> Richard, I was never taught the square root > algorithm, and I have never taught interpolation.
Interesting. I think our teacher (algebra 1, 1973-74) showed a square root algorithm to us in class, but we didn't have to learn it. We just used the tables at the back of the book. Of course, the better students (top 5% of my graduating class) knew it, as this was one of those things that all the school nerds knew (along with the then 9 planets in order from the sun, the nearest star, the fact that U-235 and not U-238 was used in atomic bombs, etc.).
On the other hand, interpolation was an instrumental part of trigonometry when I was in high school, and we covered logarithms before trigonometry so that we would know how to use the logarithm tables. As for *teaching* interpolation, I did this in the first class I ever taught entirely on my own, a trigonometry class at Indiana University in the summer of 1983. Students had calculators, and we often used them, but on the tests and quizzes I required not only hand computations for a few applied problems, but I also required that everything done on those select problems by interpolating the tables (i.e. do everything to one more decimal place "accuracy" than were the values listed in the tables). I told the students the they would still need to (at that time) interpolate tables of values that calculators didn't have. (I think I mentioned statistical tables a lot.) However, the next time I taught a trig. class, Fall 1984, I didn't teach interpolation. In fact, I've never required students to use interpolation on tests since then, but I did sometimes explain what interpolation was, as an interesting historical detour in trig. classed or as an application of linear approximation in calculus 1 classes.
Interestingly, I didn't get much, if any, protest from the 1983 trig. students, as long as I gave them plenty of time. I think many of them were simply glad to be doing something that they knew they could do, even if it was a bit tedious, than trying to figure out how to prove nasty trig. identities and stuff (which, of course, I also covered).