By marking these two things equally wrong, we punish good thinking. And the process of a child’s thinking is more important than getting the answer right. Why do I say that? When the child is of age, they will soon find out that the world is not as black…
Very interesting point! I do mark these as "equally wrong." They both get zero credit. But if a student wrote "b-f-g," I'd be concerned. Perhaps in reality, they're both wrong, but one deserves more critical attention than the other.
I had too many experiences as a students writing down long workings, marking down my thought processes clearly only to find that I get a big fat zero in the end. The answer is wrong despite having the "correct" thought process.
I'm teaching maths now. I make it a habit to ask my students how they got they're answers regardless if they got the answer right or not.