Teacher: Not THAT way, you heretic! The wAy I sHowEd YoU.
Creative:
Creative’s Parents:
The Principal: Do the math the way the teacher tells you, mkay?
Creative: *hates math forever*
In most cases that's not being "creative" it's being wrong. Getting the right answer the wrong way is bad in math because math requires repeatability. Chances are the child who thinks their incorrect way of getting an answer isn't the next noble prize winning mathematician and is just someone that ignored the correct formula and happened upon the correct answer by accident in a fluke
Yes. There’s another component too. “Showing your work” is a way to prove to the teacher that you understand the process. The next process and the next into higher mathematics will be based on understanding the processes along the way. What’s more- without showing your work- how can the teacher know you did it in your head or you somehow cheated? When you get into a field like engineering you can start to see the kids who don’t understand what they are doing but know how to get an answer because you tell them to solve a real world problem with math and even if the numbers they plug in are right- the results are wrong. They use wrong operations or apply the wrong formulas to solve the actual problem.
But what’s more- your teacher probably isn’t a Nobel mathematician- and if they are your next one likely won’t and so on. Chances are your teacher, who has 30,40,300, etc. papers to grade either only themselves know one way to do it- or are most comfortable that way. They want to see it a certain way because that way THEY can understand your answer. That way the next teacher they hand you off to can understand. Usually they’ll be using compatible curriculums, the next teacher will base what they teach on what they expect that you learned. So if you’re allowed to go “free form” in responses and as the math evolves your methods get further and further from those in the curriculum- each teacher after will likely have a harder and harder time understanding, teaching, correcting.
Thankfully most mathematical geniuses tell their own teachers to go fuck themselves and wind up changing everything \>_>/. If you are over 28 and have not fucked over your mathematical professor you never will. Do it by the fucking book.
I used to HATE showing my work. I had a very “me centric” view of education. As I got older I realized that my poor teacher had many “me’s” where I only had the one- me. I thought “it doesn’t matter. The answer matters!” Nope. Don’t believe me? If your boss asks for an excel spreadsheet send them a .pdf. If you work in a warehouse, instead of using an order picker bring a ladder from home to get something off a 40 ft tall shelf. If a spec sheet calls for one thing substitute another. Chances are that in any critical or regulated task you’ll find that HOW you do it is often just as important as it getting done. Ask and accountant or Software QA about audits. Those jobs primarily exist for the PROCESS and not the result. Yes- programming- one of the top math careers- requires you to show your work. It’s not enough a program works and is in production- because if that audit comes back dirty people- likely you too- are getting fired.
Lawyers have to show their work as well don’t they? It’s a process driven job. Judges, police, if a case is reviewed and there are procedural inconsistencies, abnormalities, or absences, a case can be thrown, appealed, acquitted, overturned. There can be counter suits and people getting fired. Innocent peoples lives ruined. What about citations in writing? There’s an accepted standard for how to properly cite references isn’t there? And we can’t simply say “yup. That’s the answer. No need to check. It’s right.” No. We do need to check. We do need to know HOW you drew a conclusion and FROM WHAT. Not just “this is the answer.”
Creative:
Creative’s Parents:
The Principal: Do the math the way the teacher tells you, mkay?
Creative: *hates math forever*