While that may be true, I consider it to be a lousy way of teaching and an even worse measure of mathematical competence, regardless of age. I was fairly adept

While that may be true, I consider it to be a lousy way of teaching and an even worse measure of mathematical competence, regardless of age. I was fairly adept at math in fourth and fifth grade—well ahead of my peers. While I didn’t know terms like NP-Complete and NP-Hard, I would have immediately recognized that such a problem didn’t have a straightforward, timely solution for someone doing it by hand. I would have considered it a trap—in the sense that it’s a time sink—and moved onto the next problem. If it later turned out that the solution to the problem required that I not actually understand it (from my perspective at the time), I would grow frustrated. I was the sort of asshole fifth grader who would not hesitate to chastise a teacher for giving us what I believed to be unrealistic, dumbed-down math problems. When in life am I going to encounter a knapsack problem that just happens to be quickly solvable that way? The chances of that are slim; the technique I’ve now learned has no application in the real world. Take factoring, for example. I would regularly get frustrated with factoring assignments: how do you expect me to factor a collection of polynomials on a timed test if you cannot describe a deterministic algorithm for doing so? “If you’re having trouble, stay after school and I’ll help you.” After school, the teacher would helpfully demonstrate factoring several polynomials. I’d ask how the teacher knew how to guess the particular numbers they chose. What if the polynomial can’t be factored, and I waste time trying to find a solution? What if the numbers are large? The teacher would inevitably grow frustrated: “I won’t give you problems like that. Stop worrying about it.” I’ll be the first to point out that I was never particularly nice to teachers who my judgmental 12-year-old brain considered incompetent, but I have little sympathy for this particular scenario. I wanted to understand the problems; I didn’t want canned solutions. My teachers knew I was perfectly capable of factoring the numbers with which we were presented, so they would get frustrated: why is an intelligent student stuck on a problem they’ve already solved? Eventually, I found a book on prime numbers at a used book store and got the answers I needed.