistently practising intertwined learning, you force your brain to realise that moving on will allow for more understanding to take place later.
For example, let’s say you’re practising algebra and you come across a question that involves finding the equation of a line. You know that you need to use the formula y = mx + b, but you can’t remember what ‘m’ or ‘b’ stands for. Instead of looking up the answer, you switch to a geometry question that involves finding the angle between two lines. In doing so, you come across the term ‘slope,’ which you remember is another word for ‘m’ in the equation of a line. You then switch back to your algebra question and are now able to solve it with ease because you’ve reinforced your understanding of the concept.
Intertwined practice can be a helpful strategy for those who struggle with retaining information or connecting different concepts. By practising topics in an integrated manner, you can deepen your understanding and make connections that you may not have otherwise. Ultimately, allowing you to become a better math student and create links that you may not have been able to previously.
This is by far the most effective strategy that I’ve found to help students improve their problem-solving skills and deepen their understanding of concepts. However, the way I go about it for my students is quite strange, but the most powerful way to use this technique. It involves studying incorrect solutions to identify where they went wrong and how to correct their mistakes. We also consider each student’s inherent uniqueness and try and create certain triggers to prevent them from making the same mistakes. By doing so, students can gain a deeper understanding of the concepts and the processes involved in solving the problem.
In essence, error analysis can be treated as a detective game where identifying the error is crucial to solving the mystery. By analysing incorrect solutions, students can learn from their mistakes and develop a more robust problem-solving approach. This process encourages students to think critically about the steps they took to solve the problem and consider alternative approaches that could lead to a correct solution.
By engaging in error analysis, students can develop a more comprehensive understanding of the underlying concepts and principles. They can also improve their analytical and critical thinking skills, which will be beneficial not only in academic settings but also in their personal and professional lives. Overall, incorporating error analysis into the learning process is a valuable tool to help students develop a deeper understanding of the material and improve their problem-solving skills.
In sharing these insights, I hope I’ve shed light on some of my more intriguing tactics to improve in maths. I firmly believe these principles, once applied correctly, can change the game for many students. They mark some of the more foundational pearls of wisdom that I’ve stumbled across over my four years in the tutoring field and capture the essence of progress and growth without being too rigid on wrote memorisation and formulas. Wishing you the best as you carry these nuggets of wisdom forward.