Just an interesting bit of theory that might help some of you out there who dont like it when the kids leave stuff in the trash.
Developmentally, the young student finds the process more important than the product. Children rarely admire or contemplate their finished work, though they may request others to acknowledge it. Young children even draw on top of previous drawings, indicating they lack the sense of the communicative or display value of a picture.
I think this idea of process being more important than the product is carried out sometimes through middle and high school student artists. And, there are many teachers who find the product is only a result and is not important either. I find this in my teaching many times too. After all it is an adult idea of saving, admiring and hanging artwork for arts sake. And your students are not adults.
Although the developmental aspect carries tremendous weight. I think it is our job to show the child the importance in reflection, and pride in their artwork. It is our job to lead the child to a state of "artfullness". I am not saying just let the child throw it out because of their developmental state. But I am saying, I hope you don't always find it disheartening.