Today in precalculus we went over / reviewed / saw again / learned Long Division of Polynomials and Synthetic Division of Polynomials. I told the kids that I had mixed feelings about teaching the L.D. because I thought it was on its way out due to graphing calculators but I still thought it was worthwhile because it was cool and it allowed them to practice their algebra skills and solidify their knowledge of factoring.
Anyway, I mentioned that I had a friend that was about 10 years older than me (so she probably graduated high school in early 1970s), and she mentioned that she had to learn how to calculate square roots by hand, and these days we don't teach that anymore.
Another student asked, "didn't you all have to look up the sine and cosine and stuff in tables?" And that got me thinking. Yes we looked them up in tables every time we did trig, and so that visual memory was there, and we had constant reminders that you took sines of angles and the result was a number and all those numbers seemed to be between -1 and 1. (now I don't remember if it was between 0 and 1, and we had to think or not).
I seem to have too many instances now where in a situation, students don't intuitively know in sin x = y which is the angle and which is the number/ratio of sides. It seems like maybe we've/they've lost something from not having that table to help.