# Should You Be Writing Study Notes for Maths?

*Written by Larissa Isakov.*

Maths is a skills-based subject. Performing well in Maths not only requires a solid conceptual understanding of the material but also the skills to apply that knowledge to different styles of questions, whether they be normal algebraic “concept-check” questions or harder problem-solving exercises. This skill set is what differentiates students academically.

So if Maths is a skills-based subject, should you be writing study notes for it? The short answer is yes, but with qualifications.

**Here is a quick summary of the types of study notes you should and shouldn’t be making for Maths:**

**Acceptable Study Notes ✅**

- Concept summaries (no longer than 2 pages)
- Mistake sheets

**Concept Summaries**

I’d suggest that you make concept summaries for every topic you encounter in Maths. Ideally, your concept summaries should be between 1-2 pages long and should include all the key formulae for a specific topic. For example, if I am writing a concept summary on Area and Volume, I would include things such as all the area formulas for plane shapes and key techniques for calculating the volume of prisms (i.e. Volume=Cross sectional area depth).

Concept summaries are useful in several ways. Firstly, they are an invaluable resource to have when studying because they are a quick reference guide for any key formulas and concepts. They are also quite portable and can easily be pulled out for some ultra-quick study (think about all that time you spend looking out the window while catching the bus to school!! Perhaps you could test yourself on key concepts instead).

Now, you might think: “I’ll have a formula sheet for my exams and my notes on hand with me when I study; why should I bother with writing a concept summary that contains all the formulas?” Well, there are a few things to consider. Firstly, the formula sheets you receive in your exams do not contain all the formulas you encounter in Mathematics. As you can see, the HSC Mathematics Advanced formula sheet does not contain all the formulas for area and volume. And for the limited formulas, they do provide, they don’t specify what the formulas are actually for. Accordingly, you will need to make your own comprehensive and complete set of notes.

Secondly, making your own formula sheet helps you with memorising the formulas and consolidating your knowledge. You may have been in a situation where you’ve taken a friend’s notes, read them, and had nothing sink in. There is a reason for this – Summarising key concepts in your own words is the first step to memory retention. It is far more effective to summarise something yourself rather than read it again and again (and again) from where someone else has written it.

And lastly, having a formula sheet is just plain convenient. You do not want to spend every study session flicking through textbooks and class notes just to find Simpson’s Rule or all your index laws. Think of summary sheets as a way to reduce friction when you are studying; you’re saving time and brainpower that could be better spent on attempting questions rather than retrieving information.

So start making concept summaries now (I mean, right now). Even better, if you start making study notes for Maths in Years 9-10, you will have an invaluable resource for Years 11 and 12. Why: Because a significant portion of the content in Junior Maths features heavily in Senior Maths. Having study sheets earlier on means that you do not need to constantly remake them, thereby saving even more time.

**Mistake Sheets**

Another invaluable resource is to have a sheet where you write down all the mistakes you have made when completing questions. This is important in several respects. Firstly, it forces you to slow your study down and reflect on *how *and *why *you made a mistake in a question as opposed to just glossing over the question, saying you got this wrong, and that you’ll do better next time. Believe me, you are bound to make the same mistakes again if you do not spend time reflecting on them.

So as you work through any exercises for a given topic, write down all mistakes you have made (including silly mistakes!!), why you have made them, and revise the sheet before you complete more questions for that same topic. Even better, any recurring mistakes can be added to your concept summaries so you can revise them there as well!!

**What Not to Write ❌**

- Content downloads

**Content Downloads**

Do not write concept summaries with extremely long explanations, every style of worked example possible, and all workbook exercises. This is a waste of time. Study notes for Maths need to be as concise as possible. Remember that Maths is a skills-based subject; we need to strike a balance between writing study notes and spending lots of time on practice. **Knowledge in Maths is best internalised through lots of practice rather than by memorising everything you encounter. **

**A Final Note**

So now you know how to write effective study notes for Maths. I’ll just add two final thoughts: Firstly, your study does not stop at the notes-making stage. You need to be constantly practising in order to develop speed and fluency with Maths. And secondly, you should be iterating your notes as you work through more questions. As you make further mistakes or learn new skills, add them into your notes. This way, your notes are constantly evolving and getting better.