It’s worth noting that there are always the fears of losing touch with the details of stuff that some along with various advances. The same thing was the case w

It’s worth noting that there are always the fears of losing touch with the details of stuff that some along with various advances. The same thing was the case when I was in junior high with calculators, “how will you add and multiply if your batteries run out?” but the fact of the matter is, not having to be able to make your own push button switch freed people to advance to other topics. Similarly, in mathematics education, when I was in high school, there were classes entitled College Algebra and College Trigonometry¹ which had the implicit message that these were materials traditionally taught in college² and not in the third year of high school. On the other hand, things like calculating square roots by hand are no longer part of the curriculum, although they may still be taught on occasion by the rare teacher who has those skills as an enrichment topic to fill some class time or as part of the math club’s after-school explorations. We may be filled with nostalgia for our own learning and think that it’s the only way to learn, but as time goes on, some skills just become less important. ⸻ 1. The backs of the textbooks included printed tables for log (both base 10 and ln), sin, cos, tan, cot, sec and csc, with the latter six tables to three thanks to the fact that sinθ=cos(θ-π/2).³ 2. The disjunction between practice and theory has led to this sequence being renamed precalculus in most (if not all) high schools now. 3. The skills to make those tables in the first place are yet another thing that we no longer dedicate long classroom hours to, although Charles Babbage would have thought that being unable to verify the accuracy of your tables was a sign of intellectual weakness.