Linear Algebra and Advanced Calculus course; Recommendation letter by a professor

I write a recommendation letter for a student, but there are 2 sentences that I am not sure about. I think they are not written well.

Please help me to improve the expression.

1. Mr. Dan joined a research group that I also belonged to.
Explanation: Mr. Dan join a research group led by another professor, I am also in this group.

2. As his professor in my Linear Algebra and Advanced Calculus course, I have had the chance to observe his outstanding characteristics.
Explanation: I taught this student two courses. The main problem of the sentence is about the first half. If there is only one course, writing in this way is ok. But in the case of 2 courses, I think it's not written well. Please help me revise the expression

Thank you!

Hello Sir,
I hope this will help you...


Mr. Dan joined a research group lead by one of my mates and I was also a part of that team.
or
I have been involved in a research group which was joined by Mr. DAN.
or
Mr. DAN joined a research group, of which I was also a team member.


I have taught him few core mathematical courses like Linear Algebra, Advanced Calculus etc. I am sure, I am eligible to judge his characteristics as I could observe his outstanding behavior in my classes throughout semester.

This is my suggestion, they might not be as per your requirement, but I am happy to help you.
Yet I request you to wait for seniors to response. I am not from a literature background, so please wait for others to comment.

Regards,

... Sure.... this is my help;


Mr Dan was a team member in one of the research projects that I too had been involved with.


I was very impressed by his outstanding skills while he was a student in my Linear Algebra and Advanced Calculus classes.

Thank you for your help!

But I think the second sentence is a little not precise. I would greatly appreciate it if you can help me with that.


In fact, it is a research group, not a research project. I'm major in physics. A professor leads a group with many associative professors and graduates to do some research in the same area. The associative professor writing this letter is also a member of the group.

And Mr. Dan joined the group this term. So I think it is better to use "join" than "be a member in".

Thank you!