When I started high school in Canada, my math grades were pretty bad. Probably in the 60%s (a C letter grade). I remember staring at a quadratic equation, struggling to understand why those 3 terms drew a curve. I had no intuition for it. The summer before 11th grade, my father decided he had enough. It was time to learn math, Soviet style. He sat me down for a few hours each morning with problems from 6th and 7th gr…
I doubt the calculators were the problem. People going through the "AP class" route with calculators finish up all of the math (and more!) that gets covered in a french high school math class (from experience of moving to France in High School and learning zilch for 3 years). Totally on point about the "analyticial and quantitative lenses". Multiple-choice questions and lack of "real" questions really hobble a lot of…
The way I see it, learning to do basic math in your head is just as important if not more important then learning a procedure via a calculator. A calculator doesn't teach you anything, it just teaches you how to use a calculator.