Says the Oxford English Dictionary:

Serendipity

[f. Serendip, a former name for Ceylon + ITY

A word coined by Horace Walpole, who says (Let. to Mann, of Jan 1754) that he had formed it upon the title of the fairy-tale 'The Three Princes of Serendip', the heroes of which 'were always making discoveries, by accidents and sagacity, of things they were not in quest of'.]

The faculty of making happy and unexpected discoveries by accident

...1880 E. SOLLY Index Titles of Honour Pref. 5 The inquirer was at fault and it was not until some weeks later, when by the aid of Serendipity, as Horace Walpole called it --that is, by looking for one thing and finding another-- that the explanation was accidentally found.

Once one has a name for something it's easier to recognize it the next time that something manifests itself. Chance is everywhere, and puts new opportunities in our paths seemingly at random. In such an environment it seems obvious that a teacher should encourage students to seek and welcome the unexpected, and to think of learning as an adventure instead of a well-trodden path. The novice is often dazzled by novelties; the connoisseur of serendipity often asks "why am I not surprised?"

addendum, 8 February 2004
I wish I could remember exactly how I stumbled upon it, but about 10 days ago I discovered that The Travels and Adventures of Serendipity : A Study in Historical Semantics and the Sociology of Science (by Robert K. Merton and Elinor G. Barber) had just been published, so I ordered it and have been enjoying it in little bits. This morning I asked Google about it, and harvested a bunch of links:

Princeton University Press page

A scholar's serendipity By Christopher Shea, 2/1/2004 boston.com

THREE PRINCIPLES OF SERENDIP: INSIGHT, CHANCE, AND DISCOVERY IN QUALITATIVE RESEARCH Gary Fine & James Deegan

An Eye for Patterns in the Social Fabric By PATRICIA COHEN New York Times Oct 31 1998

Serendipity has functioned as a silent partner in his life in other ways as well. "My life of learning has been largely shaped by a long series of chance encounters and consequential choices," he has written. Even the name "Robert K. Merton" was something of an accident. Born above his father's milk-butter-and-egg shop on Philadelphia's rundown south side, this son of Jewish immigrants was named Meyer R. Schkolnick. He aspired to be a made-in-America magician, and so, in the style of that generation of assimilating immigrants, called himself Robert K. Merlin at the age of 14.

But his next-door neighbor and future brother-in-law, Charles Hopkins, advised him to consider something a bit less hackneyed; the "l" transmuted into a "t".

Wikipedia entry for 'serendipity'

one to find: Barber, Bernard and Renée C. Fox, 1958. "The Case of the Floppy-Eared Rabbits: An Instance of Serendipity Gained and Serendipity Lost," American Journal of Sociology 64: 128-136.

A chase through various JSTOR categories finds quite a few instances of 'serendipity', the oldest in a 1939 mention in Science that

Dr. Walter B. Cannon, George Higginson professor of physiology at Harvard University and president of the AAAS, spoke on "Serendipity" or "An Accidental Sagacity" at the secoond annual meeting of the Wellesley chapter of Sigma Xi on April 28.
A year later Cannon published "The Role of Chance in Discovery" in The Scientific Monthly, beginning it with the Walpole story. It would be fun to trace the linkages among subsequent users of the word...

I looked into my own uses of 'serendipity' on Web pages from oook.info