I hope to raise questions here for you to ponder as you integrate TDD into your own practice. Some of the questions are small, and some are large. Sometimes the answers are here, or at least hinted at here, and sometimes the questions are left for you to explore.
There are really two questions lurking here:
How much ground should each test cover?
How many intermediate stages should you go through as you refactor?
You could write the tests so they each encouraged the addition of a single line of logic and a handful of refactorings. You could write the tests so they each encouraged the addition of hundreds of lines of logic and hours of refactoring. Which should you do?
Part of the answer ...