I have recently completed my thirty-sixth year of teaching mathematics. I have taught students ranging from first grade all the way up to and including adult continuing education. The methods I employ are based on a system used in Japan called "zensho itashimasu", which not only shares the concepts used in Bloom’s Taxonomy and Kolb’s Learning Styles, but also expands and complements implementation of lessons in math that might otherwise be intractable due to situations dealing with, say, math anxiety. As one colleague put it: “Zensho itashimasu is to western education as a game of 'go' is to chess.”
Education & Certification
Undergraduate Degree: UC - Santa Cruz - Bachelors, Mathematics
Graduate Degree: UW - Milwaukee - Masters, Mathematics
(1.) Latin percussion with emphasis on Brazilian samba. (2.) Gourmet Food Club which has lasted seventeen years. (3.) Development of metafields to move us away from petrochemical fuel sources.
Q & A
What is your teaching philosophy?
Essentially, it is my belief that anyone can learn mathematics. All you have to do is help the student find the right key to open their particular door to understand any concept. To help with this process, the fear of mathematics must be removed. This entails showing the student a series of paths to reach a final destination when, say, solving an equation presents itself. Patience and encouragement are crucial here. As a final note, it is of paramount importance that the student sees the "where", "how" and "why" of the problems they're studying. Instead of manipulating abstract symbols which do not convey any meaning, the student can gain greater insight to see the reasoning behind the given assignments.
What might you do in a typical first session with a student?
By the time I meet with the student, I will have discerned what topics will be covered and, if possible, which textbook is in use. From there, I will find out the student's level of anxiety with respect to the material. I will then immediately put any fears to rest as I slowly introduce my particular methods in demonstrating the problems. If the student doesn't see the initial path I'm taking to, say, solve an equation, I will change tack to find where the level of comprehension lies. I'll use differently colored pens or pencils, "artistic" drawings to show what's happening and engage the student's hearing by using songs or sayings as gimmicks to remember techniques. When I let the student try to solve a problem, I'll let the student make errors. Then, I'll have the student trace the path of logic to see where an error was made. All the while, patience and understanding are of paramount importance.
How can you help a student become an independent learner?
In addition to using a Socratic method of instruction, it is crucial to remove all fear of mathematics. To help achieve this end, it is best to encourage any innovative methods or thinking that the student develops on his or her own. Patience must be in abundance. And students must be allowed to make mistakes. Otherwise, no true learning can occur.
How would you help a student stay motivated?
Here, the focus should be on encouragement. Praise should also be applied. As the material becomes more difficult, the lessons should allow the students time to absorb, process and then demonstrate their understanding. Once they see that they can overcome previously self-imposed obstacles, the road to total comprehension becomes much smoother and progress can accelerate.
If a student has difficulty learning a skill or concept, what would you do?
First, I'd find out the point where the student begins to have problems connecting the logical train(s) of thought needed to complete or solve the problem. Next, I'd see the best approach to use in conveying the trains of thought. If it entails using more than one sense, I would employ such a tactic. Example: If it's easier to remember a technique by turning it into a song, then that gimmick has been reinforced by engaging more than one sense-- namely sight and hearing.
How do you help students who are struggling with reading comprehension?
Since math is driven by symbols, it is crucial for the student to relate something in their experience to those symbols. What often comes in handy is utilizing the same techniques I experienced in all of my foreign language classes: translate "word-for-word" each of the symbols and their steps to build up a vocabulary that is understandable to the student. (I should mention that some textbooks are not as "student-friendly" as others. In that case, I tell the student that the textbook is hard to read at times, so that he or she does not feel alone in dealing with such challenges.).
What strategies have you found to be most successful when you start to work with a student?
Step 1: Remove any fears of math. I'll use humor or knowledge of pop culture to relate certain modes of thought or certain concepts to help build a bridge of understanding. Step 2: Tell the student that I, myself, once had failing grades in all of my math classes. (This is actually true.) And, now, I'm helping the student to overcome the same obstacles that I once faced. Step 3: Express caring concern and patience right away when a student feels in over her/his head.
How would you help a student get excited/engaged with a subject that they are struggling in?
By showing them how the math is used-- how it's applied--it can help to clarify and solidify the concept in the student's mind and perspective. Illustrations and pictures help immensely with this. As soon as I see the light of comprehension go on, I immediately encourage them to try a problem or two on their own using the methods I just showed them. If they have a different approach than the usual method, I'll let them forge head. I don't want to break the spell they're under once they begin to grasp the lesson in its entirety.
What techniques would you use to be sure that a student understands the material?
During a lesson, after I've slowly demonstrated the problem set a few times, I like to have the student show me how the succeeding problems should be done. If there's enough time, I'll even challenge the student to make up a similar problem of her/his own and see if she/he can solve it. If a dead end is encountered, we'll trace back the path of logic to find out where the snag is. Of course, I also administer small quizzes or tests to see how well the lesson(s) have been absorbed.
How do you build a student's confidence in a subject?
The telltale mark of a student who feels confident is when that student can anticipate the answer and tell me what it is before I'm done solving it. This is what I strive for; what I want the student to be able to do. There will be times when the student will get an incorrect answer, but I assure the student that it's a natural process of learning. I point out that it's often best to see what NOT to do when working through a problem. That way, the student loses fear of being incorrect.
How do you evaluate a student's needs?
Each student's individual personality and perceptions demand that certain approaches need to be used. To ascertain these things, I watch to see when and where they might stumble in a lesson, or if they respond to, say, my use of different colors on a whiteboard or piece of paper. I also make it a point to see how the textbook is written so that I can point out how to translate the "language" of math and make it tractable enough for the student to be able to read it on her/his own. All the while, I make sure to check that they're understanding the steps I'm using. If they don't, I'll go back and point out gentle math reminders of how to go through the process of calculating or proving what needs to be shown.
How do you adapt your tutoring to the student's needs?
Since each student is so unique, I make sure that I don't get caught in a rut with respect to my methods of instruction. I make sure to bring paper--lined and unlined--along with a small whiteboard accompanied by markers of different colors. I also bring extra paper, pencil and, if it warrants it, a calculator for the student to use. I emphasize that the student should have the textbook for the course at hand. That way, I can "mimic" the methods used in the text to maintain consistency in the lessons as presented by the teacher of the course. Note: In the event that the student has a disability, I make sure to compensate for whatever it might be in order to alleviate any stress or discomfort while the tutoring session is in progress.
What types of materials do you typically use during a tutoring session?
Whether or not I'm online, I always bring a small whiteboard with its accompanying easel, a set of colored dry erase markers, one or two calculators, various pens and pencils and an appropriate textbook for the lesson. (If the student can supply their own textbook too, so much the better!) I find it indispensable to carry tablets of both lined and unlined paper. I'm still adapting to the new technology that makes it possible for me to take a picture with a smartphone of notes I've made and then send it to the student's email address or their smartphone.