How To Study Math

Last Updated on August 28, 2023

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How To Study Math

How to study Maths

Mathematics is a subject that you cannot avoid. Some love it but, if we’re being honest, most people hate studying maths. The importance of maths for students has never been greater. STEM subjects are the basis for technologies of tomorrow. Most university courses include some level of maths while almost every profession uses maths in some form on a daily basis. The problem many students have is that they don’t know how to study maths to get good results.

Maths is one of those subjects which you can easily spend hours studying, but end up none the wiser. However much you have studied, if you can not solve the problem on day of the test, you are lost. Thankfully, there are some techniques for studying maths that you can do regardless of your level. You may even end up loving mathematics by the end of the blog post!

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 7 Tips for Maths Problem Solving

1. Practice, Practice & More Practice

It is impossible to study maths properly by just reading and listening. To study maths you have to roll up your sleeves and actually solve some problems.  The more you practice answering maths problems, the better. Each problem has its own characteristics and it’s important to have solved it in numerous ways before tackling the exam. There is no escaping this reality, to do well in a Maths exam you need to have solved a LOT of mathematical problems beforehand.

2. Review Errors

When you’re practising with these problems, it’s important to work through the process for each solution. If you have made any mistakes, you should review them and understand where your problem-solving skills let you down. Understanding how you approached the problem and where you went wrong is a great way of becoming stronger and avoiding the same mistakes in the future.

3. Master the Key Concepts

Do not try to memorise the processes. This is counter-productive. It is much better and rewarding in the long-run to focus on understanding the process and logic that is involved. This will help you understand how you should approach such problems in the future.

Remember that Maths is a sequential subject so it’s important to have a firm understanding of the key concepts that underpin a mathematical topic before moving on to work on other, more complex solutions which are based on understanding the basics.

4. Understand your Doubts

Sometimes you can get stuck trying to solve part of a maths problem and find it difficult to move on to the next stage.  It’s common for many students to skip this question and continue on to the next. You should avoid doing this and instead spend time trying to understand the process of solving the problem. Once you have grasped an understanding of the initial problem, you can use this as a stepping stone to progress to the remainder of the question.

Remember: Maths requires time and patience to master.

It is a good idea to study with a friend who you can consult with and bounce ideas off when trying to solve complex problems.

5. Create a Distraction Free Study Environment

Mathematics is a subject that requires more concentration than any other. A proper study environment and a distraction free area could be the determining factor when solving complex equations or problems in geometry, algebra or trigonometry!

Studying with music can help create a relaxing atmosphere and stimulate the flow of information. Having suitable background music can foster an environment of maximum concentration. Of course, you should steer clear of Pitbull and Eminem, instrumental music is the best thing in these times.

6. Create a Mathematical Dictionary

Mathematics has specific terminology with a lot of vocabulary. We suggest you create Notes or Flashcards with all the concepts, terminology and definitions you need to know. You should include their meanings, some key points and even some sample answers so you can consult them at any time and recap.

7. Apply Maths to Real World Problems

As much as possible, try to apply real-world problems when approaching maths. Maths can be very abstract sometimes so looking for a practical application can help change your perspective and assimilate ideas differently.

Probability, for example, can be used in everyday life to predict the outcome of something happening and determine whether you want to take a risk such as if you should buy a lottery ticket or gamble.

how to study mathematics alone in self study

If you could understand plain English and have access to the Internet, then you can definitely study Math on your own.

After you implement everything in this guide, you’ll learn that there’s no one who can teach you faster and better than yourself.

Just a bit of a warning, though: while I said anybody can do this, I’m 100% sure not everybody will.

It’s a bit uncomfortable, actually, especially if it’s your first time doing this. (But super rewarding.)

In this post, you will learn exactly the 9-step approach I used to teach myself Mathematics without relying on someone to teach me.

  • The #1 mindset many overlook when studying Math on their own
  • The best resources for self-learning Math
  • How to take your Math skills to the next level

Let’s get started.

Can you really self-study Math?

First of all, if you think you’re not a “Math person” (what the heck does a Math person look like, anyway) you might think that you’d need someone else to teach you Math in a classroom.

But isn’t that the same thing as using online tools? The key here is to just create your own structure like the syllabi you use in school.

With the abundance of free information, lectures, syllabi, ebooks, and MOOCS around, you can certainly self-study Math pretty easily as if you were in college.

The best part is, you do it at your own pace.

No strict schedules, just self-commitment.

However, you gotta think differently about this if you want to reap the rewards.

That is, to recognize that the mental effort you spend practicing a Math topic is the price you pay for making future Math skills easier.

Or more appropriately, it’s the price you pay so you won’t make learning hard for your future self.

Mathematics is all about cumulative knowledge, you know.

Unlike school, you’re going to feel like crap because you’re not changing topics with respect to time — you’re now changing topics based on how fast you master a skill.

Steps to Studying Math on Your Own

I’m going to interrupt you for a bit to make something clear: I created this guide to help people who feel like they’re lagging with their Math skills and want to review it, or people who just want to study Math on their own for some reason.

Each example that I’ll give you is just that–a mere example to help you get the point I’m trying to make. It’s still up to you to apply these steps to your own situation.

Step 1. First, determine where you want to end up

Math builds upon itself, so if you want to learn a subject, say, Calculus, always ask:

In my own study, I often ask myself a “skill” based question, rather than a topical one.

“What skills do I have to learn to get better at this one?”

Problem Solving is a skill, after all. You can’t get better at problem-solving if you don’t have the tools; the individual mastery of prerequisite topics.

Which brings me to my next point.

Step 2. Determine where to start, obviously

Now that you have determined your end subject, it’s now time to decide which general topic to start with.

For example, Calculus and its applications are easier if you have the knowledge of Analytic Geometry and Trigonometry.

But Analytic Geometry has some Trigonometry elements included.

So, you can decide to start with Trigonometry.

However, if you don’t have the knowledge of “which is the prerequisite of which” I highly recommend that you find an online curriculum.

Step 3. Find a Syllabus to Avoid Unnecessary Depth

If you’re lost, you go to Google Maps. 

So what do you do when you don’t have a roadmap or a sequence to learn Math?

Use an already-designed Syllabus. They’ll be the roadmap to your self-studying success.

As I’ve mentioned earlier, these can be easily found online.

I mean, just a single Google Search will give you what you’re looking for.

Or, you can just look at your university’s resources and check syllabi for Math subjects.

Step 4. Gather your References, Solution Manuals, and “Solved Problems” Types of Books

Conventional Math learning requires that you go to school, attend classes, do your homework, and then wait for it to be checked before you complete the feedback loop.

I say that’s highly inefficient.

When there are solution manuals or Solved Problems types of books available, it’s better to actually use them side-by-side to your own problem-solving routine.

The problems are rather hard, the discussions are concise and straight to the point, but you’ll certainly get better at problem-solving EASILY.

Just to be clear, I’m not saying that you should look at the solutions each and every time you’re solving a problem, but whenever you get stuck, you can easily get out and actually learn the solutions faster.

This tight feedback loop is what will allow us to learn math FAST and at our OWN pace.

“What if I don’t understand the material?”

It’s either you don’t have the prerequisites mastered (or not at all), or you’re using an overly complicated book.

Lastly, common sense says that this guide is not the “end-all-be-all” of self-studying Math. You can always consult others when you really get stuck even when you have a solution manual (perhaps it has a typo error or something).

Step 5. Prioritize Deep, Concept-Based Learning

This is brought out by the point raised above, which is to use solution manuals for learning Math to create a quick feedback loop.

However, it’s highly misunderstood by some students.

They feel that when they can memorize how a difficult problem is solved, then that’s good.

It’s a BIG mistake to memorize something you don’t understand.

Relevantly, it’s also a BIG mistake to just understand something but you don’t practice it.

Learn WHY the steps work, because if you do this, you learn once, and solve many.

Since you’re going to be mainly self-studying using Digital Resources, it’s handy to have them all in one place.

Perhaps make them your browser’s homepage.

Make a shortcut or something.

The thing is: make it SO easy for you to access your resources so that you don’t feel friction when you want to study on your own.

This makes it easier to form your study habits–which is always better in the long run.

Step 7. Set aside time for BOTH studying and problem-solving

As I’ve mentioned earlier, just understanding isn’t enough.

You have to practice what you’ve learned.

Just as a beginner can’t play a piano masterpiece instantly after someone good teaches him how to do it, learning new things in Math doesn’t happen with your “aha” moments.

Learning happens when you recall information from your head, not when you’re trying to put things in there.

So, aside from your “absorbing” time, set aside time for practice.

Step 8. Cultivate Deep Work

While practicing, it’s important that you do so without distraction.

Working without internal and external distractions and focusing deliberately on the task at hand, aka Deep Work, improves how your neurons fire together when activated.

This happens because a sheath called myelin is formed whenever you retrieve a piece of information or practice a skill. 

When your attention is channeled into practicing problem-solving, you effectively tell your brain that ONLY those neurons activated during problem-solving should be sheathed with myelin.

When you’re distracted, however, this phenomenon happens poorly, and learning chunks don’t form very well.

Step 9. Avoid “Practice, Practice, Practice”, Do This Instead

This is probably the most common advice given to students who ask “how do I get better at Math?”.

We don’t need more time to practice. We just need to practice better.

Practicing is certainly vital, but there are two kinds of practice: Unproductive, and Productive Practice.

If you do everything in a long stretch of time, infrequently during the week, and just repeating the same problem for multiple times until you “get it” before moving on to the next one, then that’s Unproductive Practice.

Productive Practice is smart practice. 

Here’s how to do it. Two EASY Steps.

  • Spread your practice throughout the day, and throughout the week
  • When you get the basic idea of a concept, don’t answer multiple problems with the same solution; answer multiple, unrelated problems. (Interleaving)

By doing these, you’re saving a TON of time and energy into learning your Math.

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