Dolores starts drawing at an early age, first with Crayola crayons (1.21), but life moves too fast for her to really practice her artistic talents. When she's going through her hippy-dippy rebirthing process with Dr. Shaw, he buys her a present on her "tenth" birthday: an Etch-a-Sketch. She can't put it down (even though she's actually in her twenties). He "noted that the Etch-a-Sketch screen looked suspiciously like a television set" (18.17), but this is a TV that she can control. It's her creative outlet—it doesn't control her.
The Etch-a-Sketch, then, represents Dolores taking charge. She receives as it as part of her work on becoming more fully—and happily—herself, and with it, she stops bottling everything up and starts letting her interior world shine, if only on an erasable screen. Instead of representing childhood, then, the Etch-a-Sketch represents Dolores finally emerging from a protracted childhood.
With her psychic, Dolores Etch-a-Sketches a picture of Thayer as her future husband and, sure enough, it comes true. The craziest part of this whole story is that she tells him she etch-a-sketched him. It's a startling moment of honesty for Dolores, confessing to something that might actually earn her a raised eyebrow in response—but forging ahead anyway and being true to herself.