My experience at GVSU is pretty well summarized by this complaint from an anonymous student of linear algebra and differential equations, conveyed to me by the mathematics department.

"Up until the very last day of class we were turning in new homework and learning new material..."Go on.

"... but at what cost?"In the final weeks we discussed systems of linear differential equations, the Laplace transform, and power series solutions to differential equations. These are important topics for engineering students. Better to see them, if only briefly, than to review earlier topics, for instance. (Is this what you were expecting?) I understand this is a lot to digest in a short time, and accordingly I trimmed the homework and examination scopes. You can find in the textbook many parts of the story I left out. There's no rule against learning in the last week of class. This is regularly scheduled course time, not finals week or a study period.

Sensible or not, negative student reviews hurt you at GVSU. I was never told how they were weighted, but mine were presented as evidence of poor teaching in performance reviews. As you might expect, you then find professors telling their students explicitly about the behavioral norms of university-level mathematics. What's surprising is the constancy of this communication. It displaces the discussion of actual mathematics. A colleague who could be heard speaking to students at office hours spent most of those hours on this, it seemed to me.

Here is how I could be a more effective teacher of linear algebra for mathematics majors:

"Less proofs and more linear algebra."Proofs are important in mathematics. Consider also that they are not so different from calculation. A typical question in linear algebra is whether a set of vectors is independent. It is practically the same exercise

These anonymous surveys were rarely useful to me as a teacher. A student of linear algebra and differential equations wrote:

"Took his knowledge for granite and assumed we knew things."Yes, after Calculus I, II, and III, you are assumed to know things. If you are not responsible for prerequisite material, there is little time for linear algebra and differential equations. Still, did I not often show the steps of these methods in class to refresh your memory?

As for my knowledge, I thank my parents first. My mother taught me to read. I had years of education mostly in public schools, then went to college, where I worked hard just to pass. In the 1992 season, the AFC champions were the Buffalo Bills. The NFC champions were the Dallas Cowboys. They met in 1993 for Superbowl XXVII at the Rose Bowl in Pasadena, California. I was unaware until now, when I searched the Internet for things that happened during my freshman year at Caltech. I can tell you in great detail the geometry of my room and desk and of the cup I used to carry water there from the sink.

If you are really smart, maybe you can get a PhD in mathematics without much work, but I studied hard. In graduate school you encounter setbacks of kinds you never knew existed. Contact hours with my professors and students were far outnumbered by contact hours with desk chairs.

I try to imitate my best professors, especially those at CSULB. You have to admire people who dedicate their lives to a subject as challenging as mathematics and spend hours each week explaining it to you. I hear students complain about the foreign accents of their instructors, but let's face it, it's the mathematics that's difficult. What does it mean that I take my knowledge for granted? I have no idea. Here is a way to improve my course:

"Have it taught by an actual math professor from the math department."Hear that, administrators? They want me to have tenure. Seriously, I was an actual math professor from the math department.

Some students wrote nicer things.
In closing, here are the complete comments of one student.
*Ways in which the instructor was effective:*

"Dr. Smith is one of the best instructors at GVSU he expects a lot from his students but no more that should be expected at a 300 level class. He is very reasonable and flexible and really cares about student learning. His tests were easier than the homework & examples in class as they should be. Anyone complain, about the difficulty of this class is probably just upset that he actually expected them to learn."Thank you.

"Dr. Smith does need to return graded tests more quickly."Many students wanted this. I don't know what else I could have done but to lower the quality (and fairness) of the grading. Even that would not have helped much. I had more pressing tasks.

"Also, the way he leaves the overhead on and uses the board around it is awkward and sometimes difficult to follow."Sorry about that.

"The course is actually very well designed. Too bad its not longer."Yes, it's a lot of linear algebra and differential equations for one course. You finished, and you can be proud of that! Good luck in your future studies.