An ELT Glossary : Dangling participles

Participles may be used to introduce a subordinate clause :

Walking down the road, John saw a house for sale
Located on the cliffs, the hotel has an excellent view of the sea.

Used in this way they are non-finite verbs, and there is thus no indication of what the subject is. That is "discovered" from the main clause : the subject of the main verb is understood to be also the subject of the participle - ie

John was walking down the road...
The hotel is located on the cliffs....

A "dangling" participle occurs when this rule is broken and the subject of the participle is not actually the same as the subject of the main clause. The following is an example  "dangling" participle : 

Having recently observed a class of intermediate learners read a text by translating it word by word into their own language, it was clear they needed to work on reading strategies.

What is the subject of Having observed ?  Who observed the learners? Presumably the teacher who is writing. However, this subject does not occur in the main clause. To become grammatical it would need to be rewritten as : 

Having recently observed a class of intermediate learners read a text by translating it word by word into their own language, I realised that they needed to work on reading strategies.

Now the subject of the main clause I is also the subject of the participle verb in the subordinate clause and the sentence is grammatical -  the meaning being :

I recently  observed a ... I realised that...