[General] Linking new topic to old topic and go back to earlier point in conversation.

[arjitsharma]

I watched these sentences on youtube. A teacher writes these on the white board with no article.
Speaking of= Linking new topic to old topic.
As I was saying= Go back to earlier point in conversation.

But, when the teacher says these sentences. She adds the articles like in the following:
Linking a new topic to an old topic.
Go back to an earlier point in the conversation.

I don't understand it. Kindly explain the logic.

 

[Tdol]

The use of = shows that the teacher is putting notes on the board. They use the full grammatically correct version when talking. We talk faster than we write, and things like articles slow teachers down, so many use notes, which contain the key points.