This video takes a look at the level design of 1-1 in Super Mario Bros. and provides a good example of what you should be considering when designing "tutorial" levels. Whenever the player is introduced to a new mechanic (e.g. at the start of the game, or when they learn a new ability) you should design a tutorial into your level rather than having just a lame text box explaining what to do. Give the player room to play and experiment, give them a puzzle to solve with their new ability so you can be sure the player knows how to use their new powers before throwing a challenge at them (like what Doppleganger said about the wall jumping).