I help students get unstuck in math, from middle school through college, in live one-on-one sessions online.
“When am I going to use this?”
I've heard this question more times than I can count, and I've asked it myself. It comes from real struggle with a subject that can feel abstract and disconnected from anything tangible. Mathematics can look like it exists only for its own sake. John von Neumann warned about exactly this: that mathematics drifting too far from its real-world sources risks becoming “l'art pour l'art,” art for art's sake.
At any level, math is a set of skills that can be learned, and anyone willing to put in the work can learn them. Research backs this up. Carol Dweck's work on growth mindset and Jo Boaler's on mathematical mindsets show that ability grows with effort, and that mistakes are part of how it grows. Struggle isn't a sign that a student isn't a “math person.” It's what learning math feels like.
Math is hard, and it's easy to think the only reward is getting past that difficulty. I believe the reward is bigger. The reasoning and problem-solving habits that math builds, out of necessity, carry over to everyday life and to the problems we all face. George Pólya's How to Solve It laid out those habits decades ago: understand the problem, make a plan, carry it out, and look back. They work just as well on a hard decision as on a hard equation. John Dewey made a similar case in How We Think: careful, reflective reasoning is a skill that has to be practiced, and math is one of the best places to practice it. The National Research Council's Adding It Up even counts seeing math as sensible, useful and worthwhile as one of the five strands of being good at math.
So in every session the goal is two things: getting the math right, and building the thinking that will still be useful long after the test.
Three ideas behind every session.
A struggle with today's homework usually starts a few topics back. We find that spot first, so new material has something solid to stand on.
Knowing why a step works makes it stick. Once it makes sense, we practice until it's automatic.
A wrong answer shows exactly what to work on next. Students should feel safe getting things wrong in a session.
I'm preparing to begin graduate studies in mathematics abroad. The questions that pull me in come from harmonic analysis: the idea that a complicated signal can be broken down into simple waves. A chord on a piano is a handful of frequencies sounding at once. White light splits into a spectrum of colors. Fourier analysis gives a precise way to take those signals apart and put them back together, and the same mathematics sits behind digital audio, image compression and medical imaging.
Functional analysis is the framework that makes those ideas rigorous. Instead of working with one function at a time, it treats whole families of functions as points in a space with its own geometry, where you can measure distance and angle. In that setting, a sound wave and a light wave become vectors, and breaking a signal into frequencies becomes a change of coordinates. It's abstract, but it's some of the most useful abstraction in mathematics, and it's a good answer to “when am I going to use this?”
Further down the road, I want to pursue a Doctor of Education (EdD) so I can study how people learn mathematics and bring that research straight back into how I teach.
A free 15-minute call is the easiest way to see if we're a good fit.
Book a free consultation