> Kids are taught to memorize and often by teachers (esp in grade school) who don't understand the math.
On the flip side, if you don't know e.g. your times tables by heart, you are in for a shitton of trouble when it comes to doing the higher level stuff. The best way to achieve the arithmetical competence it takes to successfully do math at secondary levels and above is drilling. Educational history is littered with the wreckage of alternative attempts: New Math, some of the approaches derided as "Common Core", etc.
On the flip side, if you don't know e.g. your times tables by heart, you are in for a shitton of trouble when it comes to doing the higher level stuff. The best way to achieve the arithmetical competence it takes to successfully do math at secondary levels and above is drilling. Educational history is littered with the wreckage of alternative attempts: New Math, some of the approaches derided as "Common Core", etc.