Haven't and didn't

[msaeed]

Hi there,
I want to know when should we use haven't and when should we use didn't
for example what the difference between :
"I haven't done that before" and " I didn't do that before"
In addition when should we use them in the daily spoken
thanks

 

[Rover_KE]

A: Do you want to come paragliding with me?

B: Ooh, yes! I haven't done that before.

* * *

C: You got this sum wrong – you should have carried the 'one'.

D: You're right; I didn't do that before.

 

[emsr2d2]

I have a feeling that (in certain contexts) there is a BrE vs AmE difference here.

BrE
- Wow, eating lobster will be a new experience for me!
- You've never done that before?!
- No. I've never done it before.

AmE
- Wow, eating lobster will be a new experience for me!
- You never did that before?!
- No, I never did it before today.

I'm happy to be corrected if I have the AmE construction wrong, or if AmE uses both, but BrE certainly wouldn't use the latter construction.