Scroll around the IB subreddit and you will find many students around the world bemoaning how difficult Maths is. Horror stories of people crying at the sight of their AA HL paper, and being happy to even get a 2 on their finals, might scare you to think that Maths is an insurmountable subject. In this post, we discuss where this idea that Maths is difficult comes from, both anecdotally and objectively, and look at how we can systematically take down the barriers to learning maths. Most importantly though, we look at how to distinguish whether we are truly struggling with higher level maths and need to switch, or whether we are just not learning it in a way that suits us.

### Maths is difficult because...

I feel relatively qualified to answer this. Having studied Maths in uni for a year now, and getting taste of 'real maths' outside the realm of IB, it has given me some perspective on how unique a learning experience high school maths is.

The one takeaway I want you to get out of this, though, is that you don't have to be a "numbers person" to be good at maths. I don't disagree that some people have greater intuition with mathematics than others, but this is merely an enabler of studying maths, and doesn't imply that not having this intuition is somehow a barrier to learning maths.

To summarise why maths seems difficult, here's three big reasons:

Maths is interconnected.

Maths (at this stage) is formulaic

Maths is abstract

##### Maths is interconnected

I'm sure you've heard people say Maths is like learning a language. This is very apparent when you consider HOW you learn a language. You don't just decide to fluently speak German one day and expect to understand the literary works of Nietzsche. Similarly, mathematics education is built upon many many years of concept-based learning. We start with counting, then arithmetic, then geometry and then algebra and so on. In the IB, you extend your understanding of all of these topics. The trouble is, if your foundation is shaky, then as you build more and more knowledge on top, it eventually crumbles down. If you haven't mastered how to manipulate algebraic expressions, then solving polynomial equations by hand would seem very daunting, for example.

##### Maths is formulaic (at least in high school)

Now this is both a good and bad thing. Mathematics at this level is mostly about learning some formula/some concept and then applying the concepts into some problems. This is the way you have been taught Mathematics for the past 10-12 years of schooling. The good thing is that it is easily replicable by any student willing enough to dedicate effort to master the formulation. There are only so many ways they will ask you to compute the derivative of a function, for example. However, for many, it seems difficult if you cannot understand the process. Because then, every single problem seems entirely unachievable. It's like a 'if you get it, you get it" situation.

##### Maths is abstract

Many students still struggle with the purpose of Maths. It is true that sometimes we feel like learning maths just for the sake of it. The IB does encourage you to look into the mechanisms and proofs behind the important mathematical results that we study, and all the various concepts that you learn. However, I understand the difficulty to see how these concepts translate in real life especially for someone who isn't going into a STEM field later on. This spirals into a lack of motivation to learn the subject, and as we said in point 1, leads to this interconnected web of knowledge breaking down.

### How to study for Maths?

Knowing what makes it difficult, we can tackle these challenges head-on! From three difficulties, we find three "tips" for study:

Varied, tackling many different concepts together

Structured, finding out the method to solve types of questions

Don't move on to hard topics when you haven't got the basics.

Here's a helpful video with some useful tips too:

First, practice should be done on questions that span multiple topics. The IB cares a lot about the connections you make between topics. The biggest mistake I see in many people's mathematics revision routines is only doing questions from the textbook on a chapter by chapter basis. You will get very good at applying the concept when the question is all about a particular topic, but then it starts to fall apart when the question combines many different concepts together. For example, when a question asks you to solve for properties of a geometric series but the values of the series are all logarithms. Then you need to combine your knowledge of both to answer the question. If you haven't practice breaking down the walls that containerise each topic, then it becomes very difficult to "see" the connections between topics in the context of exam questions. Hence, I recommend practice from Questionbanks that link many concepts together. Instead of practicing a normal distribution question, how about practicing one that combines it with binomial distribution? Instead of practicing just integration, how about practicing it with partial fractions? This is by far the preferred types of questions I give students here at MyIBTutor to practice on. It involves far more than just repeating the concepts you learned in class in the same boring way, and actually stretches you to be a more fluid thinker on your mathematical knowledge.

Second, you need to have a structured way to practice. Often students practice without a goal in sight. They think, "Oh, I'm bad at probability, so I'll just do a whole lot of probability questions". Doing questions is never a bad way to learn, but doing so in a more targeted way will be a lot more efficient for the average time-poor IB student. The most important thing beyond just fluency that you need to gain from practicing is to identify the types of questions. There are only so many ways they can ask you questions about a particular topic - the syllabus is designed that way. Understanding the different ways they can ask you about each topic will help you master these questions and let you feel much more confident walking into an exam. As an example, for a normal distribution question, they can only ask you three things, either separately or all at once - finding the probability of some event given mean and standard deviation, finding the event given some probability and the distribution, or finding properties of the distribution with the Z-score provided you have some probability statements. As you practice, you will also notice that they like to tack on some binomial distribution questions after a normal distribution as well. It is these little patterns that you should pay attention to, so that your study becomes much more structured.

Third, struggle with your practice. I understand there is a temptation to move on from a hard topic and reserve it for later, but this will only make life much harder later on. As maths is so interconnected, you must strengthen your foundation before you could build upwards. If you are struggling with a foundational topic at the beginning of your Maths journey, don't ignore it and hope it gets better. Fix it now, so that you can move on with the rest of the course. Too many students are hamstrung in their mathematics studies because they, for example, couldn't property grasp the unit circle and so now all trigonometry questions seem hard.

### When to quit

Knowing your limits is just as important as knowing when to keep going with the above tips. It is not uncommon that students switch between AA and AI maths and Standard or Higher Level. So when should you drop down to SL or switch to AI?

Truth is, your choice of mathematics is often dictated by what you want to study after graduating.

Often, I advise students to stick with HL mathematics if you are going into quantitative sciences or engineering. You will learn the same maths at university if you didn't do it now anyways. So if that is your career aspiration, then doing it now versus when you are at university is simply a matter of maturity. I find that mathematics itself is not conceptually difficult to the average student, it is the discipline required that makes it difficult. If your mathematical foundation is relatively strong (i.e. you have been getting acceptable results throughout your middle years schooling), then I encourage you to struggle with it, and put in effort to learn the additional bit of content in higher level subjects. However, if you are already starting off on the back foot with your mathematical background, then perhaps it would be more efficient and less pressure to study standard level maths instead.

If your future career/path of study doesn't require much mathematical knowledge, then it is purely a personal preference. You could either be strategic and pick the level of maths based on your strengths or weakness, or you could be guided by your heart, and simply do more maths because you love it :)!

People mistake AI as the 'easier' maths subject. While partially true for AI SL, it is certainly not true for AI HL. You can have a look at the syllabus of both and see how they focus on different topics. AI is more varied in breadth, while AA is slightly more focused. The gripe I have with the AA syllabus is the lack of matrices, which AI focuses a lot more on. For students struggling with the abstractness of mathematics, AI may be a more helpful subject for you to see how it is actually relevant, but for those with more intellectual curiosity around the theory of mathematics, then AA would scratch that itch in a more satisfying way!

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