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5 tips to understand mathematics by Dr Chris Tisdell

This article is written by the author of the free eBook “Engineering Mathematics”

Do you find mathematics difficult, disengaging or even stressful? You are not alone! Students from around the world recently identified mathematics as their “most-hated” subject in reaction to a Facebook post by publisher In addition, researchers at the University of Chicago have recently shown that even the anticipation of mathematical work activates pain centres within the brain.

Mathematics, however, is an essential, exciting and very beautiful part of our world. It enables cutting-edge advancements within a wide array of important fields, such as engineering, science, business, and technology.

Given that many students encounter some mathematics during their studies, the following 5 tips have been created to help you form a better understanding of mathematics.



Many students find mathematics difficult because they “believe” they cannot solve the exercises or understand the material, even before they begin. Approach mathematics and mathematical work with confidence and a positive attitude – you can do it!


Time management

If you are stuck on a mathematical problem for too long then move on to the next one and come back to it later. You may be surprised at what revelations a break and a fresh viewpoint can provide.


Start with special cases and simple examples

Many students learn a new topic most effectively by engaging with concrete examples as opposed to examining general theories. For example, if you are presented with an abstract mathematical formula then try to construct some simple, special cases or look at some applied examples involving the formula. These simpler and contextualised situations will provide the basis for you to understand the more general or abstract setting.


A picture paints a thousand words

Much of mathematics involves very precise notation designed to convey deep and carefully crafted ideas. In some cases a simple picture, sketch or diagram can easily express the main idea in a powerful, geometrical way. If a mathematical statement seems like abstract squiggles on the page then consider, or ask, if there is a diagram to illuminate the “big picture”.


Mathematics is not a spectator sport

Actively watching your teacher solve mathematical problems does have educational benefits, but the most important advice is that you will learn mathematics by doing mathematics! How?! By having a positive attitude, good time management, by examining contextualised examples and starting with special cases. Furthermore, by employing insightful pictures and simply doing mathematics.

Dr Chris Tisdell is a mathematician and YouTube Partner in Education. Subscribe to his YouTube Channel where you can watch online mathematics videos. Below you can watch his latest video.


For more tips on how to understand mathematics download his book “Engineering Mathematics: YouTube Workbook“. This book is freely available on