🎯 4-step self-learning math framework

My math learning framework breaks down into four essential parts: definitions, examples, knowledge gap, and practice questions. All you need is a book, some paper, and a pen. (If you use an iPad like I do, that works too!) Choose a textbook with thorough practice questions and answer keys with explanations. In this example, I’ll use a chapter on linear equations from a differential equations textbook. Let’s dive in!

1. Definitions

The first step is understanding the topic—its definitions, rules, or theorems. These are concepts mathematicians discovered or proved long ago and are fundamental to your understanding.

• Open your book and read the definition carefully.
• Highlight key points and try to grasp their meaning.

<aside> 💡

Example: In the chapter on linear equations, we start by identifying what a linear equation is.

</aside>

Don’t worry if you are confused when you read about the definitions, it’s totally okay, and don’t get intimidated by them. Lots of times, it's more important to know how to use them than what they actually are

2. Examples

Definitions are like tools. Examples show you how to use those tools in practice.

• Work through the examples in your book.
• Study each step and understand the solution process.
• Then, find a similar problem in the exercise section and attempt it using the example as a guide.

Learning a theorem is like learning about a cup. You don’t just learn what a cup is; you learn how to use it. For instance, drinking water or watering plants with a cup. Similarly, practice solving problems using theorems or rules.

<aside> 💡

Example: After learning and understanding example 1 solving for a linear equation, look for a similar exercise question in the end of the chapter. Practice it to ensure you’ve grasped the method.

</aside>