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The core of my teaching philosophy is that you can't teach people things that they have no desire to learn. Therefore, the key to teaching is always to spark a student's interest in the subject that you're working on.

Day one with a new student is typically equal parts gauging where the student is at with a subject and establishing a relationship with him or her. I like to talk about the students’ interests and get to know them, as a more personal relationship with them builds the foundations for long-term success. When we do come to the topic at hand I ask general questions about the subject in an effort to get a broad view of how comfortable they are with the material. This allows me to figure out whether the trouble with a subject is more conceptual or more practical, and, with that knowledge in mind, tailor future sessions to the students’ specific areas of weakness.

One of the best ways to help students become independent learners is to teach them how to figure out how general groups of questions should work instead of teaching how to do specific questions. If you can teach a student how algebra should work or how an argumentative piece should be written, they can take that knowledge and use it to learn topics that they've never worked on before. Teaching how subjects should work and why they should work that way empowers students to tackle the next subject on their own.

To motivate my students, I always try to spark a genuine interest in the topic. The most common way I do this is to find a link between what the student already enjoys and the material I'm teaching. For a student very into art who is struggling in math, this might be a discussion about the math behind what makes an image aesthetically pleasing, such as the golden ratio and the Fibonacci Spiral. Alternatively, for a math buff that needs help in English, this could be a talk about the similarities between the logic that underpins argumentative pieces and that which supports mathematical proofs. If one looks hard enough, there are always links to be found between any two subjects.

I'd take a step back from that concept and start working with the student on the ideas that underlie what he or she is having difficulty with and remedy any problems he or she might have with those skills. Once I feel that the student was on solid footing I'd try to explain how the concept was a logical consequence of the fundamentals that we had just reviewed. Additionally, I might try to disguise problems containing that idea. For example, if the student was studying with x being a variable in algebra, I might rephrase algebra questions with variables as fill-in-the-blanks, turning 2x = 8 into 2*___ = 8. If the student could master these modified questions, I'd then ask him or her how they solved those and tell them to apply the same steps to tackle the original concept.

One of the main tips I give to students struggling with reading comprehension is to visualize the world of a piece of writing. If it's a novel, picture the setting and characters. If it's an opinion piece, pretend the author is speaking to you verbally. This enables them to better use the context provided by the writing to deduce the meaning of unknown words. If an author is describing a warm, sunny day in a green meadow and describes a character as "beatific", whether you know what the word means or not, it's a safe bet it means something close to happy or content.

I have found that talking informally about the subject that I am tutoring the student on is a great way to both get an idea of where areas of weakness are, as well help the student realize what he or she already knows. In many cases students know more about a topic than they think they do, and an informal discussion can help them realize this. Additionally, this is a great tool for helping students fully grasp concepts that they only partially understand by using what they already know to fill the gaps in their knowledge of the idea.

Finding a tie-in between a subject that a student is struggling in to a topic they enjoy can spark an interest in the topic. If someone who loves numbers were having trouble in their history classes, I would try to teach history with a heavy emphasis on statistics such as casualty figures from a large war or a chart showing how quickly the percentage of people living in urban centers shot up around the turn of the century. If you can find a piece of a subject that a student enjoys, it's easy to get them engaged in the subject as a whole.

To check for thorough understanding of a topic I would have the student try to explain the concepts underlying the subject. Showing the student a flawed way of tackling the material and asking him or her to spot the flaw and explain what the person in the example should have done is also a useful tactic, as a student must know how to do something correctly in order to spot a flaw in someone else's work. Finally, a good technique to check for full understanding is to introduce a related topic that depends on the one I'm trying to check. For example, I might introduce exponentiation to check for competency with multiplication. If a student can evaluate any two-digit number to any power, they almost certainly can multiply two digit numbers since exponentiation is just repeated multiplication.

I find that my approach of starting with teaching the fundamentals of whatever topic I'm working with the student on has an added benefit of being a confidence builder as students are typically familiar with the fundamentals and can do some problems concerning them. Even if the student's command of these foundational topics isn't complete, they get enough right and improve quickly enough to not get discouraged. When we move to more complex areas of the material, I'm careful to design my problem sets so that they start off easy, and gradually get harder. This approach both allows me to identify exactly where a student's problems begin and builds their confidence as they can see that they are improving over time by getting farther and farther into the problem sets before stumbling.

One of the best ways to evaluate a student’s needs is simply by talking to him/her about the subject. I simply come up with a handful of hypothetical questions, see how they answer them and ask them to explain. I pay more attention to the explanation of the answer than the answer itself as the explanation provides insight as to how the student thinks and where gaps in his knowledge might be. I also find that multi-part questions are a good way of determining a student's comfort with a subject as they not only evaluate how comfortable a student is with each individual part, but also whether or not they understand how the parts connect.

Different people learn in different ways. Some people are auditory learners, they like to hear what they're being taught and they absorb information well that way. Others are visual or tactile learners who learn better when they can see or touch the topic at hand. I try to determine what type a learner a student is and then design lessons with that in mind and bring in manipulatives such as timelines or fraction strips for visual or tactile learners.

I always use pencil and paper (a lot of paper, I like to write big when explaining things). Additionally, I often bring in colored pencils, which allow me to organize different topics by coloring and highlighting differences. Depending on the subject I might bring in a timeline with index cards that can be moved around or some pre-printed worksheets I made the night before. I also typically bring my laptop in case I want to use sites for visualizing functions in math or as a random number generator to illustrate points about probability.