A lot of students experience math as something teachers say is process-oriented, but the students' actual experience is that it is product oriented. The concerns are, in order of importance: Am I done? Am I right? And often "am I right?" is a distant 2nd in importance. For the adults, the primary concern is "have I learned the skill?" Until the students and adults have found common ground by explicitly discussing these different lenses, everyone tends to be a little frustrated and feel like the other's behavior is inexplicable/unreasonable. The adults have to realize that the students' assumptions are reasonable, as is their approach, and, especially in middle school, students will need to feel some agency in the process of changing their approach to work. "Show your work" feels like "clean your room," unless the student feels like they are in a collaborative learning relationship with their teacher, and can understand that showing the teacher their thinking is their part of that collaboration. We adults also have to realize that the assertion that we are collaborating for the student's good is highly dubious, on the surface: we offer them more choice or less choice in any given situation, but the very fact that it is ours to offer is entirely worthy of resentment and suspicion from anyone trying to assert autonomy: they have to go to this school; they have to work with this teacher; they have to do this work... but I, this willing participant in this oppressive institutional setting, swear I'm here to help! I worry more about the students who don't push back.
if their calculations were accurate, then a "wrong" answer is actually right in two ways: their calculation skills are strong, and they are closing in on the correct procedure/understanding by filtering out what doesn't work, and (hopefully) why. For those of us who have carried the right/wrong framework into adulthood ourselves, asserting this for a student can come off as disingenuous (a deeply middle-schooler-repellent thing, and also super common and obvious to students), but we need to do the (emotional?) work to truly see that it isn't! We are not pretending a wrong answer is right! We are parsing the genuine rightness, and thereby modeling the process-oriented mode of math-learning in a genuine way.
If their calculations were inaccurate, but their conceptual understanding is strong, they are right in the most important way: they have met the primary learning goal of the lesson! Plus, congratulations: you have entered the realm of the adults! You ask what does this learning have to do with real life aka when will I ever use this? Well, accuracy is the most straight-forward and disappointingly simple problem to solve, and millions of adults' jobs depend upon their ability to be accurate in areas where they 100% understand the conceptual framework and the stakes, but a mispunched key on a calculator, typo on a spreadsheet, or ambitious use of mental-math can make them wrong in a truly consequential way. So what do we do? We use inverse operations, we re-enter the data in the opposite order, we get another set of eye-balls onto the work... And most importantly, getting back to math class, I believe, in the context of right/wrong, done/not-done, this kind of "checking your work" sounds just like "showing your work" (aka clean your room, check your email, eat your vegetables....), but in the context of "wow, you have such a great conceptual understanding on every single one of these problems, so you can tear through them at light-speed! So cool. Let's figure out how to boost the accuracy piece so you don't get fired :P" or "Man, your calculations are PERFECT! I'm so jealous! It looks like you don't know that you have to multiply by the reciprocal yet, though. But with calculation skills like that, you'll be rockin' these next time around...!" it becomes a conversation about making a good thing better.