I began my position as Assistant Professor of Mathematics in the fall semester of 2007. I had just finished my graduate school work. Fresh from having earned my doctorate and armed with the knowledge I had been offered a position at ACU, I moved to Abilene and began work that first summer. Not too long after settling in, I was asked to write what my goals were for the first year. I will be honest in saying I had little to no idea what to expect in terms of teaching, scholarship, and time management. So, when I set out to write my teaching goals for the year, I tried to align my goals with the things I valued the most. I came up with the following:

• In the upcoming year, it is my goal to effectively integrate technology into my teaching methods.  It is my hope that students will be engaged by a more interactive approach and would benefit from the exposure to various forms of technology.  In particular, I want to utilize Maple for Pre-Calculus II and Calculus II as an effective teaching aid.
• I would like to develop a curriculum for the differential equations course I am teaching in the spring that would introduce students to differential equations as well as lay the ground work for special topics courses in partial differential equations, integral equations, and dynamical systems.  I could see this as a springboard for undergraduate research in this area.
• It is my goal to incorporate real world mathematics into my teaching through the use of projects and/or research.  I want my teaching to emphasize the applicability of mathematics in my students’ lives as well as broaden my students’ attitudes toward mathematics.

Over the course of that first year, I taught MATH 120, MATW 120, MATH 124, MATH 186, and MATH 361.  As I had never taught these courses before, all were new preps. Looking back on it, the first semester was particularly challenging because I had three preps and four courses total–a significant increase over what I had become accustomed to in graduate school.

Let me speak to each of the goals listed above as they related to my performance that first year.

Technology Usage

In MATH 124 (PreCalculus II) and MATH 186 (Calculus II), I frequently used the Promethean boards, an interactive white board which I had no previous experience with, to interact with slides, graphs, etc… I found this to be a use of technology for the sake of using technology and didn’t see much educational value in its use for these courses.  I try to avoid using technology for the sake of technology if it is adding nothing to the educational experience.  I know these interactive white boards are of great use to our teaching majors though and so outside of class time I kept working with them until I became proficient with their use.  I have used them in subsequent presentations with more effectiveness by simply relying on them as a device to not keep me tethered to the computer, and for the occasional annotation.  This was a more effective way of utilizing the technology in my opinion.

In MATH 361 and MATH 186, I used Maple quite extensively for in class visualizations and take home projects.  By my count 30 separate Maple documents were created and used between these two classes. While Maple was very nice for visualizing various mathematical concepts, it was not a solution for presenting high quality mathematical writing via lecture slides and homework.

I remain excited even today about the potential this software has for creating high quality mathematics which can grab an audience and engage students.  I devote a significant portion of my prep time each semester to remaking my class lecture slides in a newer and better format applying new levels of complexity to these slides as I learn to use the software more effectively.  This has been quite useful, as I have been able to pass that passion onto my students who often ask what I used to create the slides.

Designing New Curricula

One of my main goals for that first year was making the differential equations course my own.  I was not content to simply lecture from a textbook.  This was after all my area of expertise, and I wanted to make this course both compelling and challenging for my students.  Looking back, I might have turned up the knob a little too much on the challenging dial because I quickly realized I was having to cram material in to the detriment of my students.

One of the problems was to effectively engage the material in this course, students needed a high level of proficiency in the use of Maple.  The applicability of differential equations is lost on students at this level without the detailed visualizations that Maple can offer.  To be able to use Maple at that level though would require a substantial amount of class time, more than I could afford to give.  This was a blessing in disguise though as it forced me to do two things: (1) give a greater focus to the pacing of the course, (2) move to offering students video tutorials or examples of work via video.  I will discuss the video tutorials in the next section as they were implemented most effectively the next time I taught the course.

If you look at the progression of my course syllabus over the years in MATH 361 I think you will be able to see how my focus became more fine. For example, I merely listed topics we would cover in the first syllabus, but as the years progressed I became more detail oriented about the course leading to me producing a course schedule that documented every class meeting. This was the level of detail I felt the course demanded.  This was a good experience as I have adopted that habit in other classes to the improvement of all involved.

Incorporating Real World Mathematics

I felt I had a really good response to the take-home tests/projects conducted in MATH 361.  These projects promoted a “learning through discovery” model, where students would be confronted with an overall theme, like the implications of resonance to mechanical engineering or controlling animal populations through the introduction of predators.  Each project peeled back the mathematics little by little under the umbrella of asking what the real world implications are in this situation. To this day, I still author projects and assignments in this course with that idea in mind.

In MATH 120 we have students learn about annuities and mortgages, but rather than simply have my students learn the formula, we derive the formulas, and then look for real world examples of annuities and mortgages upon which to base our calculations. This was a new experience for me–using the Internet in class to reinforce the real world applicability of a particular topic.  It is an experiment I have repeated multiple times to date.  Keeping in mind that I’m teaching college students, I cater my topic selection to areas of interest for the students:  avoiding credit card debt, planning to buy a first home, paying off school loans, etc…

Scholarship

I found I had very little time for classical research in that first year, but this was not necessarily a bad thing.  It meant I had to find ways to plug into research which would help inform or enhance what I was doing in the classroom, because I was unwilling to sacrifice or trade performance in the classroom for a higher focus on research.  In fact, I stated in my annual review that I may want to consider “non-classical” ways of research as a supplement to my more classical research goals.

I was involved in presenting a series of five lunchtime colloquium presentations to our students in that first year.  These presentations were an opportunity to introduce myself to our students and stir up interest in undergraduate research.  They were effective in doing the former–not so much the latter.  The reason for this being the topics I chose to speak on did not tie into anything the students were experiencing. The level of the material was much too hard for the students to really get into.  I remembered that the next time I gave a similar presentation. I used a topic we were discussing in Discrete Mathematics at the time to demonstrate how only the slightest tweak in something that was rather trivial could make it much harder and worthy of interest from students for research opportunities. I take this approach in all my majors classes now, hoping to plant the seeds of undergraduate research among my students.

Service

In my first year, I was able to serve as the faculty advisor for Mu Sigma taking over for Dr. Bo Green. In my first year as advisor, the club saw large increases in membership, made T-shirts for members, updated department web pages, and participated in an after school tutoring, service project.  This project received a write up in the Optimist and helped to shed some light on the group.  Unfortunately, most of the momentum we gained at the start of the year was lost when a few of the student leaders were involved in study abroad that Spring.

I was also able to provide service to my profession by refereeing an article for the Journal of Nonlinear Analysis, entitled “Positive Solutions for nth Order Nonlinear Impulsive Singular Integro-Differential Equations on Infinite Intervals in Banach Spaces.”  The experience was a good one, as it was the first solo review of a paper I had done.  I did a few joint reviews with fellow graduate students as a requirement of a course in graduate school.

Overview

Looking back on the semester I feel I could have done a better job of managing the time split between research and teaching–something I improved upon in subsequent semesters as you can easily see from an increase in my scholarship activities.  I was approached by two students from the Physics department to teach MATH 361 via correspondence during the Spring semester.  This was challenging to say the least considering it was first time teaching the course and I had to structure several assignments differently for the study abroad students.  To my surprise things progressed rather smoothly and both students did an excellent job of managing the course. I was approached again the next year by the Physics department on behalf of another student, and was able to repeat the success of the first time.

My first experience teaching MATH 124 was not a good one for many reasons.  The amount of material I tried to cover seemed to bloat the course.  I adjusted this the second time around and removed a few topics and streamlined others.  The main source of contention in the course though was the large gap in skill levels among the students.  I had a handful of students that probably should have been in Calculus I and another group that struggled with basic algebra.  I was not prepared for this.  Managing such vastly different sets of skill levels was frustrating.  At some point in the semester I decided that it was sink or swim time for the students and just went on.  I had several sink, or at the very least take on a lot of water.

Looking back I could have handled the situation better.  I could have provided the students with hand written lecture notes, slowed down the pace, given more take home assignments, and done a better job summarizing my expectations for students.  I was really upset with how the class turned out, but I was able to teach the course again the next year and it went very smoothly, thanks in part to a textbook change, but also an increased level of micromanagement on my part.  I learned that some courses and some students need you to be a tutor and not just a teacher, and that there was a certain amount of hand holding I would have to do–even at the college level.  That was an important first semester experience that I remember even today.

I feel the challenges and successes of my first year prepared a foundation for me to build on in the subsequent years.  Perhaps the biggest foundational piece I had in place was a relationship with my colleagues.  I learned early on that first year that my colleagues possessed a wealth of knowledge and leaned on them for advice about everything from how to write a good syllabus to how to position the tests in a course for maximum effect.  I still rely heavily on their advice and seek it constantly.