General Discussion
In reply to the discussion: Why Would a Math Teacher Punish a Child for Saying 5 x 3 = 15? [View all]redgreenandblue
(2,088 posts)That is what makes them useful. For an individual example there might exist a shortcut, but it is good to have
a recipe to fall back on when no such shortcut exists, or when manually looking for a shortcut is not feasible. So in short, the benefit of algorithms is, or should be, generality.
I could understand it if the teachers where trying to teach some kind of general principle here, but I don't get what is gained in terms of generality when ignoring commutativity of real numbers.
An algorithm that is as general as, but uses less steps than, another algorithm is superior.
When multiplying two real numbers, the algorithm "commute until the smallest number is to the left, then use repeated addition" seems to be superior to the algorithm "use repeated addition" for every instance of this class of problems (unless you are working on some weird computer hardware where comparison is more expensive than addition...).