In my undergraduate and graduate matriculation, I have heard so many students state their dislike of mathematics for various reasons, from having a “bad” high school mathematics teacher to saying the subject is just too hard to understand or requires more than they wish to give. Most students I have taught said they lost interest in mathematics when they studied algebra in high school. Moreover, they also believe that mathematics is simply about memorizing formulas or plugging numbers into a calculator. It’s my opinion that there is more to mathematics than using a calculator, memorizing formulas, and using formulas to answer questions correctly on an examination in order to simply receive a good grade. I also feel that the teaching of mathematics should be devoted to more than simply transferring mathematical facts from the teacher and a textbook to a student’s mind. As a mathematics professor, my objectives are:
1. To invoke critical thinking of mathematical concepts in students;
2. To instill in students a deep understanding of mathematics;
3. To illustrate how mathematics is used to solve real-life problems;
4. To ignite in students an interest in mathematics where such an interest does not exist.
Doing this can be a difficult task, but it is a task I welcome and enjoy undertaking.

To invoke critical thinking of mathematical concepts and to instill a deep understanding of mathematics in my students, I try to pose questions that not only address not only the question of ‘what?’ but  ‘why?’ and ‘how?’ Each time I have taught a course in College Algebra, students in a business-related major have asked me a question such as, “When will I use ever use this algebra stuff in my life?” My responses have included, “Suppose you’re an entrepreneur in book production, and your profit can be viewed graphically using a quadratic function. You can use algebra to identify the price at which an item should be sold in order to maximize the profit you wish to make. Therefore, I encourage you to not give up learning algebra. After all, understanding it may give you the tools needed to sustain a great-paying job after you graduate.” After hearing this, several students begin to become more involved in their studies of College Algebra.

In my teaching I have noticed that many students memorize mathematical formulas without truly understanding them. Therefore, it becomes difficult for them to understand how the same formulas are applied outside the context in which they first appear.  I hope to deepen my students’ understanding of mathematics by encouraging them to combine ideas and tools they have already learned with the concepts and tools that I present.

To illustrate how mathematics is used to solve real-life problems and to ignite in students an interest in mathematics where such an interest does not exist, I use examples involving mathematical concepts and I teach students how to develop a systematic approach to problem solving. I have found that situations reflecting real-life problems increase students’ zeal to learn and apply the subject material presented in class. In my teaching, I first show students how to understand the information presented in a real-life problem. Students can then see the scope of the problem and make assumptions when necessary. Then I teach them how to translate the problem from its verbal or written statement into a problem involving the mathematical concepts they have learned. This is done in way so that students can formulate the problem in different ways, thereby suggesting multiple approaches to solving the problem. Finally, I have found it useful to encourage students to consider analogies whenever they become stuck on a particular question or idea. Once as I was discussing the concept of discrete compound interest, a student noted that if $88.72 is compounded monthly at a 6% interest rate, then a return of $100 is made after two years. The student felt that the return was rather small considering that one’s money is compounded 24 times over a 2-year period. I responded by saying that if the investment were larger and was the balance on a credit card, then one would want the interest rate to be low so the credit card balance would not be very high if the balance is unpaid. The class then began to ask questions about how the problem should be modified to increase the return on the investment. From this experience, I realized that students become interested in mathematics when they see it being used in real-life problems.

To conclude, I evaluate my students through a combination of homework assignments, quizzes, examinations, oral presentations, and class participation. Joint homework assignments and peer discussions help students to collaborate with and learn from their peers. Furthermore, I encourage my students to engage in collaborative learning. I grade all written assignments thoroughly to give the students feedback on their progress and I encourage students to meet with me to discuss their work. In my quizzes and examinations, I try to test students for problem solving as opposed to facts. I have found that if one tests students for facts, then students will learn how to memorize and recall facts. If one tests students for problem solving, then students will strive to be better problem solvers. Finally, to measure my effectiveness in achieving my objectives, I encourage students to submit evaluation forms that state their honest opinion of the subject material and my teaching ability. I then use these evaluations to insure that I teach my next course differently and with more understanding from the students’ perspective. Finally, for future courses, I plan to not limit myself to my current teaching methods. I will always be open to implement and/or develop other methods to inspire students to develop life-long learning skills so that they are prepared to function effectively in society. I feel it is important for me to be a professor so that I can make a difference in the lives of students by showing them the joy, beauty, and power of mathematics in particular and learning more about the world in which we live in general. In my opinion, a great reward of teaching is the joy of seeing a student come alive in the classroom when he/she has mastered the concepts and techniques of a course the student once thought would spell the end of his/her academic career. I receive this reward when a student comes to me and says something such as, “Thank you, Professor. Until now, I never thought I would graduate because of my math anxiety. You pushed me and made me realize I can do this if I just try harder and stop trying to make excuses. I am now ready to learn more about mathematics because of your course.”