I assisted one of the world's foremost Operations Management and Business Statistics professors in the world. One of my duties was grading tests. This professor was so fastidious that his index of test questions contained statistics comparing students' general class and academic performance with their tendency to get a particular question right or wrong. In other words, some questions inadvertently can act like "trick" questions that good students are nearly as likely to answer incorrectly as poor students. He tested his questions on various measures including this.

This professor gave partial credit. And I agree. The student got a fair amount of credit for writing the correct formula to use to solve the problem. More points were awarded for inserting the correct values for the variables in the formula, and more points were added if the math between that point and the final answer was accurate.

Sure, in the real world, wrong is wrong. But in academics, you are teaching and assessing the student's knowledge. In other words, you are assessing more than the final answer.

Yes; though we did give you partial credit for the post anyway. ;)

One of my majors in college was Finance. In one of my senior-level Finance classes, the final consisted of ONE problem. It was something like some little old lady had $750,000 to live the rest of her life on, would you recommend that she invests in a given company and how much...

We were given the financial statements of the company, and we had to draw conclusions about the risk of the company. The issue was, all of the methods were based on theory, and there were multiple ways to reach conclusions--each of which would yield vastly different answers.

In the end, the most important thing on the test was that you used a sound methodology. Finance is very different that engineering however. Finance demands a good answer now, Engineering demands the perfect answer.

Accounting situation

A blonde accountant was reading the newspaper.

The headline blared, "12 Brazilian Soldiers Killed."
She shook her head at the sad news, then turned to the person
sitting next to her and asked, "How many is a Brazilian?"

Just imagine how easy it would be to grade maths papers of there was no partial credit. Just check that last couple of lines baby - mmm. Tempting, very tempting.
Maths lecturing & teaching is my game & I've got no problems with the partial credit idea. If someones sitting a paper, then the solutions are prewritten with certain marks going for each step of the process. No doubt you will lose marks if the final answer is not correct but I think it's fair that if you show knowledge of a certain process/method/technique, you get akcnlowledgement of that.

Some of the courses I've done have had open book exams & most of the others have a formula sheet provided. This allows you to set more realistic (demanding?) questions as you're not focussed on memory & recall. Most of my students have not found the open book exams any easier than the closed book ones. It all comes down to what you're trying to assess. If you're trying to assess 100% accuracy in working then you'd give a paper designed for that (ie no partial credit). If you're trying to assess understanding of concepts then that's what you're giving marks for.