The meaning of leaving someone back [ in American English ]

I just watched a great video (a kind of short documentary) about two educators who strive to afford better education for their students in a college in Red Hook (a neighborhood in Brooklyn).
The video makers made an interview with one of the students' mothers :

The mother (crying next to her son): I've never cried like this ... I've cried like this one time ... when I had to leave him back, and I cried, I cried, I cried, that was the hardest thing in my life, to tell his teacher to leave him back ... in third grade [...] I told his teacher to leave him back, because he was struggling.

I've looked up the meaning of leaving someone back on the web but, I didn't find a relevant meaning. Here is what I think it means :

The expression, leaving someone back (in the context of the interview): is to make someone stay in their current grade even if they succeed.

• What do you guys think the meaning is? And is it common to use this "phrasal verb "?

You can find the video I saw the phrase used in here.

Solution 1:

Leave back or hold back means to make a child repeat a grade in school because of lack of academic progress, or very rarely, because of slow social and emotional development (usually in kindergarten or pre-school). Here's a transcript of an NPR show that uses the terms several times.

https://www.npr.org/2012/05/14/152683322/third-grade-a-pivotal-time-in-students-lives

The two terms are interchangeable, but hold back is far more common.
See Ngram chart below

There is great debate in the US as to whether there is any merit in doing this, with intensive summer school classes seen as a better alternative by many.