Mac – Any way to fix screen’s mishandling of line wrap? (Maybe only Terminal.app)

I'm having an issue using screen and Terminal.app. If I get a bash prompt at the bottom of the screen and I keep typing until the line wraps to the next line, I see the next line, but I do not see the line above this one change.

Here's a visual way of illustrating my problem. The | represents the right hand side of the terminal.

Before. My cursor is after the third 'example' and I'm about to type 'example' a forth time:

$ asdf                        |
bash: asdf: command not found |
$ example example example     |

After. Note how after wrapping, the screen did not scroll, but instead 'ate' the line I was on and began fresh:

$ asdf                        |
bash: asdf: command not found |
ple                           |

What I expected (and what happens without the use of screen) is that the entire screen scrolls down one after the wrap.

bash: asdf: command not found |
$ example example example exam|
ple                           |

Finally, this what happens if I move the cursor on the wrapped line to the beginning of the command line, it eats the previous line:

$ asdf                        |
$ example example example exam|
ple                           |

Any idea what is going on?