What is the difference between Symbolism and Abstract thinking in Piaget's Theory? I'm having trouble understanding the difference between symbols and abstract thinking in Piaget's Cognitive Development Theory. Piaget says that in the preoperational stage, children 2-7 years old can think of things in terms of symbols, and that abstract thinking forms in the formal operational stage. I thought symbols are a part of abstract thinking, perhaps because symbols, to me, seem abstract. So, what does the theory mean when it refers to "abstract thinking?" Can someone give me a concrete example delineating the difference between the abstract thinking and symbolism parts in their respective stages? Much thanks!
Symbolism uses a symbol to represent an existing object, while abstract thinking can be thought of as considering things that don't actually exist. 

For a rough example of each, consider representation as symbolism (this paper is the plane I'm on) and consider generalization as abstraction (what it means to be "on" something). For another, consider something (this blue line on a paper) that represents something else (this river), contrasted with considering the concepts of "blue" or "line".