I thoroughly enjoy and am excited by mathematics and the teaching of mathematics. The effect, I hope, is contagious; I feel my students can sense my enthusiasm and, because of that, become more interested in mathematics themselves. I have found that nothing is more motivational to students than genuine interest in what they are learning.
My mathematics teaching style features a variety of methods of instruction that depends on: 1) the subject matter of the lesson and 2) my understanding with how the individual student best learns mathematics. I believe that students learn mathematics best by doing mathematics and then working to communicate about mathematics. Communication is the key to success. Most students want to get the right answer and then go about their business, when in reality the beauty of Mathematics is the clear communication of the thought that derives a solution. By teaching how to communicate mathematics, the student learns to be confident in mathematics; confidence, in turn, breeds success in mathematics. To support this goal, I frequently use the Socratic Method to elicit mathematical thought and foster engagement with mathematical concepts.
I have found that using multiple representations of mathematical ideas (e.g., algebraic, graphical, and numerical) is beneficial for two reasons. First of all, different students learn in different ways, and one representation may be easier for a student to understand than another. Secondly, knowing multiple representations and methods of solution makes for better problem solving; if students know several ways of attacking a problem, then there is a better chance of them being able to solve it. I insist on the use of technology in my instruction, especially the use of calculators and the use of the internet as a resource.
I strive to improve each and every time that I engage a student. Through my teaching style and methods described here, it is my hope that my students leave each session confident with their newly acquired understanding of their subject.
The Ohio State University - Bachelors, Secondary Education - Mathematics
What is your teaching philosophy?
Mathematics doesn't have to be numbers and X's and getting the right answer. It is a way to organize your thoughts, communicate what you know, and evaluate if what you are thinking makes sense. Look past the "right answer" and focus on the process, and then you will be successful.
What might you do in a typical first session with a student?
It depends on the student's needs. If they are interested in performing better on tests, then I would begin with looking at their previous performance to determine what areas of concern I can assess. Then, I'd begin to tutor towards those needs. If the student wants to supplement their learning, I would ask probing questions to get an understanding of how they grasp the topics they have learned and look for ways to improve upon their understanding.
How would you help a student stay motivated?
Motivation is driven by confidence and success. If a concept is troublesome for a student, the motivation to work with that concept will be missing. To change this, I attempt to rebuild the concept with the student one piece at a time until the light goes off in the student's head and understanding is achieved.
What strategies have you found to be most successful when you start to work with a student?
I like to start with getting to know the student's life outside of the classroom. What are their current interests? Are they involved in sports? Do they have favorite subjects? Then, as we begin to study, I try to connect the mathematical concepts we are learning to their personal lives, try to make the concepts less abstract and show how applicable they can be in daily life. I also find getting to know the student outside of Mathematics builds a trust between myself and the student that allows for open communications and keeps the dialogue flowing. This ensures the student is mastering the material.
How do you help students who are struggling with reading comprehension?
I often ask students to rephrase what they have read, and this allows me to gain insight to their overall understanding of what was read. If I find the student is not comprehending, I like to teach the student how to ignore the "filler" and pull out of the text the important items needed, and then try to rephrase the content again. This is a very valuable test taking skill that will help the student perform better and build confidence in their abilities.
How would you help a student get excited/engaged with a subject that they are struggling in?
As I've said before, confidence breeds success, and success can be exciting. When a student struggles with a new concept, it is important to develop that concept by using previously learned concepts that the student has mastered. Once you show how his or her prior knowledge is used to build this new concept, becoming engaged comes naturally. Build the concept slowly, then move to master the new concept at a pace the student can handle. During this process, it is important to bring in real life examples of the concept to show how the abstract has a basis in reality - this will also add to the student's engagement.
What techniques would you use to be sure that a student understands the material?
There are many ways to gauge a student's understanding of learned concepts. Primarily, I will develop a series of problems that gradually grow in difficulty to see where the student may be struggling, if at all. Another means of gauging the student's level of understanding is to have them create a sample problem themselves, and then explain to me how that problem fits the material we are studying. Similarly, I will have the student explain to me their thought process when they are solving problems, step by step, to gain insight to their understanding. But the best way to ensure a student is understanding the material, is to ensure and reinforce the need to be descriptive with their problem solving. By this I emphasize the need to write down all steps, regardless of how trivial the student feels the operation is, as a means of teaching the student that math is as much of a communications effort as it is a problem solving endeavor. By insisting on this detail, the student shows their level of understanding and becomes confident in their efforts.
What types of materials do you typically use during a tutoring session?
This depends on the subject matter and the student. High level mathematics generally lends itself to pencil and paper when we discuss solutions; however, using electronic media and internet connections help demonstrate how to research mathematical concepts while urging the student to put the concepts into their own words. The internet is a wonderful tool to assist with learning. For lower level mathematics, I will use whatever tools and materials are necessary to help a student understand new concepts.