We all learn to walk before we jump and not the reverse eh? What your mother said is correct.
I put my girl in a walker when she was able to support her neck *(around 5 months old) but each time not more than an hour. When she starts to cruise around the apartment, I make sure that she does not bend her legs (if she does I will adjust the height of the walker).
My girl enjoys walking (as I barely carry her) . She is now 19 months old and she has no problem walking up and down our 3-storey house daily with confidence.
I have never used a jumper because I dont't see how it would help her as oppose to a walker.