I have a cart of iPads in my classroom for student use, so I'm very interested in STEM-related iPad apps!
According to Sylvia Martinez and Gary Stager in "Invent to Learn," "Three categories of [school computer] usage were outlined in Robert Taylor’s seminal book on the subject, The Computer in School: Tutor, Tool, Tutee (Taylor, 1980)." The first two computer uses predominate in schools. To use a computer as a "tutee," however, students must PROGRAM or CODE the computer. While Scratch software (free) is my favorite programming environment to use with students, Scratch still relies on Adobe Flash so it doesn't function completely on iOS devices like iPads. The following apps are designed specifically for coding on iPads.
This amazing interview (7 min, 39 sec) with Paige, a 4th grader, highlights the ways students can develop computational thinking and other digital literacy skills by using Hopscotch. An alternate version of this video, including just the first 90 seconds, is also available.
Scratch software doesn't work perfectly on iPads using the following browsers, but it does work more (at present) in these browsers than it does using the default Safari web browser.
The photo collage used as the header for this page is a collection of referenced iPad coding app icons.