I had an up-and-down day in classes today. I am still thinking about how linear algebra went early this afternoon.
We are now in the fifth week of the semester here at UNI, and my linear algebra class has been doing lots of tasks about the geometry of R2 and R3, especially those things that help us understand how to think about vectors, lines, planes, and the dot product in situations where we have a chance to draw the picture. Things have been getting steadily more challenging, and the tasks for this week are hard for them. For example, a task that made everyone unhappy today was this:
Consider the line in R3 given by the parametric equation
t → (-6,-2,1) + t(3, -1/2, 1).
Find the point on this line which is closest to T = (1,1,1).
That uses everything we have learned so far, and requires a little bit of thinking about the geometry. It is a great task. It was one of seven I asked them to do for today. (It was probably the hardest one.)
But Friday is the first exam.
I should have thought a little more carefully about this. I have lots of young students, and I have actually set things up in a way to make them more anxious than need be just before the exam. I set a trap for all of us, and then led the whole class into it with a big grin on my face.
Also, I am writing all of the materials myself. This means that if the students feel anxious and are having trouble with the text, that is my fault, too. There is no faceless textbook author to be grouchy at. I can’t be the friendly guy who saves them from the confusing writing.
We had a short chat in class, and I sent them a longer message by email after I had a chance to reflect. I HOPE that I have helped calm their fears a bit. Time will tell.
I am going to have to think more carefully about how I structure things when I edit and revise for next term.