As a math tutor, I want to help the student build an accurate understanding of mathematics. Math is a cumulative subject. The topics you learn in one class are often relied upon in the next class, so not understanding something in one class can make later math classes feel confusing and frustrating. Therefore, I try to steer away from memorization of ideas and focus on helping students understand why what they are doing works. Suppose I see a student is struggling due to a shaky knowledge base of old material. In that case, I typically encourage that we spend time rebuilding the basics so they can have more success with their current work. I don't merely want to help them through each session, but I want to help them build a foundation to continue to have success with their math studies, even when I am not there.
Secondly, I want to help the student achieve their goals with the subject. I recognize that many of the students I tutor do not want to become mathematicians themselves. My goal is to help build my students' knowledge, study skills, and confidence. They do not see mathematics as a roadblock to what they wish to achieve but instead as a resource they can draw upon to solve problems creatively. I try to accomplish this by genuinely listening to the student and observing how the student is working. Not all students are unsuccessful because they don't understand the material. The issue may lie in confidence or test-taking anxiety. By being observant during every session, I can think about what might be holding the student back from finding the success they want and try to come up with methods that work best for them! This may include teaching the student how to have helpful study sessions on their own or interact with their class successfully!
I believe students learn best by interacting with the material themselves. Some amount of explanation and example problems can help the student start thinking about the subject. Still, I believe real learning happens when the student is tackling the problem. When I am working with a student, I typically have them do most of the writing themselves. While they are working on the problem, I ask them why they are choosing a particular method to solve the problem to understand the reasoning behind their approach. Together we can make sure that their logic is sound. When a student gets stuck, I will only directly explain the problem as a last resort. I try to ask the questions that will help guide their thinking in the right direction about the problem. I believe when a student comes up with how to solve a problem on their own, this will stick with them much more than trying to memorize something they saw me do.
I believe a well-built community of support around the student can make a big difference in their success. I am happy to talk with the parents, guardians, or teachers about the ways to help the student succeed. I may only see the student once a week, but the teacher and the parents see and work with the student nearly every day! I am happy to discuss any ideas they might have for setting up the student for success!