I returned exams on Tuesday. Wednesday brought a steady stream of discouraged visitors to discuss performance in the class and on the exam. “This class is abstract, and I’m not comfortable with abstraction.” “This class is difficult.” “I just can’t seem to get it, and I am working so hard.”
What do I say? Sometimes I want to ask, “Well, why haven’t I seen you in office hours before now? Now that you are here, how about you open your book and start working on some linear algebra?” In reality, I find myself saying, “Yes, the class is abstract, but one of the most powerful tools in the toolbox is the power of abstraction. You have to learn to think of matrices as mathematical objects, and vectors as mathematical objects that have rules for manipulation that we can follow, rather than visualizing a rectangle of numbers or a magnitude and direction in 3-space. If you aren’t getting this, something needs to change.” I can make a list for you (and sometimes I do), the top of it is put serious effort into doing and understanding the homework as it is assigned (which has been mentioned many times so far this semester), but you, Dear Student, have to be the one to carry out the actions and the plan.
I am both amazed and not amazed at how few have their books open before talking to me about their grade, and how many leave immediately after, never opening up that book to take advantage of the time and opportunity to work some of the linear algebra that is causing the difficulty.
Thursday I decided to bring the topic of discouragement up in class as an opening activity. What would you say to someone who is discouraged, specifically a classmate who feels that the material is abstract and hard and arbitrary and meaningless? Or someone who is just discouraged about something in general?
What did they come up with?
- Keep trying, don’t stop.
- Hope is needed for hard work.
- Forgive yourself and get to work.
- Take a step back. Take baby steps forward. Figure out what you know and go from there.
- There’s always a solution and always people willing to help you out.
- Spring break is coming!
- You are not alone, find support from others.
Two and three and five and six and eight, those are some good profound thoughts.
I admitted that this was on my mind for personal reasons as well. I am dealing with discouragement and frustration, though not with regards to our class or my teaching. I contributed some wisdom from what I’m currently reading, Pema Chödrön’s When Things Fall Apart. She advises us to
Lean in to your discomfort, and learn from it.
That is what I am trying to do with my situation. And it is hard. But with abstraction and confusion, that’s where you’ve got to go to make sense. Lean in to your discomfort.
What surprises me most about this discussion is the impact. I find it mentioned in notes written on the back of the quiz we took Thursday. In emails from students received over the weekend. One that included a link to this video, passed on to her by her father, full of wisdom and a change of perspective:
Does it make a difference to talk about it, to waste valuable class time on something other than math? I hope so. Especially since that quiz had some disappointing results, indicating we need to buckle down and figure this out. I know it’s tough to learn this stuff, to learn how to think differently. But that’s our job here, this semester.