Professional Private Math Tutoring

How I Structure Tutoring Sessions

When it comes to teaching math, I strongly believe that true understanding comes from having a solid concept to “hang the algorithm on” and doing plenty of practice. I have never been someone who thrives on rote memorization—I need to understand the why behind a concept, and I encourage my students to do the same.

I often incorporate tools like Desmos, which does a fantastic job of exploring the why behind math concepts and offering multiple approaches to problem solving. For example, I love the table method for teaching unit rates. It is a visual representation that helps this concept click.

Sessions are tailored to the individual student. I typically start by checking Google Classroom to see what they are working on, and I review any relevant materials, such as Desmos lessons, teacher-created slides, and the textbook (on Bainbridge, this is frequently an Envision book), so I can align with how they are learning concepts in class. I ask a lot of “why” questions and encourage students to lead the session. That means I let them try problems first, and if they get stuck, we revisit the concept together. I may model a problem, walk through a few examples together with the student, and then we each work on problems independently, comparing our approaches and checking for understanding along the way. Sometimes, I am the one who makes an arithmetic error and the student is correct. I love these moments, as they allow me to admit when I am wrong and give the student a chance to shine.

I also often learn from my students—new ways of approaching or thinking about a problem—and I incorporate these perspectives into my sessions. For example, many of us have heard of "SOH CAH TOA" as a way to remember trigonometric ratios. One of my students rewrote it as "S O/H, C A/H, T O/A," which I thought was absolutely brilliant because it highlights that each ratio involves division.

I try to avoid what I call “knowledge dumping”—overloading students with information without giving them time to think or take ownership. I have found that when students lead the process and talk through their thinking, they build real confidence in their abilities.

I always provide paper or a whiteboard so they can write out their work in more detail. Even with digital platforms like Desmos, I find that drawing pictures and writing out problems helps students stay fully engaged in the problem-solving process and solidify the concepts. In fact, this NPR article explains how handwriting activates more areas of the brain and can support deeper learning and retention than typing.

For older students, sessions usually focus on homework help and test preparation. I will often work with them to identify and catch up on any missing assignments. I also support younger students with their homework and design custom lessons using Desmos or IXL when homework is not assigned. If time allows after practicing a concept and completing homework, we often play a math game to wrap up the session. One of my favorites is Equate—essentially math Scrabble—which reinforces multiplication, addition, subtraction, and fractions in a fun and relaxed way.

Another strategy I love is using concept maps to help students see how different ideas connect. These maps help students understand the bigger picture and why they are learning specific strategies. For example, when some of my Algebra 2 students were introduced to matrices, they felt confused and like matrices were disconnected from prior content. So we created a concept map to show how matrices are another method for solving systems of equations. They were already familiar with substitution and elimination, and now they were beginning to learn a third method. Once they understood that matrix operations were a prerequisite for solving larger systems, things started to click. One student even said something to the effect of, “I finally understand why we are learning about this weird box of numbers!”

"Skill is only developed by hours and hours of work."

— Usain Bolt

“Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.”

— Abigail Adams