Sessions are built around working through problems together, but not in the sense of demonstrating steps and having students copy them. Instead, I ask students to explain what they see, what they think might work, and how they are making sense of the problem. We use that thinking to decide what to try next. The goal is not just to solve the current problem, but to develop a way of thinking that applies to new ones.
This approach comes from nearly a decade of tutoring, teaching, and mentoring. I began as a Physics I tutor and lecturer during my sophomore year of college.
I later applied and refined this in a research lab setting, where I was responsible for training students to design experiments, operate equipment, and write code to analyze their results. In that environment, it was not enough to follow instructions; students needed to understand how to approach unfamiliar problems and make decisions independently.
The most productive sessions are the ones where the student is actively working through the thinking, building their own way of approaching problems.
Starting from the Student, Not the Method
Many students are taught to look for the “right steps” to apply. That works when the problem matches something they have seen before, but it breaks down when it does not.
Rather than starting with a fixed method, I start with how the student is already thinking. Even when that thinking is unclear or incorrect, it usually contains something useful. Working from that makes it possible to address misunderstandings directly and build understanding that actually sticks.
Doing this well is not just a matter of asking questions. It requires listening closely, recognizing patterns in how students reason, and adjusting instruction in real time. I have developed this through both one-on-one tutoring and classroom teaching, where students are working at different levels and need different kinds of support.
Making Math Make Sense
A common source of difficulty is that math can feel like a set of disconnected rules. Students are often asked to apply procedures without seeing how they fit together.
I focus on helping students see structure, including why a method works, how different ideas connect, and what a problem is really asking. This sometimes means slowing down, revisiting earlier ideas, or approaching the same concept from multiple angles.
My background in physics research also shapes this approach. In research, problems rarely come with a clear method, and progress depends on understanding structure well enough to try something new. That same kind of thinking is what students need when they encounter unfamiliar problems.
Struggle That Leads Somewhere
Learning anything involves some amount of struggle. Mathematics is no different. Successful understanding is whether the struggle leads to clarity or to frustration.
A large part of my role is managing that process. I want students to be comfortable trying ideas, being wrong, and revising their thinking. At the same time, I make sure they are not left stuck without direction.
There is a balance here. Too much guidance and the student stops thinking; too little and they stop progressing. Developing a sense of that balance, including when to step in and when to step back, comes from years of working with students in both individual and group settings.
Building Confidence That Carries Over
Confidence in math is not just about getting through assigned work. It comes from being able to approach a new problem and having a way to start.
As students develop a clearer way of thinking through problems, they rely less on memorized procedures and more on reasoning. They begin to recognize what tools they have and how to use them, even in unfamiliar situations.
I have seen this shift happen with students across levels, including those in introductory physics courses as well as more advanced work. It is what allows progress to carry over beyond a single class or unit.