If the teacher feels that she has no control on how the standardized test will be graded, isn’t she better off marking the answer wrong, and then telling the student, “yes, I see exactly what you’re doing,and I have nothing against it, but the fact of the matter is you have to take a test where we don’t make the rules, so that’s why you need to change…”
Off-topic, but during the Jurassic era when I grew up, sans calculators (log tables and slide rules only), we often needed to do things like 2 digit times 2- or 3-digit multiplications, such 75 * 18 or 63 19 and we spent a lot of time working out techniques of doing them in our heads, or with minimal writing. eg. a slightly more complicated version of 53 like 5 * 358 may have been done in our heads as 10* 358/2 or perhaps 10 * (350/2 + 8/2) or 10 * (360/2 - 2/2) - If you checked with ten of us in class, the problem would have been done in a half dozen ways.
It’s funny how different the effects of technology have been, even among my own kids - one of them used it as a tool to get more time to attack more complex problems than trying to outdo a calculator, while for the others, the calculator just gave them a way out and didn’t bother use the advantage elsewhere…