"Teacher, I don't know this character."
I think 认识 (renshi) is more like "I don't recognize", but I might be wrong.
In the sense of "be familiar with", but we often use "know" for this same meaning.
I was initially wondering about this too, but I believe it's because the to know of 认识 can mean being familiar with something, whereas 知道 can mean be aware of something or understanding of a general topic. Therefore, in this case 认识 works better for this sentence, and the sentence could also be read as I am not familiar with this character
Happy that 个 is a suitable measure word here.
But wondering if there’s another measure word for 字 that might come up?