This free app lets you create notebooks that incorporate audio, drawings, type, and images.Its goal is to mimic a paper desk and become a notebook replacement.
This note taking app includes multiple pen and highlighter tools and functions much like a paper notebook. For $5.99, it offers a lot of organizational and editing tools. Additionally, Noteshelf exports notes as PDF or image files to either Evernote or Dropbox.
This free app creates a private diary that stays completely on iPad. For elementary students without the ability to create accounts, this could be a good solution. Notes can be exported via email.