Going From "good" To "great"!

Is it just luck or ;good fortune ;when a student achieves a grade 9 in Maths? That`s how it seemed to a few of my students last year in the build up to their exams when they were scoring grade 7 and 8 on their mock papers. They believed that, unless the stars had aligned and luck was on their side, they were never going to get that top grade. But is it really down to luck? Of course not! At least not to the degree that those students believed. It all comes down to putting in the effort in the right places. It`s not just about enhancing your knowledge by revising all the topics and remembering all the key facts, it`s the personal habits and exam techniques that contribute to their success. So below I want to give you some insight into the key traits and strategies that the grade 9 students all have in common so that you, too, can achieve the top grade.

Rigour and Resilience

One trait that separates the grade 6 and 7 students from the grade 8 and 9 is the quality of their working on every question worth two or more marks. A personal bane of teaching for me is the sheer energy I need to put into convincing some students to show their working in class because it seems tedious and requires effort. Why is it a bane? Simply put, a significant proportion of the marks in your exams will be awarded for demonstrating the correct mathematical method. A cursory count from the June 2024 set of papers showed there were 104 marks awarded solely for method. This means you could technically get every question wrong but if you demonstrated the correct method then you could still achieve a grade 5! That seems insane, right? Passing while still getting every question wrong. But it makes sense because the exam boards don`t want to award students for being lucky ;and potentially getting the correct answer; they want to reward the students who can demonstrate that they know how ;to get the answer. This is why method marks are so significant. And the grade 9 students understand this, so they work on clearly showing their understanding, checking carefully that they haven`t made any crucial mistakes, and they apply this to all the questions. It provides that safety net. Make a mistake with no working? 0 marks. Make a mistake with the correct method shown? You lose 1 mark out of 2, 3, 4 or even 5 marks. It`s worth the effort, regardless of how tedious.

Visualisation vs. Imagination

As humans sight is considered one of the, if not the ;most, valued sense we have. The way we navigate this world relies significantly on our ability to see, so it stands to reason that being able to represent certain mathematical problems visually would be key to finding a solution. The top students often employ this strategy to wordy questions. Maybe there`s a sneaky hidden right-angled triangle in the situation that your good friend Pythagoras can help you with? Or maybe a simple two way table can help highlight which missing value you need to find a certain probability? There are many scenarios where a sketch or diagram can help guide you to the solution.

Don`t be reliant on your calculator

Another bane of mine is the utter reliance some students have on using calculators. Don`t get me wrong, I`m not expecting you to calculate Sin(73) without a calculator and, of course, you shouldn`t be deterred from using one in the two calculator papers. However one third of your entire grade comes from a non-calculator paper so if you go straight to your calculator to work out something like "34 x 75 =" then your are potentially disadvantaging yourself in the long run, particularly if you struggle with calculations involving decimals or negative values. As well as securing the marks in the non-calculator paper, having strong numeracy skills can also be beneficial with sense-checking your answers. As humans, we will inevitably make mistakes when typing values into a calculator. For example we may accidentally type "Sin(31 x 8" when calculating the opposite side of the right-angled triangle. Forgetting that close-bracket gives an incorrect value of -0.9 that you may not notice. The students who put the time into practising their non-calculator trigonometry (exact values) would most likely notice that Sin(31) is close to Sin(30), which is equal to 0.5, so their answer should be approximately half of 8. Another instance is the dreaded "-a^2" vs. (-a)^2 mistake we too often see as teachers. If you want to find the square of a negative 3 and you type in your calculator "-3^2", you`re most likely going to get "-9" appear on the screen, which is incorrect. You are significantly more likely to miss this mistake if you consistently use calculators to work with negatives instead of going through the mental process of squaring a value mentally.

Make the most of those opportunities

A common theme for this article is all to do with effort. There`s no escaping it, really. The old adage is true after all; "Fail to prepare then prepare to fail". But as teachers, we endeavour to support the efforts our students put into their work and we will reciprocate this by putting in a lot of effort on our end such as running after school sessions, providing resources for you to use and taking the time to go through and provide feedback on any additional work you give us. We provide these opportunities in the hopes that all our students use them. The grade 9 students certainly do. If your teacher provides you with any extra, non-compulsory opportunity then don`t let the non-compulsory part sway you. Take them up on it. It can make all the difference!

Practice, Practice, PRACTICE!

The all important one and, yes, the obvious one. And I know it`s obvious but I think a lot of students miss the point of why we give you so many past papers to practice. There are three assessment objectives that you are tested against in your papers and the third (AO3) tests you on your ability to solve problems within and outside of mathematical contexts, and this contributes to 30% of the marks in all three papers, often within those difficult big mark questions. One of the success criteria for this is your ability to make connections between different parts of mathematics. This might mean, for example, incorporating algebra in solving probability or using proportionality to solve geometric problems. It`s a challenging skill to do and one that`s difficult to be taught explicitly, which is why the teaching of the skill needs to be supported with personal experience. The more you practice, the more likely you are to recall a similar link required to solve the problem your attempting. The reason many teachers seem so good at solving exam questions (myself included) is because we have multiple years of experience answering exam questions. When we read a question, we often link it to questions we`ve answered before and this then helps us with finding the solution. It will seem daunting and difficult at first but I assure you, in time, you will make those connections more frequently and more easily. You just need to practice.

Ultimately it all comes down to time and effort, not just practice for the sake of practice but instead refining the habits and strategies necessary to support your knowledge and skills.