There are very few times throughout the year where an entire department from the whole school district are able to get together. Yes, we are able to collaborate with out team at the school we teach at, but that can only get us so far. Having the ability to collaborate with the entire district department through a Wiki would be very beneficial. Departments could discuss new ideas they have, assessments they have used, or things they are struggling with and they need advice. Being able to have the entire district team collaborating on certain topics rather than just your home team of 4 people, would really help in problem solving.
The other way that Wiki would be beneficial in education would be for students. They could use it in any different ways. If they are doing a project outside of school, everyone gets busy and it's hard to actually come up with a time to meet and complete the project. Using Wiki helps solve that problem, all participants are able to contribute at their own time and throughout the day or weekend. Another way that students could use a Wiki is for homework or study help/questions. I'm sure there are many times when they have a question but do not know who to turn to, if the class had a private Wiki board then they could post their question for all classmates and the teacher to see.
These are two different ways that Wiki could be used in education. Although I am sure people have thought of many other ways too!