Hi HSC maths students! What you are about to read will change your life, determine your success, your marks and your outlook on how to do well. So please grab a cup of your favourite tea or coffee and get ready to learn what the top students have been hiding unintentionally from the rest of you in how to do well.

Over the past year and a half working at Tutesmart and ATAR Notes I have been developing Maths Advanced students in the skills and knowledge that allows them to succeed in their tests at school and in the final HSC exam. Over this time, I asked myself one of the most important questions

“What do the top students intentionally or unintentionally do to prepare, study and take the maths exam that allows them to get the best marks?”.

I will describe in detail my findings and answer to this question for the duration of this article.

For many, learning maths can be quite challenging. In fact, I had difficulty learning maths and performing in maths exams from a young age. I was not your typical prodigy genius who ended up with an ATAR above 98. I am not here to tell you that I got 99.95 and 100% in the maths exam, because to be honest those students work almost inhumanly hard to pull it off even if they tell you otherwise. I worked so hard and have always wondered what skills or methods I could use to get the best marks.

I have been researching effective studying and learning methods for maths ever since I sucked at it and it has led to some incredible discoveries about how we learn and how we all can improve our maths ability well beyond band 6 level.

Take notes now as you do not want to forget this next part.

Students in maths can be split up into 3 different categories,

The first group of students are called the grinders. These students who put in a huge effort to complete all their homework, do assignments early, seem to have an uncanny maths ability way better than yours and ace tests all but a few errors here and there. These students would rank in the top 10% of your class in most cases but, spend a huge amount of time just doing maths.

The second group of students are called the stars. The stars seem to have life easy, they play sports or music, have plenty of friends and appear to have a golden gift for life. They appear to pick maths up quickly and perform in exams incredibly well with rankings between just above average to the top of the class without much work.

The third group are the battlers. This article is written mostly for the battlers. The battlers find it difficult to pick maths concepts up or understanding how to crush questions quickly. They also find it hard to rise to the occasion in exams, run out of time in exams and make large numbers of silly mistakes.

However, battlers can become stars by learning and implementing the right set of tools. I was a battler who thought that there was a better way to learn and perform in exams and I reinvented myself as a star; crushing the competition and doing it in far less time than the grinders.

By reading deeply the following model of success you too will have the tools to develop your inner star and achieve top marks in way less effort than you could imagine.

Mental Model: The First Principles Tree

By understanding the First Principles Tree you will have the ability to attain 100% in the maths advanced exam if you choose. This model is the fastest way to improve, learn and ace questions.

What do I mean by first principles?

First Principles thinking is a way of solving complex problems by breaking them down into their fundamental truths and then building them back up to form a solution.

What do I mean by tree?

The mind and its ability to learn can be thought of as a metaphorical tree. This can be similar to a hierarchical mind map.

The tree has 4 components:

* The trunk – the stronghold of maths knowledge and truths (algebra laws, numbers, operators).

* The big branches, (the topics of maths including, calculus, finance, stats, functions and trig functions)

* The smaller branches off of each big branch – (the dot points from the syllabus/ the specific types of knowledge to learn inside a topic) for example, inside of calculus, we have differential calculus which is a small branch off the big branch of calculus.

* The leaves off the small branches – The leaves are the specific types of questions you are asked in maths based off of the sub-subtopic in the course (simply just the dotpoint in the syllabus).

Okay so simply we all have a first principles maths tree. You might be wondering why this matters at all? Depending on the size of your tree, the amount of leaves off each branch and if you even understand how each topic relates to each other completely determines your success in maths.

Ask the top students and they will answer any question successfully, this is because they have a mental solution for every type of question in the course.

How do you learn maths quickly and strive for 100%?

Maths is learned by storing a mental method for solving a given type of question in the course. There are only so many types of questions that can be asked and by exposing yourself to them, solving them and understanding them conceptually you will be able to solve it in the future (in the exam where it matters).

Learning quickly and well is based off of how well you remember how to solve a similar question you have seen previously.

So, for every question type in the course (each leaf on the tree) once you encounter it in the course, add a worked example, a general method of approach and a numbered set of steps for how you will get to the answer from start to finish.

By adding to your tree in this way you will leave no room for error. All that is left is a little bit of practice to refine speed and reduce silly mistakes.

How does this relate to the three categories of maths students?

The grinders unintentionally build up their tree of knowledge by bashing their heads against every maths topic wall until it breaks. The brute force approach. All these students are doing is trying to learn the method of how to solve a particular type of question without knowing that’s what they are doing.

This means they will achieve success by very slowly and painfully. But if you do the long hours of work every week you can achieve success. Will it be painful and yield mental breakdowns? Definitely.

The stars however use the first principles tree usually unintentionally or intentionally. These students rise to the top of their class through simply using the right framework of thinking and storing of knowledge so they don’t forget it even, if they barely do their homework. This is the highest reward for the least effort.

The battlers are the stars without the right tools and either find themselves banging their heads against the wall like the grinders but without the gruesome 50 hour weeks that they put in. So what happens is you bang your head until you are bleeding and the wall isn’t broken down. This very quickly leads to burn out, a belief that you aren’t good at maths and other lies you tell yourself because you are trying your best but not succeeding.

With all of this in mind. GO out and make a mind map of all the different types of question in the course (it’s your syllabus). Then spend your class time finding a step by step general easy to follow method of how you will answer every single different type of question in the course.

I know it doesn’t sound fancy, but if you do this, you will have no gaps in your knowledge and with just a little bit of practice you will have complete mastery over the entire maths advanced course and any other subject.

As a final note to the future stars that will be born from this, you deserve success and you deserve to succeed without giving up the things that make you unique like sport, friends, family and a life.

If you really want to succeed without the long hours and pain of the grinders and the hard knocks and doubts of the battlers, then give this method a go and you will be surprised by just how much you can kick ass.

Good luck for your studies!