Thank you for your response.
I tried a soft boot before I posted this problem. It did not help.
Let me explain further. If I am trying to correct some text I am typing that is near the bottom of a page, the text is covered by the keyboard. I can dock the keyboard and see what was typed, but when I try to place the cursor in a certain location to correct a typo, the keyboard pops up as soon as I touch the screen. It covers the text, making it impossible for me to see where the cursor is or to adjust the location of the cursor.
In the past (before upgrading to iOS 8.3), the keyboard would push the text up to the top half of the screen, so I could always see what I was typing, and correct it if necessary.
Also, I tried your technique of moving the keyboard, but I couldn't make that work. If I tap the keyboard button, the keyboard docks. If I tap an hold the button, I get a drop down list to Dock or Split. I couldn't find a way to drag the keyboard.