I am making a calculator app that uses some new ideas for data manipulation. The details aren't important, only that the user needs to be taught new principles.
Recently, there has been some talk going around about how 'instruction screens are evil' and 'bad UX!!!' However, some of the most successful apps use it, notably Clear.
I am wondering what the community here thinks about this issue, and, more importantly, what I should do in my app.
Should I have a well-designed welcome screen, little bouncy animations, tooltip things, or a video of Martians teaching kittens how to use the app?
NOTE: The last option is not possible. I don't have the resources to make it, and no one knows what Martians look like anyway.