Why is using 'this' mid-sentence incorrect?

I am an English Literature teacher at university level, and a trained EFL teacher, so it's a bit embarrassing to have to ask this, but I can't find a satisfying answer anywhere else.

My students regularly use 'this' mid-sentence, usually after a comma. E.g., 'The room is small, this indicates that...'

I think it should read: 'The room is small. This indicates that...' or 'The room is small, which indicates that...'

I am fully aware of the rules (whether you adhere to them or otherwise) that govern the use of 'that' and 'which', but I've yet to find a convincing way to explain to my students that 'this' is incorrect mid-sentence.

At the moment I try to explain that 'this' should only follow a full stop or semi-colon as it refers to the subject of the preceding clause, but that's not actually an explanation of why 'this' is incorrect mid-sentence.

Of course, I may be completely wrong, and it's actually fine to use 'this' in this way.

Can anyone help with an explanation that I can offer my students?

It's because you can't use a comma to separate two independent clauses without their being joined by a conjunction, etc. The type of sentence construction your students are writing is known as a "comma splice".

There is nothing better than a dictionary when explaining to others in terms of grammatical usages.

If you look up "this", there is a specific usage which is similar to yours:

Referring to a specific thing just mentioned: 'They build the car in their Turin plant, and this brings the expected levels of quality.'

The dictionary uses "and" after a comma. This is an example that students should follow.

There is another example that doesn't use "and" after a comma as follows:

This is not a role model, this is a terrifying ideologue and a fundamentalist, if you will.

[Oxford Online Dictionary]

Here, "and" is not used because the subject of the second clause is the same as the first clause.

You have to explain to your students:

You can only omit "and" after a comma when the subject of the previous clause is the same as that of the second clause.

This is not quite an answer but rather a hypothesis that might prove helpful to you. If not, don't kill me.

As Lunguagemaven pointed out, technically, your students seem to be excessively fond of the comma splice. In reality, they're merely accustomed to talking (and thinking) in short block-like sentences that follow one another in quick succession. They are loath to pause after each sentence lest their listeners take advantage of it and start talking themselves. The resulting patterspeak is reflected in their writing.

One way to remedy this would be to teach them to write longer, more descriptive sentences (adjectives and adverbs galore). Instead of letting them write "This room is small," insist on details, metaphors, humor - anything. "This otherwise perfectly serviceable room with off-white walls and quaint-looking windows is ludicrously small." It would be pretty difficult not to pause and take a breath after a sentence of this length. And, just like "a good cigar is a smoke," a good dramatic pause is an invitation to put a period where it belongs.