Dreams are of course a very important element of this play, which examines the realities of growing up in a single parent household. However, as this question indicates, there are clearly two types of dreams that are presented: those which are impossible and already lost, and those which are potentially realisable. The latter are of course represented in the character of Tillie and her desire to better herself, which is sparked by her love of science and the experiment she undertakes for the science fair. Note how Tillie herself is presented in the stage directions:
In the midst of chaos, Tillie struggles to keep her focus and dreams alive. Tillie--keeper of rabbits, dreamer of atoms, true believer in life, hope, and the effect of gamma rays on man-in-the-moon marigolds.
Tillie is therefore presented at the beginning of this play as a character who has to strugge to keep her dreams alive in an atmosphere and setting that threatens to destroy them. Those "shattered dreams" are of course represented by Tillie's sister, Ruth, and their mother, Beatrice, who both express the dreams that they have missed out on or still yearn for, but have very little hope of achieving. Ruth's dreams, for example, can be differentiated from Tillie's dreams, through the way that she has so many different dreams: she variously expresses the wish to be a dancer and opening a tea shop. Tillie however remains focused and concentrated on her dreams, which is one of the differences between these two characters and their hopes of achieving their dreams.