Hi @dcarolin
I am sorry your Canvas experience has been less than satisfying. I have been using Canvas since 2012; and of the five LMSs I have used over my long career, I like it best.
The purpose of the Quiz Moderation feature is not for grading quizzes; but rather, for managing individual student interaction with the quiz - thing like adding extra time to a timed quiz, adding extra attempts, submitting a quiz and more.This is how it is described in the Once I publish a quiz, how do I use the Moderate Quiz page? guide lesson.........
"Once you have published a quiz, the quiz sidebar shows the Moderate Quiz link, which allows you to moderate the quiz for each student in your course. On the Moderate Quiz page you can view the progress of student submissions and view the number of quiz attempts each has taken. You can also grant students extra attempts, grant extra time for timed quizzes, and manually unlock quiz attempts."
For grading quizzes, you should be using SpeedGrader. Learn how in the SpeedGrader Chapter of the Canvas Instructor Guide. Specifically, you might find this lesson illuminating, How do I grade quiz questions in SpeedGrader?
And please note that there are next and previous student buttons available in SpeedGrader.
Good luck,
Kelley
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