My primary goal in teaching is to instill a sense of curiosity, excitement, and admiration of mathematics in the students — the same attributes that have continued to motivate me. The challenge and potential to instill these qualities is why I enjoy teaching.
Not every student will think the same or have the same motivations. What has worked for one particular student, will not necessarily work for another. Thus, any approach to teaching must be diverse and adaptable to the student. When I co-taught an undergraduate class on Operations Research during the fall semester of 2010, we created an online student survey before the semester began in order to get a sense of the type of course materials the students were interested in, e.g., applied and/or theoretical mathematics. We also asked about their mathematical background. This information was very helpful in designing a more appropriate syllabus for the students. Furthermore, we used the survey data to adapt the lecture materials and assignments in order to maintain a good balance between different aspects of the subject material. For example, we had lectures and assignments that focused on theoretical underpinnings, such as theorem/proof type lectures and assignments, as well as lectures and assignments that incorporated computational aspects. We also introduced an opportunity for students to pursue a final project in lieu of a final exam. This option was instituted on a volunteer basis, but it was a great opportunity for the students to apply the course topics to real world problems.
Regardless of the motivations behind an individual student, I universally believe that student learning is long term commitment. It is a slow and steady process that cannot be hastened. I cannot emphasize this enough to my students. It often takes time and numerous approaches to understand the subject material. I always tell my students to review the class material after every class. If they still have difficulties after reviewing the materials, they know that they can come to me with questions. In order to aid the students in understanding lecture material, I provided students with typed notes for every class, allowing them to focus on material lectures rather than note-taking.
An equal commitment must also come from the teachers as well. It is extremely important for a student to obtain a proper foundation in any mathematics course, applied or theoretical, advanced or basic. Having a solid foundation will prepare students for later development in more advanced courses in mathematics or other fields, or for a future career. Therefore, one must invest a considerable amount of time and effort into teaching. From the perspective of the student, a teacher needs to ask themselves “Why should a student take my course, rather than just read a book on the same topic?” As a student and a teacher, I believe that a teacher must provide a thorough and diverse perspective of the subject area, and articulate and clarify the significant aspects of the material. To prepare for the course, my co-instructor and I spent several months prior to the start of the semester studying the subject material. We reviewed books from a diverse range of academic backgrounds, including engineering, mathematics, and computer science. We designed the course from the bottom up based on what we thought was the most thorough, intuitive, and illustrative perspective. Moreover, the questions and challenges that we faced while investigating the materials were used in the creation of the assignments and exams. Thus, the assignments and exams were created in a way that modeled what we believed to be the best approach to learning the course material and testing students’ understanding.
While adaptability is a necessity in designing a course, a level of discipline and rigid structure is also a must. The syllabus, including main topics and general structure of the course, should be decided before the semester begins. To help with this, I have used information from previous classes and collected student survey data about student preferences. This syllabus was reviewed many times, but finalized before the class began. In addition to a thorough review of the syllabus, a strict homework policy must be maintained. The policy that I have used included weekly homework assignments, for which late assignments were only accepted under special circumstances. Without weekly assignments and strict policies on late homework, students might be less inclined to complete the necessary work. Currently, I am working with a student in an Independent Study project, in which I give weekly or bi-weekly homework assignments to help progress the research. This approach has worked very well in comparison to having informal assignments without detailed instructions. Implementing a strict grading policy, which may include outlining relative weights between homework, midterms, finals, and projects, is also very important. A strict grading policy eases the burden on the instructor when grades need to be calculated, and it clarifies for the students, the criteria for desired performance in the classroom. In addition to some degree of rigidity, it is also important to have some flexibility as well. Depending on the performance of the students as the class progresses, which can be evaluated via homework and exam grades, one might need to adjust the speed and the focus of the class from time to time.
Another important part of the classroom is to setup a collaborative and productive learning environment for the students. Collaboration is a very important part of research and I encourage students to work together. However, it is also important that students complete their own assignments in their own words, even if they collaborated on an assignment. In addition, the use of technology is an important tool for encouraging collaboration and promoting a more productive learning environment. In particular, the creation of a class website and online class forum can be very useful. In my class, I set up a course and homework forum for the students to ask questions about homework assignments and subject materials. I spent a great deal of time to ensure that the forum interface was as user friendly as possible, so that the students would feel comfortable using it. The main course website was used to post homework assignments, notes, corrections and clarifications, and important assignment and exam dates, which allowed for the students to anonymously post comments. This made it easier for students to access and share information, provide feedback, and promote open discourse between students and teachers.
I see teaching as not only a chance to share my enjoyment of mathematics with students, but also a fundamental component for the advancement and betterment of the next generation of students. It is because of these two aspects that I take great pride and enjoyment in teaching. With a philosophy built upon a strong commitment from student and teacher, adaptable and diverse teaching styles, and a collaborative and productive learning environment aided by technology, I believe I can instill, in the students, the same sense of curiosity, excitement and admiration of mathematics, which has continued to motivate me throughout my academic career.