The two art history texts that we recommend are both excellent in their different ways. Which one you choose to use if primarily a matter of how much emphasis you want to give art history (Janson is nearly twice the length of Gombrich and is much more densely written) and also budget (Janson is also more than double the price of Gombrich.
The Story of Art, by Ernst Gombrich
Gombrich's text is conversationally written, occasionally strongly opinionated, and although it is not aimed specifically at young people, it's certainly written for the non-specialist student. One of the most engaging things about the books is that gives the student a strong feeling for the author's love of art and opinions about art. Students who already have their own opinions about art may at times find themselves disagreeing with Gombrich, but his ideas are generally sound and presenting in a charming fashion. For those who are in danger of finding the study of art boring, Gombrich does a very good job of helping the student develop an interest, or even a love, of the subject.
Our only hesitation in making this book our only recommendation is that it is very light in coverage on the earliest parts of art history. Art before the Classical period is only very briefly presented, and even Greek and Roman art gets fairly short shrift. From the high Middle Ages on, the coverage is much better, and I would have no hesitation in using him from the Renaissance on.
The link above is to the hardcover edition, the book is massive enough that the hardcover binding is helpful for durability, and the price difference isn't great. (In addition to the full-size paperback edition there's also a "pocket" edition, which I wouldn't recommend since that significantly decreases the size at which you see the pieces of art shown in illustrations.)
Gombrich has gone through sixteen editions, so there are plenty of used copies available. However, I'd recommend buying a relatively recent edition in order to get the maximum number of full color illustrations.
Janson's History of Art by Anthony F. Janson
Janson is one of the most standard, old guard art history texts for the college level available. The current edition (the seventh) weighs in at 1200 pages and some eight pounds. Although it has become something of an institution (the project is now maintained by the son of the original Janson) Janson's History of Art does not suffer from the committee-written-paralysis disease so plentiful in modern textbooks.
In regard to the ancient period, Janson is far more complete than Gombrich. While Gombrich shows only a scattered few pieces of Egyptian and Mesopotamian art, Janson not only covers them but covers the arc of development from Sumer to Babylon and Assyria, and from the Old Kingdom to the Middle and New Kingdoms of Egypt. The Classical period is also covered in much more depth than in Gombrich.
However, Janson can frankly be far more information than the average high school student (even an exceptional reader) is interested in. This tendency only becomes more marked as it moves into the more recent periods. The writing style is also rather more dry than that of Gombrich.
As with Gombrich, try to find a fairly recent edition of Janson so as to get the most color illustrations. Older editions were illustrated strictly in black and white plates. Also, be aware that there are several alternate editions of Janson on specific subject areas or for specific levels of student.
If funds and shelf space are not a restriction, I'd suggest using Janson up through the Middle Ages and using Gombrich thereafter. However, shelling out $100+ for a pair of massive art history books may not fit in every family's budget, in which case, see if you can get a look at each book at a library or bookstore before making a decision.
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