Teaching Philosophy: On Some Aspects of Teaching Style and Student Advocacy

The mediocre teacher tells.
The good teacher explains.
The superior teacher demonstrates.
The great teacher inspires.


- William Arthur Ward

 

Dr. Atma Sahu, June 2011
This is copyrighted material. All rights reserved.

 

I have instructed students in mathematics for over 31 years at four University System of Maryland  (USM) campuses -- University of MD College Park, University of Maryland Eastern Shore, University of Maryland University College, College Park, and I am currently teaching mathematics at Coppin State University, Baltimore, Maryland. In pursuing my professional career as a Professor , I have attempted to become an inspiring mathematics teacher.

As I reflect on my acquired experience, my educational philosophy has come about over my long and productive years as a mathematics teacher. During the period of my tenure in USM, I have encountered a variety of teaching and learning experiences as well as some challenges that greatly have influenced my teaching style. Even more, my enriched teaching experience that is gained in USM has provided me with a distinctive foundation to my philosophy of teaching and student advocacy.

I have taught a number of mathematics courses ranging from developmental mathematics to full calculus sequence, differential equations, linear algebra and methods courses to pre-service and in-service teachers. I have taught courses in a variety of formats (large lecture, small groups, team-teaching, hybrid and online using web 2.0 technologies, etc.) and have employed a diverse instructional delivery and learning assessment methods.

            In the mathematics classroom, the students differ greatly in their ability to acquire knowledge depending on their previous backgrounds and learning styles. Therefore, it is a very challenging task as a mathematics teachers to create a fertile learning environment for such a diverse group with dissimilar needs in a class of 25 students or so, and to be able to achieve not only the targeted course objectives, but also inspire students into becoming independent problem-solvers and good thinkers. So, one practice that has been very useful to me as a mathematics teacher is to be able to identify student’s skills and their conceptual understanding levels early on in a particular course. After early intervention, then with ease, I can develop appropriate experiential activities that give students a sense of belonging, and thus help them make connection between the concepts, spirally.

Taking into consideration the ideas about writing an instructional activity, I designed problem-solving items that involved numerical, graphical and analytical methods of solutions, and I place mathematics content in a proper context through an authentic mathematics-based experience (application) of their lives. On many occasions, when I asked students to make presentations, describing their problem solving processes and the strategies they used to solve problems, and to share lessons learned from their errors, they felt safe to talk about their difficulties and feelings about problem-solving experience.

Nevertheless, the designing of such a complex experiential activities for students, has been a challenging and time-consuming task. Nonetheless, the process of developing instructional activities, test- items, and project assignments that range from the cognitive skill levels of knowledge to synthesis and making judgments (Bloom’s classification), gave me a very fulfilling experience. I met the challenge, and in this process of developing classroom activities and problem solving projects, I taught myself new software such as Math Type, Bb, Mathematica and Maple applications. In addition, I delivered courses integrated with publisher’s software based on Blackboard Course Management system, when appropriate. Consequently, I was able to provided alternative learning aids for students nurturing their conceptual understanding and advanced practice.

Once more, it has been important for me to create a fertile learning environment that allows students to think freely to exchange ideas, and feel safe and confident, and such an environment is conducive to long lasting learning. Students are then willing to take risks in employing alternative problem solving strategies, meet to do class projects, and collaborate on a regular basis. I make all attempts to promote the class as a community of mathematicians where the teacher acts as a guide, and the students perform as scholars. To encourage collaboration, when students are assigned discovery-based problems or projects, I divide students into small groups. In small groups, students hypothesize, test, estimate, justify, prove mathematically, graphically, and discuss and interpret the results. They write reports and communicate results. Outside of class, they e-mail each other and to me, hence communicate effectively to resolve issues, if any arise.

In other words, when working with students in classroom, I employ Bruner's two rules: a) emphasizing to grasp the structure of mathematics and b) employing discovery approach to gain knowledge of concepts and rules. These pedagogical principles are fundamental to my teaching style.  By employing these principles, students learn to initiate problem solving processes and become active learners, they take action by making connections and devise plans to solve problems (G. Polya), test hypothesis, consolidate information, think sensibleness about their thinking, and make judgements.

Besides making use of the instructional skills and methods, I am also engaged in employing other pedagogical practices which include:  a) a reliable assessment methodology for students’ learning outcomes and overall measurement of success in delivering a mathematics course, and b) the effective use of technology in teaching and testing.  The following paragraphs, detail these practices that are pivotal to my style of delivering mathematics instruction.

I use formative evaluations tools to initiate identifying students’ difficulties and their preparation levels for the course. The summative evaluation methods are used to evaluate students’ learning outcomes and effectiveness of the course delivery methods.  I make use of one-minute-quizzes, long quizzes, pre-tests, Maple-projects, chapter tests, cumulative final exams, and student teacher evaluations as some of the course outcomes evaluation tools. Additionally, qualitative data are collected when students express their feelings and appreciations about the subject while work in groups, make presentations, and demonstrate their confidence in taking advanced mathematics courses.           

I am currently, pilot testing the use of Blackboard engine to communicate, deliver course information, and test students’ learning, securely.  I have made some progress and hope to be fully operational shortly. The traditional way of communication in this new knowledge-worker’s world is becoming more and more ineffective. Students now have access to all multi-media systems, and I have acquired the necessary skills to function proficiently with the incoming diverse students population (most of them are already enrolled) and provide effective technology-solutions to meet their changing learning styles. Students should be well equipped with all the advanced tools, technology and skills, as well as possess a sprit of inquiry and enthusiasm for problem solving. Furthermore, I believe that my students should be clear thinkers with rich and diverse know-how in mathematics and have mastery of mathematical language. In addition, they should be able to communicate effectively. 

As I have reflected on my instructional experience and classroom practices over the years, I have synthesized my teaching philosophy. Trial, error and innovation have brought to a notable change in my teaching style. In brief, my teaching philosophy is best described as student-centered, problems-based, and process-oriented, which is completely different from being a teacher-centered, content-based, and product-oriented.

 

References:

 

·        Boyer Commission Report on Educating Undergraduates in the Research University-Reinventing Undergraduate Education: A Blueprint for America’s Research Universities, Stoney Brook, State University of New York (1998). From: http://naples.cc.sunysb.edu/Pres/boyer.nsf/

·         Bruner, J. S. In search of mind: Essays in Autobiography. New York: Harper and Row, (1983)

·         Polya, George. How to solve it. Doubleday, New York (1957).

 

“Education is not the filling of a pail, but the lighting of a fire" - William Butler Yeats

_______________________________________________________________________________________________

 

Atma Sahu, Ph.D

Professor of Mathematics

Coppin State University

Baltimore, MD 21216

sahuatma@yahoo.com

410 951 3464 [work]                                                                          

 

Note: This is copyrighted material. All rights reserved.                            June, 2011