I have had success in assisting mathematics and physical science students during my time as a tutor at both Morton College and Triton College.
Admittedly, it was not easy at first. As time went on, I became more effective. I began to recall my own thought processes as I struggled with certain concepts through the course of my education, and was able to place myself in a student’s shoes. In high school, I was an enthusiastic and competent science student, having taken honors biology, chemistry, physics, and finally, AP chemistry senior year. I was very fortunate to have a future Golden Apple recipient as my guide into the intricacies of the periodic table.
My thinking today has the benefit of being peppered with professional experience as an engineer. I have a socialized (and self-serving) construct as my main motivation for learning. I often ask myself questions such as, “How can I diagnose a problem or create a solution to satisfy the customers need, so that we may mutually benefit from this project?” I long ago realized that, I am worthless, or at the very least, worth less, from a financial standpoint, if I have to inundate another person with questions to help me solve a problem. There is also the possibility, which is often the case in the real world, that no one is able to help you solve a problem, but yourself. You are the best possible authority on the matter available! If you cannot find an answer, the customer will send you on your way, and begin a search for someone who can.
If one wishes for a vocation in any of the physical sciences, there is no substitute for total immersion into the questioning of the nature of matter and energy. Not long after I began my sophomore engineering classes, I read a quote from Nikola Tesla that stuck with me. After having collectively delved into chemistry, applied mechanics, electromagnetics, and signal processing, this statement is now self-evident to me:
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
It is dogma to me, and I have found it to be key concept for teaching myself, as well as teaching others.
Most of the students I worked with at Triton came in for introductory or college algebra, and chemistry. Being a former chemistry major, I was able to use teaching tools given to me by my Morton College instructors, and my Illini professors (as well as Tesla’s wise admonitions). I would also be remiss to leave out my dearly departed father. He was an electrical engineer for 39 years. When I had trouble with trigonometry and calculus, he was always there.
I will never forget when I was having trouble with calculus I. He bought an extra copy of my textbook. In his free time, he refreshed himself, and neatly worked out solutions to dozens and dozens of problems, and helped me understand them all. What that man did for me, I will be grateful for, for the rest of my days.
After that course, I never needed his help again (except financially of course). Even my second course in differential equations came relatively easy.
During my junior and senior years, I developed the habit of getting my hands on any relevant books that I could. I checked out alternative textbooks for my difficult courses from the engineering library, usually 8-10 at a time. I also acquired a collection of selections from the REA Problem Solver and Schaum’s Outlines series, on a broad range of topics. I still have them all (not the library books, of course), and continue to buy more.
I have always emphasized copying this behavior to all of the students I have worked with. When a certain step is unclear, my first line of attack, is the Socratic Method. I can usually get ideas through by backtracking a bit, asking a series of questions not only to draw individual answers, but also to encourage fundamental insight into the issue at hand. I personally am a combination of a visual learner and tactile learner. I can usually absorb something, even if I have to resort to copying a graph or a free body diagram directly from the text. I have shown this method many times. I believe most of the students I have worked with, who took the time to share this approach benefited greatly.
There are also some magnificent tools these days that were not available for all previous generations of students. Information on internet is not 100% reliable. This is especially true if one is seeking facts regarding issues of controversy, politically, historically, economically, etc. However, if one just scratches the surface, there is wonderful world of knowledge and learning tools for mathematics and the physical sciences online.
I have seen many thousands of interactive java applets and animated .gif files that instantly describe better than a thousand words, trends that take place over a time interval, or difficult to visualize 3-D phenomena such as atomic orbitals. For example, I was recently reviewing Fourier series. A Wikipedia article included an animation which demonstrated a sine wave begin to resemble a square wave as successively more odd harmonic terms were added.
Overall, these teaching strategies must be uniquely blended in accordance with the official instructor's own philosophical beliefs of education. All efforts must be governed by the pupil's background knowledge and experience, situation, and environment, as well as learning goals set by the student and instructor.
In closing, I would like to relate a fond memory. After a particularly trying semester, a group of students that I had worked with since week one, stopped by the center, to let me know they had gotten mostly A’s and a couple of B’s. After twisting my arm and ignoring my warnings about mixing business with pleasure, they summarily dragged me off of the campus to the Pizza Hut on North Avenue and bought me dinner. I think they were just buttering me up for next semester.
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