Learning Mathematics

Why Learn Mathematics?

Technology is everywhere around us, and we need mathematics to master it!

Taking Blood Pressure

stock exchange

In fact most top-paying jobs need good math skills:

  • Doctors
  • Vets
  • Engineers
  • Scientists
  • Software Developers
  • Marketing Analysts
  • Financial Officers
  • Investment Managers
  • and more ...


Computer Games



And Mathematics is not just numbers, it is about patterns, too!

So jobs like fashion and interior design can benefit from math skills.


Mathematics is also useful in everyday life:

Mathematics also improves your mental ability as it teaches you logical ways of thinking.

And it is just plain fun: what other subject is about solving puzzles?

How to Learn

This advice is based on research, read Bibliography for more.

There are two major steps:

learn get use

Get the information ... read, listen to a teacher, watch a video.

Use the information ... sketch it, explain it to someone, answer questions.

Using it is so important! It ...

Just reading or watching videos can give you a false sense of confidence in your knowledge, which may not really be that good.

Do plenty of practice each day. It is OK to go back and reread. You will feel the knowledge clicking into place!

Study Schedule

Create a schedule where you study different topics for short periods of time each, so that:

interleaved schedule

This is based on the ideas of Spaced Learning and Interleaving:

How to Read Mathematics

Mathematics says a lot in a short space.

Example: In English we say "We don't know what staplers or trays cost, but we do know that the office manager bought 15 staplers and 11 trays for a total cost of $73"

But in Mathematics: 15s + 11t = 73

So it is good to re-read, go back and forth and play with the ideas.

Reading Math
Reading Mathematics is different to reading English

Read it, think about it, read again, write it down or sketch it out, and then use it. This all helps to get the ideas into your mind.

Example: Converting Celsius to Fahrenheit

°F = (°C × 9/5) + 32

  • Read it once first to see there is °F (which means Fahrenheit) on one side, and °C (Celsius) on the other side, with some calculations.
  • Now go over it again and see that °C is multiplied by 9/5 and think "I wonder why that is done? Why 9/5?"
  • Then notice that 32 is added ... why is that?
  • Maybe you could make a sketch as shown below.
  • Use it yourself, do a few conversions and see how it works.
  • Explain it to someone else, even your dog. 

Make Sketches

It really helps your understanding when you sketch what you are learning.

Make large and bold sketches with plenty of labels and notes.

Like this sketch about Celsius and Fahrenheit:

Temperature Sketch

Sketches are also very helpful when doing questions. So become a good sketcher.

Work Neatly

work neatly
Working neatly helps you think more clearly
and also gives you good mental habits.

Have pride in your work, even if nobody else will see it.

Take Your Time!

Math is not about reading pages ... it is about building concepts in your mind.

So don't think "I read 2 pages today", instead think "I understand graphs better now".

Important: If you skip past a section, the rest may not make sense. You will get confused, frustrated, and you will begin to hate the subject.

The cure?

  • Go back to where it made sense,
  • then move gently forward again,
  • do plenty of practical things like solving questions and doing sketches

And you will soon be "back on track"

Practice, Practice, Practice

Do lots of questions.

That is why we have the Mathematics Question Database.

If you need to pass an exam, find past exams and do them.

Aim For 85% Success

Research* has shown that we learn fastest when we get things right about 85% of the time. So aim for a level of difficulty that slightly pushes you out of your comfort zone but doesn't result in too many failures.

Read a Lot

Get some books, and read them. Spend time on math websites (like this one!), and join a forum (like the Math is Fun Forum).

Come Up With Your Own Ways

You have your own learning style.

Don't just follow the steps you are shown, try your own ideas!

Play with the ideas you are learning.

And try reading about the same subject from different places, you may find some that make a lot more sense to you.

Your mind is an amazing and unique tool, and you want to use it the best way you know how.

And studying mathematics is a good way to improve it!

All About Ideas

It is more important to know the ideas than to remember the formulas.

If you know how things work, you can always re-create the formulas when you need them. And you also gain the ability to do more clever things with your ideas.



For further research look up Retrieval Practice, Spaced Learning, Interleaving, Elaboration, Concrete Examples and Dual Coding