I am a math person. I went school for engineering and computers. A Great deal of mind math is don’t because a person is both intelligent and lazy. As noted in the story above the writer basically to lazy to grab tool to solve the problem and so they discovered a simplification to fix the problem.
Not everyone will be able to do that. Most people won’t even care to. I don’t think it matters how they are taught or how much they understand the process, they will walk out to the car, and grab a pencil and paper to write down the problem and solve it. That or they just find their phone and ask google.
Making math more difficult for parents, teachers and students is not the answer. I don’t know if there is an answer.