First, I put more emphasis on knowing how to solve a problem then on the correct solution and thus a student's ability to explain their work is a part of how each question is scored. As a capable mathematician we need to be able to clearly communicate our reasoning and our work in way that others can easily follow. Building up one's communication skills is important as one of the 21st Century skills that is in high-demand.
Using this method I have found that it cuts down on cheating because even if a student does copy down the correct answer, they rarely also copy down a correct and logical explanation to go with it. It also values a deeper knowledge of the content rather than a surface level understanding. I started grading using this system after reading this article and doing some research on best practices in math education when I was frustrated with the outcomes of more traditional methods. I hope this helps to better understand my test grading system, but please always feel free to contact me with questions.
Anytime a student does not like their test grade for anything less than an A- they can do test corrections to bring up their grade. This involves redoing each missed problem on a separate sheet of paper and including a 2-3 sentence explanation that identifies what their original error was and what the correct procedures/process is for the type of problem being corrected. For every problem that is correctly corrected with a good explanation, they will earn back 1/2 of the points they missed on the problem and then I re-average their score and update their grade. Again, the emphasis is about understanding the process and deepening their knowledge rather than just getting the correct answer.
The average is converted into a letter grade using the table below.