I take my responsibility to instruct those entrusted to my care very seriously. As a result, my approach to teaching is exemplified by three major characteristics:
1. A Strong Emphasis on Students Practicing Mathematics Themselves
2. Close Interaction with Students
3. Use of Technology When Pedagogically Appropriate
I believe it is axiomatic that to learn mathematics one must do mathematics. More important than the examples I do in class are the homework problems students do for themselves. Unfortunately, many (probably most) undergraduates have never learned the benefit of fighting through a problem until they completely understand it. Too often students attempt a problem, check the answer manual or back of the book, and then doctor their work to make their answer “look right” without gaining real understanding.
To remedy this problem, I employ several different tools. Most recently, I have begun assigning Calculus I homework via the online WebWork system. The system recognizes when students’ answers are algebraically equivalent to the correct answer, so there is no need to limit questions to multiple choice format. Students may enter their answer directly into the web form and are told immediately if their answer is correct. This serves the same pedagogical purpose as having them check their answers against the solutions manual, but without giving away the correct answer. Most students find staring at a screen which keeps repeating “The above answer is NOT correct” extremely frustrating, but they keep trying – or email me for help – until they understand.
I also routinely give problems for students to work on during class, usually in small groups. Forcing students to do mathematics for themselves while I am still available to answer questions, has greatly reduced the number of students who complain “I understand when you do it in class, but I can’t do it at home.” I employ this technique in almost every class I teach, from my graduate Complex Analysis course to my Business Statistics course taught in sections of nearly 200.
Secondly, I believe students learn best when there is the most interaction with the instructor. Such direct interaction occurs naturally in small Honors sections with 20 students, but it is even more critical when teaching large sections with nearly 200 students. One important method I employ for connecting with individual students is to “float” around the room answering questions and providing guidance during group activities. My Computer Literacy course for elementary education majors is conducted almost exclusively in this manner.
Of course, there isn’t enough class time in most courses to speak to each student individually; thus I strongly encourage students to visit my office, even outside my official office hours. Even more importantly, I have designed WebCT supplements for 8 different courses to facilitate communication with students. Inside WebCT, students check their grades, download supplemental material, and post questions to the bulletin board. For larger sections, I also hold online office hours in the chat room on the night before exams. There is also a link to send me email on every page of every WebWork homework assignment.
Finally, I believe in the pedagogically appropriate use of technology to assist learning. Indeed, the major focus of my Computer Literacy course for elementary education majors is to help future teachers understand when technology can be a blessing and how to keep it from becoming a curse.
The communication tools built into WebCT and the online homework facilities of WebWork have proven invaluable in my teaching. Similarly, in my Business Statistics course, I usually have students collect data and analyze it using Excel. Since the focus of the course is understanding statistics, not simply computing them, Excel is an excellent tool. However, the most exciting new technology I have integrated in my classes is the LearnStar interactive response system. As part of a 4-year interdisciplinary NSF grant, I am studying the effect of LearnStar competitions on student achievement. As students compete against each other in the multiple choice online quizzes, they focus much more intently on the material than they ever would otherwise.
On the other hand, there are definitely limitations to the pedagogical usefulness of technology in certain situations. For example, in my Calculus I course, I give two parts to each exam. For word problems and other numerical computations, students are encouraged to use their calculator. However, calculators are not allowed for questions such as finding derivatives or evaluating indefinite integrals. The development of these critical skills would not be served by permitting dependence on the technology.