I suspect that your accessibility features have been activated. The iPad is reading to you everything that is on the screen while simultaneously trying to interpret the taps/touches you enter on the screen. Leave it alone (don't touch the screen) until it stops reading.
Tap "Settings" to highliight the icon. Tap again to enter settings.
Tap "General" to highlight it. Tap again to enter "general."
Use the same techniques to enter accessibility.
If at any time you need to scroll, use three fingers.
Make sure the following items are toggled "off." voiceover, zoom, speak selection Speak auto-text.
Thanks for responding. I did as you suggested, but all the items were already off. The problem now is that it doesn't do this random jumping all the time. I drove to the Apple Store to get help. In the parking lot, it was still jumping around. I walked into the store, and it would not do it! I tried for ten minutes to get it to start jumping, but no success. I went back home, and later that night it started again! I'm very frustrated. Guess I will continue to try to demonstrate it at the Apple Store.