Appalachian Trail on Whitetop Mountain in Virginia
Date: 8/28/2026
Over the years, I have had this one particular imagery repeatedly come into my mind that seems to encapsulate what I am looking for when it comes to teaching math and helping others. The scene is relatively simple – I am sitting on a bench in some remote village, I overhear a child walking by who is struggling with some math question from school, in that moment I offer whatever I can to help the child (with his or her homework, confidence, understanding, etc.), then we part ways and continue on our day. For some reason, this scene tends to play over in my mind frequently, and I often find myself describing it to others when asked about how I want to offer my math skills to others in need.
As someone who has worked in a traditional classroom, I have encountered every frustration and limitation that most educators inevitably face teaching a room full of different students, with different interests, different abilities, different home situations, and with a curriculum that is artificially imposed on them that must adhere to a contrived timeline to fulfill certain educational “requirements”. It’s a nightmare right? How did we get into this situation? What meeting took place to decide what’s considered “important” for students to learn and who are these people making decisions for billions of the rest of us? Are the flaws of the system buried too deep that real change is next to impossible to achieve? When I first started teaching, like many I suspect, I was filled with energy and determined to make a difference and offer my best to my students. I wanted to share what I personally enjoyed about math and tried everything I could to bring the subject to life for others. I was particularly interested in challenging the perceptions of those who had preconceived notions of not liking math or rigidly assuming they’re bad at math, I wanted to show another side of math that perhaps they could actually connect with. And while, overall, I did have the support and encouragement from my department heads to “do my thing”, I could not help shake this feeling that the momentum of the current trend of math was so strong that my efforts to try something different felt inconsequential. It was as though there’s this raging river going downstream, and I was just this one lone person trying to go upstream, I had no chance (so it seemed). Inevitably, the weight of the current got to me and I became tired, but rather than go down with it and sell my soul so to speak, I got out completely and took a break from teaching math. It’s not easy, when the world around you is doing one thing, to go against it and do what feels true and right for you.
So what exactly didn’t feel right. Before I attempt to answer that, I need to be clear that I am not assuming my personal thoughts and feelings on the subject are undeniably correct while others’ views are absolutely wrong. Furthermore, my feelings quite naturally evolve and change over time, so these reflections are less about some absolute statement set in stone on what’s right and wrong in math education, but more about one human being sharing his personal experience and feelings in a particular moment. So, with that in mind, let’s start with my perspective on where was this current of math education going and what was driving it. As I sit here reflecting, I notice one word that keeps popping into my head “answers”. In the most simple terms, this raging current of math seemed to be driven ultimately by one thing – getting answers. Not understanding concepts, not cultivating creativity, not asking deep questions, not persevering despite struggling, but simply getting answers. As long as the correct answer was produced, we were happy and conditioned to think we were doing a proper job, whether or not the student actually understood the meaning behind the numerical derivation to the problem was largely ignored. And it almost didn’t even matter if the student truly understood the concept, as long as the answer was reached, we rushed onto to the next thing, and if that answer was reached, again with or without understanding, we rushed to the next question and so on.
Snowy Day At Doctor's Park
Something about that culture didn’t feel right to me. Was there much value in someone being able to produce a numerical answer but be unable to truly understand the meaning behind the answer and how they got there? Some of the most memorable research I encountered in graduate school was from an experiment where it was clearly demonstrated that there was not necessarily a direct correlation between getting A’s on tests and understanding the concepts tested. In other words, many students were getting A’s on their exams, but when pressed about the concepts they had supposedly mastered and asked questions that tested more of their actual understanding they struggled. To be honest, I was one of those students. I could get A’s on most my math tests, I could produce answers in algebra and trig and calculus in machine like fashion, but what my correct answers and high grades weren’t revealing was that in a certain sense I actually had no idea what was going on. That would change in graduate school when I encountered two of the most terrifying professors I’ve ever had, Dr. Thompson and Dr. Saldanha. I still remember, every night before class, being scared and anxious as I walked into the classroom because for the first time in my life, producing answers wasn’t good enough, I had to understand the math and be able to talk about it and explain it in plain English, let alone in front of experts who understood it deeper than I did. It was humbling, terrifying, and ultimately the most meaningful and influential time in all of my educational journey. I finally became confident in math on a deeper level, because not only could I derive answers, but for the first time ever I actually understood what was going on. Furthermore, and crucially, I also became more comfortable not knowing things at first and was no longer ashamed to admit I didn’t understand something because overtime I learned to trust my ability to patiently question things and reason my way through to some level of understanding, no matter how long it took.
This leads us to the other dominant force in this current of present-day math culture – the curriculum and its artificially prescribed timelines for understanding concepts at a given age/grade level. I wonder if this is where eventually teachers recognize the ship is sinking in the middle of the quarter/semester but simply go down with it. You know for this kid the material is way too easy, for that kid it’s just right, and for the kid in the back it’s hopeless. Yet, we continue to march forward because….the curriculum says we must. “This many weeks in, students should master concept x, that many weeks in, students should master concept y” and so on. Imagine someone walking up to Albert Einstein “Hey, the board had a meeting and we’re going to need your E = mc2 equation by the end of October”. That’s clearly not how meaningful insights and understandings arise, they don’t adhere to some artificial child-like timeline, they arise organically when the time is right. And when they finally do spontaneously come, they really stick and are of lasting value. I wish in some world students could have their own mini-Einstein experience with whatever concept interests them. They could “chew” on some concept again and again, keep pressing and questioning, keeping getting close but not quite there, and then, one day, the “Ah ha” moment finally hits them and they feel a tremendous sense of satisfaction because they persevered and developed their own unshakable understanding through their own efforts. That’s powerful, to me anyway. And it’s not to dismiss the curriculum entirely or say it’s futile, but just me imagining the best learning experience for a student to have. Of course, a curriculum can provide some general necessary direction for a quarter/semester. I only think we should be more flexible with it and use it to steer students into experiences that provide satisfying and long-lasting insights. Imagine someone walking up to Einstein in the middle of his E = mc2 struggle and saying “Sorry sir, we’re going to have to move onto the next topic to keep things moving”, completely depriving him of the powerful experience that awaited if he only was allowed the time to persist a little bit further. Curriculums can strip away that extra time, leaving students in the middle of conundrum that potentially could yield a lot of growth, to simply plow ahead to the next concept. No wonder so many students are lost in math, we keep marching forward compounding their sense of confusion. But if we can somehow give students the time they need to develop their understanding, then I would argue something meaningful is happening. But the trick is it has to be on their time. Einstein could not force himself to have figured out E = mc2 by a certain deadline, just as kids should not be expected to have a deep understanding of whatever it is their learning by a specific deadline. As I have repeated many times before, we are all different and learn at different rates. That shouldn’t be a problem but rather seen as completely normal and understandable. My hope is that educational systems somehow find ways to give students the time and space they need to work hard, persevere, and reach their own understandings.
So what does any of this have to do with a village kid needing help in math? I think the reason that imagery pops into my head frequently is because in that world I am removed from the weight of a curriculum and am simply responding to a real need in the present moment without any pressure to move onto the next artificially imposed thing. I simply get to help a student who has a pressing need, offer them my best, and once the problem is resolved, whether it took a few minutes or a few hours or a few days or a few months, we go our separate ways with no forced need to cover the next thing. That’s what I am ultimately looking for, responding to real sincere needs and offering whatever I can to help.
Share this: