Passive voice use

Tony asked about the comma, so....

Yes. the comma is required before "which" when "which" is used to introduce a restrictive clause.

The general rule is "that" is used to introduce non-restrictive clauses, and no comma is required. "Which" requires a comma to introduce a restrictive clause.

Restrictive clauses limit the possible meaning of a preceding subject. Nonrestrictive clauses tell you something about a preceding subject, but they do not limit, or restrict, the meaning of that subject.

When Tony dropped the "which", he eliminated the need for the comma. But ... what Tony created is ALMOST a sentence with a compound predicate. In Tony's sample, replace the comma after "progressed" and replace it with "and is".

"Since the beginning of the term, his confidence has grown as the lessons progressed and is reflected by his ability to work more independently."

Unfortunately, while now propoerly punctuated, the second predicate clause remains passive. This can be solved by reversing the order of the clauses:

"Reflected in his alibility to work independently, his confidence has grown since the beginning of the term and as the lessons progressed." 

Ideally, restrictive and non-restrictive clauses should be located close to the subject. In the original sentence above, the clause is greatly separated and makes the construction awkward.

The only thing I see is a missing comma after 'progressed'...and I don't think that it is REQUIRED, just a stylistic choice. There are a few words I would remove, but even those are not incorrect, just a difference between your style and mine (I think). I do not see this as passive voice.

Since the beginning of the term, his confidence has grown as the lessons progressed, reflected by his ability to work more independently.

What you could do is make the dependent clause the subject of the sentence:

"Since the beginning of the term, his ability to work more independently reflects the growth of his confidence during the course of his lessons."

However, Grammarly wrongly thinks there is a missing comma and sentence fragments.  You could make "term" possessive - "Since the term's beginning, his..."  Plus maybe we can make this less awkward:

"Since the term's beginning, his ability to work more independently reflects how his confidence improved during the course of his lessons."