Our Teaching Philosophy
I guess you could say I am a bit old-fashioned in my teaching philosophy. Though the current trend in the field of mathematics is to incorporate computer programming, computer labs, group projects, and the writing of papers in high school math classes, I try to focus on the teaching of mathematics. I am not opposed to computer programming, the use of technology, or even writing assignments, but I do not want to incorporate those things into my classes at the expense of the mathematics. I like to stick with algebra, geometry, functions, and trigonometry, for the study of those subjects not only prepares students to use math practically, but, perhaps more importantly, teaches students to think.
Math is a study of logical and analytical thought. Though technology can be helpful, and I certainly use my fair share of it teaching online classes, it is ever changing and often more of a distraction than a help for high school math students. Logic and analytical thought, however, are timeless. Thinking logically is a must for a person to excel as a doctor, engineer, lawyer, writer, pastor, scientist, detective, computer programmer, architect, or web designer. Logic will serve a student well in any career or life in general. Often, the modern trend in high school math is to move away from the teaching of logic and analytical thought and replace it with more attention-grabbing, fun activities and assignments. Math is reduced to practical arithmetic, following the steps, group discovery, and dabbling in technology. A diet of this type of math instruction is much like a diet of candy. It is attractive and readily digested but of little lasting value. Traditional math instruction, however, is more like a nutritious meal. Though not so brightly colored and a bit difficult to digest, it has sustaining, life-giving value. A student of traditional high school math subjects will learn to enjoy the less easily digested problems and shun the candy-type ones.
I teach math one definition, postulate, property, or theorem at a time. I seek to have the students understand how postulates and properties reflect truth and how theorems build on them through proof. Especially in geometry, I teach students to prove statements themselves, and give plenty of practice so they can become confident in writing proofs. I try very hard to teach in a way so that students understand concepts rather than memorize steps. When I don’t think a student is following me, I try again from a different angle. I give assignments that mimic problems I have completed as examples so students can become comfortable doing such computations themselves, but I also assign problems that are not as straightforward. That is how students learn to think analytically. High school math students may spend as much time sitting and thinking as they do writing. That is a good thing. If students learn to think through problems for themselves, they have certainly learned a lifelong skill.
I am ever mindful that my students may have plans to enter a math related field of study in college, and they are expecting adequate preparation from Liberty Tutorials. That is why I have chosen top-rated textbooks and teach them in their entirety. Although I feel very strongly that proceeding in a textbook when a student has not mastered the concepts at hand is a situation to avoid, if I slow the pace to accommodate a few stragglers I will not finish the textbook. I am always available to answer questions by way of email, and encourage stragglers to get the help they need, but it is their responsibility to do so. Parents and students should realize Liberty Tutorial tutorials are honors level classes and should be prepared to spend the necessary time to keep up.
Finally, I love math and try to pass that love onto my students. I see challenging problems as puzzles to conquer. I find satisfaction in figuring out a proof. The orderliness and precision of math is truly beautiful. Most of all, math is a reflection of God, its Creator. As my students gain in its understanding, I hope they will gain in their understanding of God as well.