The Dr. Math Philosophy
You might think that all math teaching is the same, so how could one tutoring company claim to be different from all of the others? You might think that math is just memorizing some facts and rules and then practicing until you know the procedure backward and forward. For many people and some teachers," learning" math is remembering tricks and acronyms that help you know what to do in a given setting.
We strongly disagree.
Effective math teaching is about listening to students, determining where their deficiencies and misconceptions lie, and then addressing those issues in a deliberate, logical fashion. Learning cannot occur unless new knowledge is built upon the student's existing knowledge base. Connections must be made between what the student already knows and what he is trying to learn because without these connections, any "learning" that occurs is short-term and not permanent.
Dr. Math had always been this type of teacher during his career, but he did not know that there was a formal name for this type of teaching until he returned to graduate school in 2003. There he discovered that this approach to learning was known as constructivism, and it is this philosophy of learning that drives the way we approach our tutoring sessions.
A good tutor gets at the root issues and treat the problems, not just the symptoms. For us, it is all about helping students understand the math and build on what they already know. We help students connect the dots and make sense of what they are learning, because without doing so, the chance of long-term success is unlikely.
This approach requires that tutors have an excellent understanding of the entire curriculum, not just what they are currently teaching in school. For us to be able to help students make the needed connections for deep understanding to occur, we must be able to put all of the pieces together as well. In addition, for us to be able to diagnose the issues that a student is having, we must be able to listen to what a student is saying and ask good questions that help get at the root of the problem. This is a skill that not all math teachers possess.
Some teachers believe in long lectures and lengthy explanations as the way to convey knowledge. Yes, there is a place for a good lecture, but we believe that good tutoring sessions are discussions, not monologues. We listen to our students and ask many questions to get at the underlying issues that the student is having. One of our favorite questions is simply "Why?" We ask this of our students because it forces our students to explain not only what they are doing but the "why" behind it. When someone can explain something to another person, it is evidence that he understands the concept well.
Furthermore, having students explain their thoughts and actions helps improve their mathematical vocabulary. For most of us, learning mathematics does involve an expedition into uncharted territory, with new words and symbols that make this almost like learning a foreign language. We help our students gain a better understanding of the material by having them explain and discuss concepts, and that is one of the ways in which deep learning is ensured.
Several years ago, when Dr. Math was teaching at the college level and working with preservice math teachers, he wrote a letter to them describing what he felt was the right way to teach mathematics. It resonated with his student teachers so much that he eventually submitted it for publication in the Virginia Mathematics Journal. Entitled "What is Good Mathematics Teaching," the article summarizes some of the points made here and mentions several other facets of good mathematics teaching. You may find it an interesting read.
The Covid crisis has necessitated changes In the logistics of tutoring, so most sessions are now conducted online via Zoom. While the interactions may be virtual instead of in-person, the same tutoring approach prevails. Until conditions improve and allow for a resumption of face-to-face meetings, the Dr. Math virtual approach is the next-best thing, allowing students to continue to receive quality instruction and academic support.