Most students seek out a tutor because they are having an acute problem. My first priority is to help them address this problem—whether it's a homework, an upcoming test, or a project due soon. My second priority is to help the student build deeper conceptual knowledge and acquire study skills to help them improve their grades, become more self-reliant in the subject, and ultimately gain more appreciation for what they are learning. When working with students still in K-12, I like to have regular check-ins with the parents. I want there to be a dialogue, so the parents can give me feedback and I can let them know how their child is doing. I have also included some details about my approach to math in particular below, for those interested. * [[Philosophy#Math|Math]] <div style="text-align: center;"> <img src="Fish transformation.png" alt="Fish transform" style="width: 500px;"> </div> ## Math Most students have not been taught how to understand mathematics in a way that will allow them to excel at the subject. In K-12, math is often presented as a series of seemingly disconnected problems with canned solutions. Most students, including very good students, get the impression they are supposed to memorize the answers. They come to see these as *ad hoc* and hard to remember. As they progress in math, there becomes more to memorize and conceptual understanding seems increasingly impossible. Most students go into their final required math classes wishing it would all stop. <div style="display: flex; gap: 10px;"> <img src="Equiangular spiral.png" width="200" /> <img src="Spiral with tangent.png" width="150" /> </div> Some students, on the other hand, realize mathematics is a unified subject. They understand the abstract principles behind homework problems, practice enough to internalize those principles, and draw connections between the new material and what they already know. They see math as an integrated body of knowledge, with practical methods of solving real-world problems. They often enjoy math and may go on to study it or a related field in college. ![[Operculum diagram.png|500]] How do these students get here? Maybe they have a parent who taught them this approach, maybe they learned to do it from a teacher, or maybe they have a mind that led them to think that way without outside help. ![[Operculum.png|300]] However it happens, my experience is that most students are completely capable of adopting this same approach. All they need is a teacher who will make this process explicit to them and assist them as they learn to think this way in their own classes.