|This novel for middle school aged children seems at first rather similar to the Phantom Tollbooth, which was apparently a source of inspiration for its author. The plot is familiar: a boy and girl travel to a mystical land where they learn important truths that eluded them in the real world. However, the mathematics it contains is a bit deeper than usual, with references to such interesting mathematical concepts as the density of the rational numbers in the reals and geometric transformations of the Cartesian plane as well as more subtle references to mathematical history (such as the famous number 1729).
Some sample chapters can be downloaded from the official website at www.lostinlexicon.com, but apart from a brief mention of "the origin" as being "(zero, zero)" these free pages focus only on the linguistic aspects of the book and do not reflect the mathematical content which becomes significant later.
Using geographical directions in a ratio, north/south : east/west is a practical and understandable way in which middle school students can develop the concept of slope of a line. Embedding these references in literature in a way in which children can relate is makes so much more sense than simply telling them that slope is rise over run.
I also appreciated the way in which Daphne works through the math that she thought was too challenging for her. It is so important that girls realize they can be good at both math and literature.
I thoroughly enjoyed reading Lost in Lexicon and plan to use it in my middle school classroom. The author has done a wonderful job writing a book which can be utilized as part of a shared ccurriculum between math and language arts. It is also a fine casual read, with excellent role models for both girls and boys. I'm working my way through a list of math fiction books, and this is the most enjoyable book I've read thus far!
September 2012 Update: A review this month in Teaching Children Mathematics Magazine says "Noyce’s imaginative, playful use of words and numbers keeps readers engaged throughout the story." Also, the sequel The Ice Castle, which focuses mostly on music but does involve a little bit of math, is now available.