Mike

Certified Tutor

Teaching Philosophy

As a graduate student in teaching mathematics, I have taught pre-calculus to first year university students and been a teacher assistant in the math department at Concordia University for almost two years. Currently, I teach crash courses for preparing university students to pass midterms, final exams and prepare students to pass SAT, GMAT and GRE math.

My teaching philosophy creates an environment in which students learn by interacting, participating, discussing, writing, comparing, contrasting and analyzing, testing- as they explore the exciting concepts behind all mathematical formulas.

My teaching is currently guided by the following principles:

To motivate my students to learn in a dynamic and supportive environment
To keep students focused, centered and motivated
To take out math anxiety and let students learn in an enjoyable environment
To talk with my students and be open to them
To act as a mentor, a guide, and provide heuristics in problem solving
To teach my students to think in a critical, creative ways and communicate effectively
To transmit my enthusiasm about mathematics to my students
To create an exciting learning environment
To do whatever it takes to effectively convey to my students the mathematical ideas and concepts
To avoid students making common mistakes by anticipating difficulties that students may face with the material
To avoid students saying, after graduating college: "Math? I hate Math!" or, more politely: "Math has never been my strongest subject in college."
To let students pursue excellence in learning, studying and be high achievers in mathematics
To let students become self-directed life-long learners
To integrate technology into math to better serve my students
To keep improving my teaching strategies



For me, mathematics is not only about understanding concepts, being able to operate with them, and knowing their applications in real life, but also about developing logical and critical thinking.







When I think of mathematics courses from which I retained the most, I recall motivated teachers who were passionate about the course material being taught. Their interest in the material not only encouraged me to want to learn mathematics but showed me that mathematics can be beautiful. I always strive to engage my students in the courses I teach and bring mathematics to life for them as it was for me. In order to do this, I try to find aspects of the material that interest me and share these with my students. I also encourage my students to share aspects of the material that interest them.

I realize that not all my students will appreciate mathematics as I do. I believe that an educational institution should prepare students to become productive citizens in society. With this in mind, I try to keep the courses I teach interesting by showing that the material is relevant to other fields of study. By linking students' other courses to the material seen in my course I express that an individual never knows when their thoughts will influence the face of a subject. For example, I often tell the story of how Gaussian
elimination, a topic seen in an introductory linear algebra course, was described by Gauss who needed the process for studying the orbit of asteroid Pallas! Could one use eigenvectors in measuring the importance of a web site regarding links to it that come from other important webs?

The above two examples would instill in my students the pleasure of thinking for themselves in logical, creative ways. In class we examine how to analyze mathematical problems and discuss numerous creative possible methods to solve them. I also challenge my students to further pursue what has been seen in class and give weekly challenge questions.

The trick is that I often and constantly award extra credit points to students who solve it fast, or elegantly, or using a different method from the one I showed them. Extra credit awarded wisely during the class is a great way to keep students focused and motivated.

Since motivation plays a very important role in teaching mathematics, then one of our biggest challenges as teachers is to show students that learning mathematics is important and enjoyable. So, the effort that I make to broaden my students' perspectives of mathematics and its relevance to their fields of interest is by regularly integrate applications of mathematics to various areas such as economics, business, biology, chemistry, physics, engineering and everyday life. I am particularly interested in reaching out to those students who do not think of themselves as liking or being interested in mathematics or who are afraid of any mathematical theory, while the other group of students who need particular attention are the well-prepared students, who need new challenges in order to progress further

One of the best "tools" in this respect is being enthusiastic about the topic being presented. I have repeatedly experienced that my excitement as a teacher eventually sparks my students' interest in the subject. This is another aspect stressed out by my students in the end-of-semester evaluations.

It is very gratifying to work with students and motivate them to do mathematics. Showing them ideas, some of which go beyond the courses, and watching them take off with their own ideas has been a very rewarding experience. I am proud of my teaching record and take great care to build interest and excitement in my students. When at the end of a semester I compare what my students know with what they knew it the beginning of the semester and I see good progress, I know my work was well done.

At the end of each semester, many of my students stop by my office or e-mail to thank me for the course and to tell me that they enjoyed it. A student in my Pre-calculus course wrote on a course evaluation \I felt I learned a lot more from him than many of my friends did in their calculus courses. Another student said \I just wanted to take a second to thank you for this math course. I will openly admit that I have hated math ever since I was in grade school. I just never had the experience of enjoying math. However, this math class I thoroughly enjoyed. You made it so much fun to learn, and another plus, especially for me, you made it easy to learn." Many other students that I saw later told me about how they were still using their notes from the course with me because they were so thorough. This is the type of feedback that I love to receive. It tells me that I am reaching my students and that I am achieving my goals in the classroom, and it encourages me to continue to approach every class with enthusiasm and the continued desire to offer an enjoyable mathematical experience for my students.

I love to teach. I incorporate different teaching techniques when they will help the students develop a deeper understanding of the material, and believe the same approach should be applied to the use of technology in the classroom. For instance, graphing technology should not replace a student's ability to graph a vector field, but it can help students understand the local behavior of a vector field with positive divergence. I look forward to further developing an effective teaching style with and without the use of technology.

Following these principles, I have been a very effective teacher and my intention is to continue on this path, while being open to any possible improvement.