I disagree that you have to get them young... but I do think that math classes need to start involving proof-based work rather than calculation-based work by th

I disagree that you have to get them young... but I do think that math classes need to start involving proof-based work rather than calculation-based work by the time students hit middle school because it's such an explicit exercise of critical thinking muscles. Recalling my own experiences with middle school and high school, I saw my peers frequently fall into the trap of trying to memorize pipelines of steps while we were learning algebra, geometry, trig, pre-calc, and then calculus. The ones who "didn't get it" would fall apart to varying degrees when confronted with problems where you had to think in terms of combining toolboxes of strategies to unfamiliar but analogous patterns, but I don't necessarily think it was their fault, because they didn't know better and rote memorization had worked consistently until this point. I often feel a bit sad about it because I did a ton of proof based stuff outside of class (as a mathlete), and that was a HUGE part of my development in logical reasoning, intellectual rigor, and critical thinking.