There is more than meets the eye when it comes to 'thinking with a pencil.' Adults who problem solve on a regular basis as part of their work often prefer to write notes or draw when brainstorming or drafting ideas. Pencil work often includes vague sketches, symbols, keywords, and descriptions of movement.
The sketches below are from Alexander Graham Bell's model for a telephone. Below it, Feynman's stamp with his very spare doodles of electrons repulsing each other.
Some of the processes appear to working memory (just getting all the ideas down on paper)-related, while other seem to be searching for salient features or connections, whether perceptual (for instance visual or spatial features), or conceptual. Some technical tools like the graphics pad described below in 'Sketching Interfaces' seem like they are valuable for storing trains of visual associations (artists at Pixar have these). Because drawn ideas are not necessarily verbal, they can be more difficult to recollect. Interestingly, mathematics also benefits by some pencil work - something for which keyboarding may not easily substitute.
The picture below is from an excellent Oxford study of the processes involved with sketching a human subject. By infrared and EMG monitoring of eye and hand movements, researchers found a complex and almost continuous feedback cycle between observation and sketching. During a 12 minute drawing, the artist fixated on his subject 150 times, and alternating movements of the hand and eye were seen to occur in clusters of 10-20.
The Sketch in the Industrial Design Process
Dr. Feynman's Doodles:Science News
fMRI of Artist Sketching
Geometer's Sketchpad in Math
Drawing as a Means to Design Reasoning
Computer algebra & paper-and-pencil