>Different textbooks and different teachers all have their own way of >presenting the subject. The _Mathematics Teacher_ often has articles >describing a nifty ways of presenting various topics. Lots of these >methods seem like they *ought* to work. How do I choose one method >over another?
The approach that you like the best is likely to work well, even if the research says otherwise. Teaching is more an art than a science, and the teacher's understanding and enthusiasm is likely to be the most important variable.
Research is still important, but not for your particular question. Try things out, learn new techniques, try those out, learn from your experience, and gradually you will become a better and better teacher.
Connect with good teachers and ask for their opinions. Those will differ, but you will need to make them your own anyway.