If you want to understand fully the meaning of any word, it is important to look up the derivation of that word. For example, in looking up the word "perceive", one reads all the definitions but fails to look up the ancient root meaning of that word, one is limited in one's understanding. The first part of that word "per" means "through" or "by means of", the second "-ceive" comes from an ancient word meaning "to grasp". When one perceives something, one grasps its nature or shape or sound or whatever other quality it has, grasps by means of the senses and the mind.
What does this have to do with really "getting" how music is written down? Everything.
After my students learn to perceive and name the various intervals, recognize each one with effortless confidence, then it's time to tackle how to read and write the intervals. I spend one fruitful hour telling my student the history of music notation. Each important symbol of music was created for a reason, solved a problem of some kind. I explain exactly why the symbol is shaped that way, why there are five lines, who created this system and why did they make the choices they did. Understanding that real people created the method of permanently preserving music helps the student to know that practical issues were part of the process of developing our system of music notation. Some of these commonsense problems and solutions are as simple as "the monks who wrote the religious chants down to preserve them had TIRED HANDS, so they had to make it easier on themselves and come up with a simplified method."
I can't instruct you here on all the historical and practical reasons why the signs and symbols of music look the way they do, but I WILL share with you that understanding WHERE something comes from and WHY it was created, is an effective way to have it (literally) at your fingertips...