Translation:Teacher, I don't know this character.
Yes 知道 works. But 认识 is better because 认识 means to be familiar with. That's why we use it when we talk about people. 我认识他 technically means "I am familiar with him (recognize him from a previous encounter)". 我认识这个字 means "I am familiar with this character" or “I have encountered this character before”.
To my knowledge, in some Western culture people call their teachers "Sir" or "Mr. /Ms. /Mrs. Smith" This is not used in our culture, we almost always call them "老师" or "教授"(professor). Addressing your teachers/professors with their name, even "林先生"(Mr. Lin) may be considered impolite by some people.
http://grammarist.com/spelling/recognize-vs-recognise/ British English lists an alternate spelling as recognise, but the main entry is recognize. North Americans (yes, that includes Canada) prefer the ize spelling, and this is accepted everywhere. However, outside North America some prefer the ise spelling and it is not incorrect. This spelling change goes across all derivatives including: recognizability, recognisability, recognizable, recognisable, recognizeably, recognisably, recognizer, and recogniser.
The ize/ise change is based in English being influenced by French, and every other language. The Greek words changed to Latin, which used a z, but the French spelled it with an s. Purists in England promote the original ize while others stick with convention, ise.
There was a neat article in The Economist about this just a couple of weeks ago: British English used to recognize (heh...) BOTH spellings as correct until roughly the advent of spellcheck in word processors. The American word processors could just correct "-ise" to "-ize", and Bob's your uncle. The British ones had to pick a single spelling or risk passing a document that used "-ise" in one place and "-ize" in another, so word processor publishers standardized (heh, heh) to "-ise" only.