Some students take longer to grasp a concept than others. The goal of education is for students to learn, so why shut the door on students who need more time. A grade's standards should be met by the end of the year, so why not allow students that time to master them. A student may struggle with long division at the beginning of the year, but have it mastered by the end of the year. They have still met their goal. By turning grading into a year-long process instead of a by-topic approach, students are given the time they need to achieve mastery.
The teacher needs to establish what demonstrates mastery and make it transparent to students. I continue to give traditional assessments, but students are free to 'retest' to demonstrate mastery on specific standards at any time. Mastery is 4 out of 5 questions correct. Approaching is 2 or 3 out of 5 correct. Not yet is fewer than two. As students demonstrate an improvement, more parts of the bar are colored in. Advanced students can be challenged to learn the same standard at a higher grade level--6.OA.2 for a 5th grader, for example.
To ease the grading burden, I use Google Forms with flubaroo autograding for my 'make-up mastery' quizzes. The questions are of the same difficulty as the test and are free-response, not multiple choice. This allows me to quickly and easily update the student mastery pages and make sure the quiz is always ready when the students are. The quizzes are broken down by standard, so students don't have to re-test on standards they have already mastered.
Ultimately, the goal would be to have the student and teacher come to an agreement on what demonstrates mastery--ideally through a real-world application.