First of all, this is my first year doing any type of serious gardening.
That said:

I was cutting the tops off strawberries this morning while thinking about
something I heard on a gardening show that plays on the radio here. A
lady called in, said she cut up banana peels into dime-sized pieces,
worked them into the soil around her roses, and the rose bushes took off
and made roses like crazy. So my question is: why can't I just take the
fresh strawberry scraps, chop them up a bit, then sprinkle them around the
tomatoes, the bell peppers, corn, and whatever else I have growing out
there? I'm not trying to re-invent the wheel here. I know why people
compost in a pile, but it seems like a lot of the nutrients from
composting would also wash directly into the soil where the compost pile
is located. Why not put a few things directly in the garden so the
growing plants get more of the nutrients?

Damaeus