The mind is like a muscle that must be trained in a progressive manner. In math, this would mean NOT moving on too quickly from one concept to the next, which is what separates good math teachers from the not so good ones. I make absolutely sure my students have internalized step A and can perform it by themselves before moving onto step B. Like the floors of a building, math concepts build on each other and must be fully understood so the structure remains stable.
In short, knowing and teaching are two different things. I know my Algebra and Geometry through and through, but perhaps most importantly, I have a knack for teaching it as well, with efficiency. I connect well with people, and am committed to making sure my students strive for success.
What is your teaching philosophy?
Information, especially in math, builds on itself. If a student doesn't understand concept A, concept B will be that much harder to grasp. This is why it's important to make absolutely sure the student understands a concept before moving onto the next. If he or she "sort of" gets concept A, and "sort of" gets concept B, the building that is their math skills will be an unstable one, more like a house of cards.
What might you do in a typical first session with a student?
Most importantly, a first session would include seeing where the student is in regards to the material. Are they stuck on a particular problem or concept? Do they fully understand the concepts the troublesome problem inevitably is built upon? In other words, I would make sure they have a firm grasp on the information needed to solve the current problem, before actually helping them solve it step by step.
How can you help a student become an independent learner?
I would try to motivate the student to want to do well. Almost like it is him or her against the material, and they must win. Make them the hero of their learning journey so they can save the day.
How would you help a student stay motivated?
I would see where the gaps are. How are they going to find the circumference of a circle if they don't know what the radius is? How are they going to find the length of the hypotenuse of a right triangle if they don't know what side the hypotenuse is? Or what a right triangle is for that matter. It's so vital that the student understands A and B, before they move onto C, which is built upon both A and B. I would make absolutely sure they know both A and B by writing example problems that they can solve on their own, before moving on to C.
How do you help students who are struggling with reading comprehension?
I would try to write the problem in a simpler form. In math, problems are often written in intentionally confusing ways in order to stump the student. If the students know this, and knows the tricks they use, they will have a better chance of comprehending what the actual question is when it's test time.
What strategies have you found to be most successful when you start to work with a student?
When I tutor, I found the most important element in internalizing/solidifying the material, is to practice it. The student might "get" a concept, and be able to solve a few examples that are similar. But can they solve a similar problem when the variables are switched? Can they solve it if all the negative values are changed into positive ones and vice versa? Repetition is key, and it has worked for me and others I have worked with.
How would you help a student get excited/engaged with a subject that they are struggling in?
In math especially, the student should understand how important of a subject it is. When I was in high school, people who were good at math were looked at as being smart, thus were looked at as being cool. Not only will the student feel smart, look smart, and please their parents, they will develop a satisfaction from defeating each math problem like they are the hero of their own story.
What techniques would you use to be sure that a student understands the material?
Examples, examples, examples. Practice, practice, practice. Not just 1 example, or 5, but 10, 15, or more if needed (on their own of course once it's believed they understand the material). The student needs to be able to recognize the problem, know what needs to be done, and do it, often quickly, especially during a test or pop quiz.
How do you build a student's confidence in a subject?
First, as I was tutoring him or her, I would encourage them through the learning process. It's important that students receive affirmation, that they know they are doing a good job along the way, that they hear "you can do this", "you know this", etc. Most importantly though, I would make sure the student is able to work through the problems on their own, without any help, and that they can do it in a timely manner in preparation for any future exams.
How do you evaluate a student's needs?
I would spot where the gaps are. If I were to write an example problem, I would take note where the student gets stuck and has to rack their brain on what to do next. I would stop and explain that step of the problem by itself, making sure the student knows it, internalizes it, and that it's practiced, repetitively if need be. Time is valuable during an exam, it's important that a student develops fluidity in solving math problems.
How do you adapt your tutoring to the student's needs?
For example, some students are good at memorizing. A large part of being successful in math is the ability memorize the formulas so one can work through the steps of the problem. For these students, emphasis will be placed on applying the formulas to the problem. For other students, time will have to be devoted to first memorizing the formulas, and then applying them, which they might be better at than the student who is good at memorizing the formulas. It's all about spotting where a student’s strengths and weaknesses are, and addressing the weak points.
What types of materials do you typically use during a tutoring session?
I always have a pencil and notepad. It's important to be able to quickly write out an example problem for a student to solve step by step. The student must also have a pencil and paper, it's vitally important that a student is able to have a thorough "cheat sheet", full with formulas followed by examples where the formula is applied. It's also important that a student writes these notes themselves to help internalize the information. In geometry for example, this paper would consist of things like, what the radius of a circle is, what the diameter is, how to find the circumference using the radius, etc.