In modern society the best and brightest scientists are going into research related positions with small teaching loads leaving minimal time for the effective teaching of undergraduate and graduate courses. The United States is falling further behind other countries in the mathematical ability of the students going through our educational system. I want to be part of a new trend in science of motivating and facilitating some of the top thinkers into becoming top teachers. One researcher may work on projects that affects 20-40 other scientists working in a related field. One effective instructor can positively impact 50 future scientists in a one semester course. Over 30 years, 3000+ students have gained a new appreciation for mathematics. While some young mathematicians have a personal goal of being the next great researcher, I strive to actively mentor and guide my students to develop the skills necessary to be the next great scientists. Teaching mathematics is not only teaching methods and algorithms, it is teaching people how to think logically and efficiently.

I try to convey a three central ideas in any course I teach. The first is that a student should, over the course of the semester, develop critical thinking skills. For mathematics specifically, this means being able to adapt to different problems within the same general regime of the topics being taught. The beauty of the subject is realized when one can step back and discover that a whole class of problems can be solved using a given method and not just the exact example solved in class. This is not easy for student since it requires the development of critical thinking skills and the ability to look at a given situation from a more general perspective. The second objective is to cultivate problem solving strategies. This is directly related to thinking and working efficiently. In mathematics there is often more than one way to solve any problem, but why spend 40 steps deducing the solution to a problem capable of being solved in three steps? My hope is that a student leaves my class knowing not just how to do problems #2-32, but confident he or she could solve any problem within the course textbook. Once a student develops the skills of problem solving and critical thinking no problem should be too difficult. Finally, my most important objective is to encourage students to appreciate and respect the subject of mathematics. My goal is not to turn a room of 50 students into 50 mathematicians, but to provide through high energy presentations and motivation the realization that math is important for the world around all of us. Once students respect what they are doing mathematically and see the value, they will spend the time necessary to excel in the course. This last objective is the most challenging. Some bright students can ace all assignments without ever truly understanding the subject. Mathematics is a tower in which each course builds on the next. If a student passes a course without developing critical thinking skills, problem solving strategies, and a respect for the subject the next course begins on an unstable foundation. Thus it is important to work towards these goals from start to finish in every class taught.

Having objectives is a good start, but one must devise ways to meet these objectives in the classroom. I begin the first class with the statement that this class with be based on mutual respect; I will treat each student with respect, but students must return that respect by being present in class and paying attention. In my personal experience placing the burden equally on student and instructor has been essential at stopping most potential problems before they even begin. The second thing I convey on the first day of class is for students to turn to the last page of the syllabus where I have outlined four keys to success in any mathematics course:

1. Do all the assigned homework problems. Practice is essential for mastering the skills in any mathematics course.
2. Find a group of friends in this section or another that you can work on homework together with and discuss solution methods and ideas. No one can solve every problem on his or her own, and it is important to gain from other's strengths. Teaching a solution method to another student is a great way to reaffirm the ideas in one's own head. On homework students practice the skills learned in class, and a student learns far more by working with others than on his or her own.
3. Do many practice problems from the chapter review section or sample exams and come in to office hours when stuck. This is the best preparation for the course examinations.
4. As soon as something is unclear, make a point to ask me to clarify either during office hours or before/after class. It is crucial to identify areas in which students are struggling before they get to the exam.

Objectives are great to possess, and strategies for implementation are even better, but one needs to be able to measure the effectiveness of both. Ronald Myers, Associate Professor of Veterinary Pathology, states ``I have come to realize that ultimately students learn what we examine for. If we test learning of facts, students learn facts. If we test problem solving, then they learn to be better problem solvers." I believe if we make exams that test critical thinking, then students will learn to think more clearly and develop the necessary problem solving strategies to tackle reasonable problems within the subject matter of the course. Mathematics is not the learning of facts as some students might cite, but instead it is learning how to learn and think deeply. There is no greater feeling as an educator than witnessing the process of learning. Once the light bulb goes on in a student's head and that student is energized by the subject, it is like a torch that cannot be smoldered. Teaching is a delicate practice, the impact one teacher can have on a student is immense. A good instructor can motivate students to work hard and learn, but a poor instructor can foster in a student the attitude that he or she lacks some genetic trait for being good at mathematics. As an undergraduate student, I looked to my professors for a model of how to approach a subject and how to work to succeed. I want to be an instructor who students feel comfortable sharing their academic problems with and seek help from. I want to be the teacher that makes the difference in each student's education.