This morning I finished grading the third and last of my final exams for the semester. This particular class was small and did well overall, so it was easy to take specific pleasure in their achievements.
On some level submitting term grades brings closure to a class. An immediate exception is when a student challenges a grade; occasionally I enter a typographical error into the grade-book and have to correct it. I work hard to avoid it out of pride in my work so it doesn't happen too often. (Other challenges are unfounded and wither quickly; I offer many assessments during the term and do not suffer students to ask for changes to the grading schema after the fact.)
Some classes naturally lead to other math classes. This doesn't happen much with the classes that mainly serve as general studies graduation requirements but past that I'll often have students take a second class with me. Sometimes that's a scheduling requirement (only one section, no way to avoid me) and sometimes that's intentional when the student has more options.
When a student does take me for a second class (or a third, ...) the rapport starts further along. They let down their guard a bit as do I when they ask for flexibility about due dates, etc. If enough students in a course have had me before the discourse is much simpler; I don't have to start from ground zero quite so much in addressing concepts.
One of the nicer things is that I can share more of a sense of aesthetics about our content. If you study any discipline long enough, including mathematics, then there should be aspects of it that are appealing, whether it be an unexpectedly useful technique or a pattern that resonates with previous learning.
On this last final exam (for a course on different kinds of geometries) I asked the students to pick one of the non-Euclidean geometries we discussed as their favorite and explain why. I had told them ahead of time of the question so that they could think it through, and told them truthfully that I would grade their responses solely on their articulation of why they had that preference.
I need to do this more often. Students need to be encouraged to articulate and embrace what they like about the math that we discuss.
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