"[D]iscover algorithms for yourself" -- The Little Schemer (mentioned recently by shokwave) is this, but for things defined in terms of themselves (i.e., recursive data structures and recursive functions). It is a programmed text, which means you read it with a card in your hand covering up part of the page. The book asks a question, then you come up with an answer, then you move the card and check your answer. The authors play around with this format a bit, sometimes asking you questions that you have to make an educated guess at, or asking you questions that you have to think about long enough to realize that you don't yet know how to answer them.

From the preface:

What You Need to Know to Read This Book

The reader must be comfortable reading English, recognizing numbers, and counting.

The notational system the book uses is (a small but powerful subset of) the Lisp dialect Scheme. In the opening pages, you learn what atoms and lists are. By page 21 you have seen how to write a recursive function that tells you whether every item in a list is an atom. Later you write recursive functions on lists of lists (i.e., tree structures) and define Peano arithmetic, and by the end of the book you have written a Scheme interpreter (a function that can evaluate any other function).

Recursive functions were mind-benders to me at first. Now, thanks to The Little Schemer, I eat them for breakfast.

To check your understanding, you can type this stuff into a Scheme interpreter (or a Lisp one -- the book has footnotes showing what you'll need to change), but it's possible to go through it with nothing but a pencil and paper. (I went through most of it just typing my answers into a text editor.)

The authors have honed the book (through several editions) with actual students, and it shows. Several times while reading it I thought, "Why are they asking me this again?", then it turned out the question they were asking required me to make a conceptual leap not required by the similar question from a previous page.

Disclosure: I have not yet gone through the last couple chapters frame by frame. (Edit: I finally got back to the book and finished it in June 2013.) (I have, however, written a Lisp interpreter [with lexical scope, the scoping style used by Scheme and other modern Lisps].)

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