Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doi

Real understanding of concepts has been replaced with step by step methods that allow you to arrive at a solution without needing to understand what you are doing. This is exactly what happens with multiplication (and simplify fractions and taking derivatives). That’s been exactly my claim all along. Virtually no 16 year olds know why the procedure they were taught to multiply 123 x 456 produces the correct answer. Not today, not 20 years ago, not 50 years ago. They know how to execute the algorithm. That’s it.