I don't necessarily know what book he's referring to, but the book that taught
me solid state was Ashcroft and Mermin.
That's a book that deliberately starts out with the silliest possible model and then gradually introduces more and more sophisticated models until the book runs out of pages or your head explodes, whichever comes first. ;)
An important insight, however, is that the simple models are incredibly useful. When I was a teenager I used to fret that the teachers were showing me the simple models first because they were fools, or because they thought we were fools. But it turns out that they are doing so to call attention to certain important general features without distracting you with irrelevant detail.
My favorite class in all of science was Roald Hoffman's chemistry class, the highest numbered class in the Cornell chemistry department, a class which represented the point where chemistry and physics merge to become the same subject. And Hoffman deliberately used a relatively simple model of molecule-molecule interactions in a solid, the Hückel model:
http://en.wikipedia.org/wiki/Hückel_method
Moreover, Hoffman would communicate in pictures as much as in math.