Conceptual Understanding is to understand each step of your solutions. You need to question each step of the solution and how you derive the steps. The steps of the solution can be logical to you and can be commonsense but you may not understand it. Take an example “A right angle is 90º”, why 90º not 100º and why a circle is  360º. You need to check and question those information that you have applied so as to understand your solution better.   

Conceptual Understanding starts from day one when you start to learn mathematics. There are no guidelines or list of items you need conceptually understanding it. There is only a list of topics you need to learn to help you to advance in mathematic. Conceptual Understanding will help in making your foundation in Mathematic strong. You need to conceptual understand most of the topics so as to advance well in mathematics.

To improve Conceptual Understanding, you need to ask Why? Why?  Why? You also need to know what are the topics you are weak in. Some topics are prerequisite to another topic. You need to understand it before you can advance to the next topic. Go through the list of topics you have learnt in the past and check which topics you are unable to understand. Address those topics you are weak in first before you start to learn the next topic.

Some concepts are for application and it is difficult to understand through practicing of solving problem sums. You need someone to explain to you its application. Some concepts are too abstract and you may not be able to understand at your level. 

Understanding your basic concept is very important. Some of them are taking things for granted. They view the basic concept as commonsense and ignore it. Take an example why the circumference of a circle is C =2πr? How do you derive the formula? Understanding the proving of the concept is always the best way to strengthen your conceptual understanding.