The teacher criticized him in front of the whole class, trying to shame him into correcting his mistake.

shame 是名词，意思是"羞耻、羞愧"，在这里用作动词，表示"使某人感到羞耻"。 shame into doing something 这个短语表示"通过让某人感到羞耻来促使他们做某事"，即"用羞辱的方式迫使某人改正或做某事"。