Database programming design question

Hello there,

i'm working on a programming framework for a pretty large database application. One of the issues i've encountered is the usage of database connections throughout the the application.

I want to keep down the number of connections and i want to keep up the performance as much as possible.

Would the following idea be suitable:

Create a connection class;
At the start of the program create an instance of the connection object;
As i  dynamically create userobjects (forms and what not) where needed, i give a reference to the connection object as a constructor parameter of such an object.
Use the connexion where needed in methods contained in my user objects.

Thanks for the advice!