TEACHING STATEMENT
Olasupo John Felemu
Like any other science, I firmly think that mathematics cannot exist in a vacuum and can only thrive when its practitioners actively communicate ideas. Teaching is one of the most crucial steps in the process of doing mathematics since students make up a significant portion of the mathematical community.
I base my teaching philosophy on the following principles.
Developing a powerful motivation. I share with the pupils my own enthusiasm for mathematics each time I give a lesson. I demonstrate to them that mathematics is the study of concepts that logically follow from one another as well as the art of determining the optimal viewpoint on a certain aspect of reality. I explain to my students that the organised thinking they learn will be useful to them throughout their life. Indeed, knowing mathematics helps students be more logically discriminating in their future activities, regardless of what they may be, and it provides a particular perspective on reality that helps students see its hidden beauty. Additionally, I think it's important to emphasize the significance of mathematical concepts and processes as real-world abstractions. The applications given as well as the examples used to illustrate a concept play a significant impact in this regard, so these should be carefully chosen.
Putting the focus on the value of acquiring mathematical experience. I take advantage of every opportunity to convey to the students that learning mathematics is not primarily about memorizing specific definitions, theorems, and computation techniques but rather about gaining experience in the subject and maturing to the point where they can tackle an ever-increasing variety of problems on their own. What do I mean when I say I have math experience? First and foremost, the capacity to think creatively and select the best suitable method(s) rather than adhering to a particular approach and adopting a strict mindset. The capacity to employ logical reasoning in mathematical proofs is a requirement for mathematical experience; one must be able to recognize how one or more results lead to other results, how different components of a mathematical proof fit together, and the primary idea of a proof or a lecture. Last but not least, having math experience implies starting from a strong foundation. I explain to my students that learning mathematics is similar to building a house, which requires a strong foundation and each brick to be placed precisely when and where it belongs. This is crucial in all facets of teaching mathematics, including creating a course syllabus and determining prerequisites, managing a class of students from various backgrounds, giving advice to students, assisting them in selecting the courses that are most appropriate for their interests, etc.
Learning actively. I always place more emphasis on this than memorizing since I believe it is the best method to develop mathematical experience. First off, I believe that homework is an essential component of the instructional process. In fact, until one is able to apply concepts, procedures, and theorems (together with their justifications), one cannot understand mathematics. Therefore, it is crucial that the teacher carefully choose the homework assignments so that they effectively demonstrate the content covered in class and have a range of difficulty. One of the best teaching materials, in my opinion, is the actual pupil. I have encountered pupils that are eager to impart their knowledge and clarify concepts to their peers. This is incredibly helpful since kids can clearly comprehend the struggles of their peers because they have already experienced those same struggles. I consistently promote communication within and outside of the classroom, between the students and myself, as well as between the students themselves. in addition to among the kids. The students become more actively involved and the typical mistakes/weaknesses are easily corrected, for instance, when I ask students to work in small groups or present in class (of solutions to homework issues or other course material supplied in advance). When students converse with one another (for example, about schoolwork), it's important that they receive enough feedback so that the teacher can ensure they stay on task.
The use of technology. In my opinion, learning by doing and using mathematical software are the best ways to learn. As a result, I use Sage and Maple, two computer algebra systems, into my lessons. I also actively support Sage's use in our department for both teaching and research. By using visualization and demonstrations, I am able to better explain the ideas and procedures, and the students are able to verify their hypotheses and manipulate the things they are learning about by using straightforward programs. As a matter of fact, kids are more used than ever before to thinking analytically and visually. On the other hand, by delegating the computations to the computer, one is free to focus on the core of the issue. In addition, the associated notions are no longer abstract ideas but rather concrete things. Using mathematical software is a highly helpful technique for research students to learn about research and to conduct computer experiments to get new results. Sage is a research tool that the majority of my most recent B. Sc. students use frequently. Although I haven't yet taught an online course, I am aware of its advantages. On the other hand, I've used the online methods for assigning homework that different publishers offer, and they were very effective for me, for example in the mathematics classes I taught.
My instruction is adjusted to the students' abilities and interests. This, in my opinion, is a crucial component of teaching. I have taught a range of courses during my career, from introductory undergraduate to advanced graduate courses. I place a strong emphasis on using a variety of tactics and strategies in the lower level classes while also ensuring that the students can choose the one(s) that are most suited in a particular circumstance. I continuously urge these kids to raise questions and to visit my office hours because they require the most help from the teacher. I place a strong emphasis on formal reasoning and mathematical proofs in my honors and upper division courses. Whether a student wants to apply mathematics to different fields (such physics, computer science, biology, or business), teach mathematics, or conduct mathematics-related research, is something I also take into consideration. As a result, I use relevant examples from these areas of interest to demonstrate the content I teach. I place a strong emphasis on innovation in my graduate classes; for instance, I present multiple perspectives on a certain issue. Additionally, I demonstrate to my students how the knowledge they have gained relates to current research issues, which boosts their confidence in their capacity to solve these issues. I place a strong emphasis on the significance of tackling specific circumstances first and doing tests/experiments (often by utilizing a computer), as it is easy to feel discouraged by a research problem.
Focusing especially on numerous practical teaching facets and subtleties. Being a math teacher is a difficult job that requires attention to a variety of specific details in addition to the overarching ideas. I list the ones that I am particularly interested in.
• creating a syllabus with information on the subjects covered, the standards expected, the resources available for assistance, and the grading procedures (including details on homework, assessments, quizzes, and the final exam).
• treating the students as mature adults, allowing them the freedom they require, and motivating them to become more and more self-reliant as well as to communicate with me and one another.
• presenting the lesson information in a variety of ways, including as through the use of diagrams, formulas, descriptive statements, algorithm-style descriptions, computer simulations, and experiments.
• Writing accuracy and strong board work.
• Going over the homework in class. If I have a grader, I make sure to provide him or her with sufficient details regarding how to evaluate the homework.
• Using the math software that is provided at the computer labs.
• Making oneself available to students outside of the classroom.
• Preparing for examinations and exams with review sessions.
• The students being treated fairly. I always utilize a grading key, especially for tests and exams. Along with ensuring that students receive adequate feedback on their performance and opportunity to improve their grades, I also make sure that the final grade best captures their entire performance during the semester.
Integrating teaching and research. At Adekunle Ajasin University Akungba Akoko, I have already created a number of new graduate courses in a number of my interests (see below). In these courses, I continually update the supplemental material in accordance with the interests of the students and fresh information in the relevant fields, in addition to the core material. My graduate coursework is being coordinated with courses in the algebra group that are being taught by my colleagues. Offering independent studies and asking students to conduct computer experiments using the structures of interest is, in my opinion, a very effective strategy for introducing students to research. Additionally, I teach students how to write up a mathematical proof since I think it's important and that failing to do so can be detrimental to learning. Along with writing a survey paper specifically for graduates on the connections between combinatorics and other branches of mathematics, I have also given several speeches in our Graduate Student Seminar. All of my guests are still encouraged to connect with our students and present colloquium and seminar sessions that are accessible to them.