Writing a recommendation letter for student with low GPA
When I write letters for undergrads (in math, in the U.S.), I usually aim to speak exactly and only about things I know from first-hand experience. For that matter, transcripts (whether high-GPA or low) are usually part of the application, so second-hand comments from me add little.
Now and then, I am surprised to learn that a student of whom I think quite highly has had some rough spots earlier. I can only infer that they've done a great job of turning themselves around, and I'm happy to vouch for the positive things they're doing.