@carols
Canvas doesn't directly support linking to SpeedGrader from external sources, so they are not going to document how to do it.
Not supporting something is not the same thing as it not working, though, and you can create links that will work, but you will need to reverse engineer from the URL or look at the source code.
In /spec/coffeescripts/models/EntrySpec.js, they define
SPEEDGRADER_URL_TEMPLATE: 'speed_grader?assignment_id=1&student_id=%3Astudent_id'
That %3A is an encoded colon, so it's really student_id=:student_id.
There is a note a little later in that file that states that the :student_id gets replaced with the user ID.
Putting that together would give you 'speed_grader?assignment_id=88888&student_id=99999'
Of course, that's just a test to make sure it gives the right thing. The actual code that produces the URL is found in the AssignmentAPI.js file. There it defines the full path.
/courses/${courseId}/gradebook/speed_grader?assignment_id=${assignmentId}&${studentType}=${options.studentId}
The last part is to allow for anonymous users, so it is either anonymous_id=77777 or student_id=99999.
To solve your problem about getting the wrong student, you could first check enrollments to make sure the student is enrolled.
