On one end you will hear people equate math to calculating, this is almost exclusively how math is taught in school today, and on the other, people like to talk

On one end you will hear people equate math to calculating, this is almost exclusively how math is taught in school today, and on the other, people like to talk about math ideas, and how we shouldn't really teach people how to calculate anymore since we got computers for that. Like in many aspects of life, learning math is about balance. In truth, people should learn from both areas simultaneously, since they are mutually connected. Calculating is a tool that makes you a better problem solver, and being a problem solver will allow you to find new tools to calculate faster. You can't separate either discipline from one another. In my view, I think students should take one calculation, and one deeper math class a year starting in high school. That wat they could delve deeper in learning how to calculate (learning different methods for multiplication that might come in handy when doing mental math, for example), and start dealing with real, thought-heavy math from an earlier grade (learning about combinatorics, graph, game, and probability theory early in high school, etc).