I believe that one of the greatest things we can do is learn. It enriches our lives, strengthens our minds, builds our self-esteem. But I do not mean simply learning facts. Although facts are useful and necessary, mathematics is more about learning how to think. This is why logic is at the core of virtually every mathematics course. Instead of memorizing facts, I emphasize understanding why things are the way they are, how they got that way, and what things would be like if they were another way. Flat two-dimensional formulae become rich three-dimensional objects with depth, color, and beauty when they are understood as opposed to simply being memorized.

It is my goal in every one of my courses, from College Algebra to graduate level mathematics, to impart this vision to my students. I want whatever material is being taught to be more than memorized (although that must happen at times also). I want it to be known. Like to know your name or your address. I strive to accomplish this in a variety of ways. First and foremost, I make class an enjoyable, interesting, and vibrant place to be. Students understand more when they pay attention to details, and they pay attention if the instructor is not boring. So whether it is an enthusiastic presentation, a humorous anecdote, or simply an engaging dialogue I always try to keep my students interested.

Another way I attempt to help my students truly learn, is by giving them honest feedback. I enjoy praising students who give helpful suggestions or offer insightful comments. It helps them feel like they are a part of the class. Even poor students can receive this kind of assistance. Students always have something they understand, even if they do not realize it. For students who are struggling, I will guide them to information they understand, and then show them the way to the material we are covering. Like giving hikers points of reference that they are familiar with, this type of guidance encourages students and that it turn motivates them to try harder. Of course, honest feedback also entails criticism. Disruptive students are very troubling in a learning environment. It is my job, and I take it seriously, to ensure that those students who come to class have the opportunity to learn. I make it fun to learn, but I also have to make it possible to learn.

Finally, my theory with assessment varies from course to course. In the lower levels, I believe that the material should be absorbed into the student’s body of knowledge, and therefore regular exams are the perfect tool for assessment. I assign homework, but I rarely require it for a grade. I believe that students who are treated as adults usually respond in a mature manner. Exams are rigorous and emphasize not just performing problems similar to the homework, but also thinking about what they are doing. I will ask on almost every test a question of the type "If I had answered problem 1 with (answer), how would you know, without working out the problem yourself, that I was wrong?" I teach critical thinking during class, and questions like this remind them to think this way during a text as well.

In my upper level classes, the material is much more abstract, and creative thinking plays a larger part. Therefore, timed in-class exams can be a misleading indicator of ability (or inability). So in these classes, I typically assign problems to turn in, proofs to present at the board in class, and take-home exams. I usually give at least one in-class exam as well, because different students test differently. But the overall theme of assessment in upper level course is much more interactive than the lower level classes.

Is learning in this manner always easy? No. Do students always like being made to think? Absolutely not. Do I in fact know everything I have been taught? Certainly not! But imparting my philosophy to my students is my goal nevertheless, and I will continue to expect a lot out of my students, and even more out of myself. I believe that students who leave my classes, whether they go on to careers in education or business, or just adults in today’s world, go forward better prepared to think.