i have always questioned this, not only is it inefficient and even confusing at times if you normally work perfectly fine in your head but often the reasoning i

i have always questioned this, not only is it inefficient and even confusing at times if you normally work perfectly fine in your head but often the reasoning is to "show youve done it correctly" which i qualm simply because it gives the idea that there is only one possible approach to something which kind of stifles peoples ability to accept that things can be done a different way just because Pythagoras came up with a way to calculate the length of a hypotenuse doesnt mean its the only way but thats what youd be led to believe and as such no one considers other methods and will probably even dismiss any alternatives without even bothering to check thats not to say that we shouldnt check that people understand how to do things but this can be achieved by posing a few questions, if the answers are consistently right then we can generally assume the method used to get there is valid (or they cheated which will be pretty evident when they attempt to apply it to a real situation) but i have a strange way of working with numbers, as long as i understand the theory my brain works more abacus like than using arabic numerals so it essentially creates an extra step in having to sort of convert the working out back into something thats writable, in my school days i found that more difficult than the problems themselves, thankfully its something i havent had to do for a great many years