Why on earth am I learning this? ~{Math Syntax struggles}~

I'm a math tutor. I've been doing it part-time for over 7 years, and notice that a lot of students struggle with syntax. I mean, it is a science, but how the information is communicated in symbols makes it a language. Logically, if it is also a language, that means it should also be taught in ways that people easily ingest language.

Not suggesting that math has to turn into an English and Linguistics subject, or that ELL teachers suddenly have more on their plate to get involved with math departments in schools, but let me just use an analogy:

My current student initially struggled a lot with summation and series. She memorises formulas, such as the sum to infinity of a geometric series, or basically counting the number of terms in a series. Initially, she did not understand what this meant:

All the math peeps out there, and also social science/data science/ML people, you guys know what this does. It's a summation operator. It does something, to something. To my student, when she first learnt it, it is like a 'thing' you automatically put in front of a general term to represent the sum to N terms of a series. So she was understanding it as a rule, like how you put a "?" after asking a question. No questions asked (haha). Pretty straightforward. Then how about this:

All the math peeps out there, this is very simple too. But for someone learning it for the first time, and especially for people who do not have a knack for details, squinting their eyes is an additional (arguably physical) obstacle to overcome before mentally breaking it down. This math professor I learnt from (shout out to Robert Winters from Harvard Extension school) has a very effective general method of teaching math and I started to adopt it. Simply, introduce the overall concept in an intuitive way that anybody, even a 5 year old can understand. So, just literally looking at the shape of this symbol, to me, the most intuitive way of understanding it was a zip. Yup, a zip, sideways. 

"See it as a zip - you have a bunch of stuff with some similar trait, and you want to put them all together in one place. So you 'zip' them up." 

Then what about the other stuff, like N and i and u? 

"Those would be the details describing that stuff. You index each item by i=0,1... just like how y'all got index numbers in primary school, and then the value of each item depends on index i". 

And after all this detail, I would say: "And why on earth did somebody invent this way of writing things? It's just more efficient. Otherwise, if you had 1000 terms summed together, you would have to write each term and a '+' a thousand times." 

Doesn't take a genius to bother trying to explain things in a way other people understand. In fact, most geniuses are bothered with more advanced and complicated ideas that NOBODY can understand, which makes them brilliant. But for me, what I find valuable is to help somebody understand something, in a fun and easy way. And if only the mood for this highly technical, abstract and obscure subject can be made more tangible and relatable to how people usually perceive objects in the real world, then we would have a wider variety of personalities that can accomplish and succeed in mathematics. 

I'm not a mathematician, but I've been teaching it for years and since there's no rule saying that non-mathematicians can't try grooming people to understand it better, hence this post :-)