Hi. I'm Scott Zweydorff. I've been a tutor for about 5 years. I am trying to tutor more frequently, now that I have a math degree, while I wait to begin graduate school for math in the fall. Before I developed a passion for math, I was a student of visual art and music. In fact, I became interested in math because I began (suddenly, with a little help from art manifestos) to see it as sculpture. (In my free time, I create computer animation using both math and programming skills.) As I tutor, I like to communicate this enthusiasm. For instance, learning to graph functions is simultaneously to learn how to draw various curves with algebraic formulas. So the symbols and numbers can be looked at like a code for drawing pictures with as much precision as desired. Along the same lines, solving equations is lot like playing chess. The 'x' piece has to be moved around according to the rules of the game so that it ends up along on one side of the equals sign. But bigger than any particular type of problem and solution is the way that understanding math can sharpen a person's perception of the world. Math as a discipline trains us to think more logically and more exactly. We become more aware of what we know and how well we know it.
University of Louisville - Bachelors, mathematics
GRE Quantitative: 160
GRE Verbal: 170
What is your teaching philosophy?
I have tutored enough students to realize how differently all of us learn math, so my philosophy is to set goals and act as a helper on the way to the attainment of those goals. In my opinion, it's very important for a student to understand how to check their answer, so I like to encourage students to tackle the problems they can handle on their own, checking them in the back of the book or with a calculator. In short, I show them the basic technique, let them use it to the degree that they can, and then we recognize and address difficulties together. The student will have to face difficult tests in the classroom alone, eventually, so there is really no way around the development of a confident mathematical independence. Of course we all have questions as we learn math (and even doubts about the rules!), so it helps to have someone who has worked through those concerns reassure them that the rules are well-designed by explaining the necessity or justification of the rule in the particular, troublesome case.
What might you do in a typical first session with a student?
When I start with student, I want to get a sense of their current skill set and current level of enthusiasm. I encourage them to work through for me, step by step, the sort of problem they are currently wrestling with for school. If they are not that enthusiastic, I try to reframe the math as a game or a puzzle to be solved. If they are creative or artistic, I might briefly discuss how the seemingly boring math in question actually opens up a world of creative possibilities. There is poetry in math. Just as we need basic grammar and spelling in English before we can write a sonnet, we have to learn the basics of mathematical language in order to get to the creative math. Of course even basic math is already fun, if not yet creative.
How can you help a student become an independent learner?
I am a firm believer in wrestling with the odd problems -- or with whichever problems in the text are answered in the back of the book. I do not believe that tutoring alone can make an independent learned, but a tutor can indeed stress independence and self-checking. A student should attempt the odd problems before seeing the answer. If they get the wrong answer, they should try to see where they went wrong. This is something we can do together in a session but is itself a skill to be learned with practice away from the tutor. Depending on the level of the material, a calculator might provide an easy check for the solution of an equation, for instance. So I also stress using the calculator or other tools to speed up the feedback process. I show the student how and why the answer can be checked with a calculator in many cases. This helps the student become independent from any individual text.
How would you help a student stay motivated?
Doing math well is something to be proud of. It's not unlike learning to play guitar. I think sincere praise and enthusiasm goes a long way to help the student stay motivated. If the student has ambitions in science and technology, then math skills are especially important. So, if all else fails, I can paint a brief picture of the math ahead and stress how mastery of the fundamentals will pay off all through one's technical/scientific education.
If a student has difficulty learning a skill or concept, what would you do?
I believe that math is more linguistic and metaphorical than is perhaps usually recognized. Sometimes we need to unlearn before we can learn. So I like to listen to the student’s concept of what is going on in order to see what incorrect assumptions are blocking the assimilation of the correct concept. As one famous mathematician said, math is refined common sense. As another mathematician has said, math is exactly what we do understand. So I believe the ability to assimilate the concept is natural. It's just that mistaken concepts can get in the way so that cognitive dissonance interrupts the learning process.
How do you help students who are struggling with reading comprehension?
I am passionate about the paraphrase. In my opinion, there is no greater test of one's own understanding than putting an idea in one's own words. So in such a situation, I would offer several paraphrases and then invite the student to paraphrase these paraphrases. Learning to read more formal or adult prose is not unlike learning a new language. I think paraphrases can build bridges from the student's everyday language to the more formal or adult language use that is required at school.
What strategies have you found to be most successful when you start to work with a student?
I believe that a basic rapport and trust must be developed. A student has to want to learn, and this desire to learn fostered by a safe and encouraging interpersonal environment. I cast myself as their ally in what is really a grand project, namely self-education. The tutor’s job is to encourage and facilitate what is finally the struggle of an individual intellect to assimilate the difficult but often beautiful thinking that came before them. We don't only learn from tutors and teachers, but, perhaps more importantly, we learn HOW to learn, by example and encouragement.
How would you help a student get excited/engaged with a subject that they are struggling in?
I believe that each student must be recognized as a valuable and unique individual. Certainly they are interested in something, and this is a good place to start. How does math connect to their interest? Of course reading connects to every interest, since reading skills allow us to find out for ourselves on our own schedule.
What techniques would you use to be sure that a student understands the material?
There is something slippery and subjective in understanding, especially in math, since two different intuitive pictures can both lead to the correct result. In my view, being able to find and check the correct answer is understanding enough. While I offer what I consider the best intuitive pictures of what is going on, I do not believe in forcing one particular intuitive picture on the student. I would, in short, test the students understanding by watching them solve and check a sufficient number of problems.
How do you build a student's confidence in a subject?
Again, this is where self-checking comes in. As a student myself, I felt prepared for a test once I could work through the problems in the book and consistently get the right answer. Ideally, the student learns how to check even the problems without answers in the back of the book. In short, we just keep working through problems together until the student is ready to tackle such problems on their own. Once they are confident they have assimilated the new skill, we move on to slightly more complexity. In math, this usually means adding one more twist to the theme in question.
How do you evaluate a student's needs?
I encourage students to interrupt me with question at any time. I strongly believe in the value of interactivity. As a student myself, I always benefited more from classes that were open to questions and interaction. Furthermore, I endorse the cliche that there are no stupid questions. Any sincere question is a great question.
How do you adapt your tutoring to the student's needs?
Fundamentally, I want the student to learn solve problems without any help, and, for me, this includes being able to check their answers whenever possible, so that they can enjoy their success. As a tutor, I use the ancient human technique of trial and error. If an approach is not working with a student, I switch my approach until something works. And I listen when the student tells me how they prefer to learn --- as long as it leads to their ability to solve and check problems.
What types of materials do you typically use during a tutoring session?
I like #2 pencils, blank paper, and the appropriate calculator. It's often handy to have the internet available, since so many necessary formulas are on Wikipedia. It's often faster to google than to search through a paper book.