I strive to make every course I teach a valuable learning experience for my
students. Lecturing to students of differing experience and capabilities in
the same classroom can be challenging. I believe that we are better
prepared to meet this challenge if we understand well the human as well as
technical sides of teaching and learning mathematics. So I have taken
active steps in this direction by exploring and comparing different ideas
and teaching techniques.
An essential component of my teaching is the conveyance of my enthusiasm
for the discipline. I make lectures interesting by
explaining the intuitive ideas behind the technicalities. My students
seem to appreciate it--- the enrollment in my classes is usually high and
many enroll because of recommendations of my former students.
In all the undergraduate and graduate courses that I teach, I encourage my
students to be critical, independent and creative.
Regarding my undergraduate teaching, my philosophy of ``instruction with
instructions'' has proven quite successful in my classes. It is my
impression that many students do not do well in mathematics because they
don't know how to study it. So I do my best to provide structure for
them. I explain to them that learning mathematics is somehow like learning
how to drive: you don't try to memorize the solution to every homework
problem you have done as you would not try to memorize which traffic signs
are posted at every intersection of the town. In mathematics you learn some
key things and ideas (as for driving you learn how to operate a vehicle and
traffic rules) the rest comes with practice.
Structure is especially important for lower level undergraduates. To them I
give detailed instructions for writing their homework emphasizing that they
must provide sketches of graphs when appropriate, clearly indicate the
formulas that they use as well as carefully write all the important steps
of their solutions. For the courses that is available I use the homework program Webwork but also have the students
hard copies of the solutions. The hard copies
are only graded for presentation while the correctness is checked through
Webwork and quizzes. As a result students write better exam
solutions than they did in the past when I only had them focus on the
correctness of the homework problems. The students can immediately see the
connection between doing the homework with care and doing well in the
I am also a vigorous proponent of technologies that extend or enhance the
delivery of the traditional mathematics course. I use internet
technologies to expand the classroom in many ways. Through my website I
distribute a variety of course information and materials, including links
to websites that relate to the content of the course. I do this in a
way that is appealing to the students and will stimulate their learning.
I use Maple when I teach honors sections of Calculus and Differential Equations and in the
graduate course on Grobner bases.
Working with graduate students through courses and individual advising is also a very interesting and rewarding aspect
of teaching at a Ph.D. granting institution like Texas Tech. I make my graduate courses a form of research
experience. Depending on the level of the class I may even not adhere to a particular text but rather encourage the students
to go to the library and try to find relevant literature. I also encourage the use of computer algebra systems
such as Maple and Mathematica as a research aid. Through interaction in graduate courses the students can learn about
my research and see the viability of a possible advisor-student relationship.