TEACHING PHILOSOPHY
Philosophy
This philosophy is very complex because people are complex. I must reach each student, and since no two people are alike, there is a need to have a very flexible and individualized approach each semester and possibly for each student. Thus, my philosophy cannot be expressed in one page—it is simply a “template” for generating interest to reach all students.
Teaching Philosophy of David Seff
Use of humor: The use of humor creates a pleasant and friendly classroom atmosphere.
“Hands-on” math: This concept varies with the course being taught. For advanced classes, on the first day, I may challenge them with problems that show how the math to be taught in the course can be applied to real-life problems in the students’ desired professions. For elementary courses, on the first day, for example, I give them strips of paper, scissor and tape, and ask them to make a loop which they tape together. Then I ask them to draw a red line on one side and blue line on the other—a task that they can easily accomplish. Then I show them how to take another strip, give it a one-half twist before taping together, making a Moebius strip, and then I ask them to draw a red line on one side and a blue line on the other. They cannot, and are amazed. I then mention that not everything has two sides. We then cut the strip down the middle and count the number of sides and edges. A homework assignment is to tabulate how many sides, edges, and twists there are in strips of paper that are taped together if first there are anywhere form 1 to 4 half-twists, and then we cut it 0, 1, or 2 times down the middle. Then we find patterns in our results.
Another example: By developing a little march I show students how to add and subtract signed numbers. One student, who was a kindergarten teacher studying for her master’s degree in ed, took my course, adapted my method for her kindergarten students, and reported to me that every single student, without exception, could add and subtract signed numbers without a single mistake within one week. Here most students may spend months trying to learn how to do so in the seventh or eighth grade, and are often frustrated, and not successful, but using my method, which I would like to demonstrate, an entire kindergarten class, mastered the task flawlessly within one week.
Only teach one idea at a time: Break a complicated concept down into smaller simpler ones: This idea was essential to teaching addition and subtraction of signed numbers. There are many things happening simultaneously. I break the topic down into over one-half dozen smaller topics, each one of which is easily learned. Yet I have never seen a text book break it down into such small pieces.
Non technical math: For elementary math, many students who have math anxiety, and math without numbers is a good way to start. The Moebius strip is just one such item we studied, and there are many others. For more advanced courses and students, I emphasize the concept of precision and the need to communicate in a precise “mathematical” way. Students are taught how to understand the technical wording of a math text or problem and to communicate orally and in written fashion that is clear and concise.
Don’t teach—let the students discover the ideas themselves: Games and Puzzles are a key to self-discovery: Of course, I do try to explain things, but first I try to present an interesting game or puzzle and challenge the students to figure it out for themselves (often for extra credit). Students will teach each other and they will also learn as they play. Enclosed is a game called “Magic 15” and one puzzle entitled “Knights and Knaves.” “Magic 15” was used in both elementary courses and in more advanced courses in introducing the concept of isomorphism. “Knights and Knaves” puzzles were also used in elementary courses as well as in some advanced courses, such as logic or technical computer courses involving the underlying mathematics Please see Appendix A.
Aesthetics and Beauty: Another enclosure is a picture of the “Lo Shu,” a Chinese Geometrical Pattern based upon Magic Squares. It is just one of beautiful patterns that can be appreciated, seen, and studied that are mathematical. All of mathematics contains physical and abstract beauty that can be appreciated if presented properly. Please see Appendix B.
Build Confidence—I never call a student by name to answer a question unless I feel confident he or she knows the answer. Please see Appendix C for one of my happiest teaching experiences.
Let the students teach each other—to lead the class, to answer questions, or to break into small groups. They are not as scared of each other as they are of the teacher, and a student, even if not as talented as Janet (please see Appendix C) can often do a better job of reaching other students. There is no need to stand on ego. My goal is that the students should learn the material in a happy and comfortable way, and if stepping aside will do it, then I will.
Be a taxicab driver: I tell my students, my job is not to teach them math, but how to think mathematically and how to utilize their brain and thinking ability to the maximum. My goal is not to make mathematicians out of them, but to take them where they want to be. I am only showing them how to utilize their innate abilities better in order to go where they want.
Take all questions: I tell them the only stupid question is the one that is not asked.
Fill in the gaps and understand: Many students get lost at an early age, and then they merely try to memorize gibberish that makes no sense, and eventually get frustrated or give up. For some classes, I emphasize going back to basics—even using flash cards so students know their tables. We are not to move ahead until each idea is clearly understood by all. I explain math is not like world history whereby a person can fail the “history of England” test, but still ace the “history of France” test. One missing idea from the second grade can make math impossible for them. It is more like trying to build a castle out of Lego blocks. Remove one from the bottom, and the whole structure crumbles. It is necessary that every basic idea be explained and fully understood clearly. Without a firm foundation, everything crumbles.
Example: Many students have not heard of the distributive law. Those who have and use it properly do not usually understand it. I show how this law is nothing more than the mathematical way of saying a fact they already knew--that the grand total of a rectangular array of numbers may be obtained either by first adding the rows to get row totals and then adding the row totals to get the grand total or by first adding the columns to get column totals and then adding the column totals to get the grand total.
Go slowly and review often—then give interesting homework problems. Our goal is not to be able to boast about how much ground has been covered but to have good comprehension and a true grasp of the material so the students will feel confident that they now have new knowledge and new skills. If filling in gaps or extra review is necessary to attain this goal, then we will provide it. We want to be sure the students understand the material, and become confident that they can advance.
Everyone deserves a second chance: I tell students that even if they fail a test, they can still pass. The purpose of tests is NOT so I can give a grade, but so the student will learn where they need extra help and come during office hours to get it. If they do, I will give a make-up or ask similar questions on the next test. If they do better, the earlier mark will be erased and replaced by the next mark. It is theoretically possible to fail every test and get an A in the course. I tell my students it is not a race to see who learns the material first—they simply have to learn the material during the semester—if they can do well on the final, it means they learned the material and will get a good grade regardless of previous performance.
Student responsibility: Students must recognize that learning is NOT a passive experience. They must be VERY active and do their share. They must come to class, pay attention and follow directions (please see enclosure called “Knack of Following Directions,” Appendix D), turn OFF all cell phones and put them away out of sight, do all required reading and exercises, be honest and ask questions if something is not clear, come in for extra help when necessary.
David Seff
Appendices >>>