I think now-a-days it depends on the teacher. There's multiple ways to get a solution and different ways students learn and understand.

For example, there are 3 ways to solve a quadratic.

1). Graphing and finding the intersections
2). Quadratic formula
3). Factoring and solving

I was never concerned with which method a student chose. The process and understanding is more important than the solution in my opinion (at least when learning the content in school).

And personally for my classes, I LOVE when students have shortcuts. It shows that they're thinking and learning outside of the classroom. I'd make them share the shortcuts in class too because you never know if that one way will click better for another student (provided the shortcut is mathematically correct).

But the reason for me to want to see work was to GIVE credit, not take away credit. I'm assessing what they know, NOT what don't they know (well, to an extent...yes I want to know what they don't know so that I could re-teach).

But what I mean is, if you just put down a solution, and nothing else, and the solution was wrong, I couldn't tell where the mistake was made or see the thought process.

Versus when they show their work, I could see "Ah ha...you just forgot a decimal, or "you had the correct answer but just plugged it in wrong on a calculator", or "you simply forgot a negative sign". To me, it shows you knew what you were doing and I'm more interested in how the student worked out the problem, not what their final answer is.

I do see your point, and it is a little bit of a balancing act to allow students some freedom to work it they're own way, but also in some way showing how they worked through it.

Does that make sense?