>Does this mean that the student must be able to find the sine of 30 >degrees without anything but pencil and paper before being allowed to >use a technical aid (even a table)?
My daughter came to me with help on trig (she's in IMP) and I was unpleasantly surprised to find thet they didn't have any trig tables. In working with her on some problems I used tables, and let her verify with the calculator.
I DO believe that there is more learning with use of tables than with the calculator, because she got to see the numbers in the context of other sines. How else does she get reinforcement on what reasonable values for the sine of a particular angle are. or begin to understand that small changes in angle lead to small (but not proportionate) changes in sine? I'm sure that the teacher covered or will cover all of this, and will do it well, but since my daughter didn't grasp that topic too well, the reinforcement was useful.
Similarly, I would really like to make her plot (by hand, on graph paper) a few sine curves. I don't believe that seeing the curves on a graphing calculator can possibly teach as well as doing them by hand, and having to THINK about what value to plot at 45 degrees, or where the curve of sin 2x touches the x axis.
Sure, use the calculators for calculating, but I think only very few students are likely to sit with them and experiment for long enough to gain the same understanding that's to be had from even a small visit to the trig tables.