Q&A with Arthur: You’re Probably Not Bad at Math

A: In my experience, there are three primary reasons that students struggle with math. First, math is a cumulative subject, meaning that new concepts build upon previous ones. If students never fully grasp a foundational idea, they will struggle when more advanced material requires that knowledge. I see so many students face hurdles in advanced math courses that have more to do with mastering basic math concepts than working out the specific advanced problem that is tripping them up. This issue has been especially pronounced since the Covid-19 pandemic, which disrupted many students’ learning—these students are now taking high school-level courses while lacking fundamental algebra skills they should have mastered in middle school.

In addition to these knowledge gaps, many students develop a fixed mindset about math based on misguided stereotypes. From a very young age, many students (particularly in the U.S. school system) are exposed to the idea that some people are “left-brain” thinkers who excel in STEM disciplines and others are “right-brain” thinkers who excel in the humanities. This binary thinking leads many students to stigmatize themselves as someone who is “bad at math” as soon as they encounter friction in their math learning—rather than simply being a learning challenge, this friction comes to signal something about their identity and threshold of capabilities.

For the record, I simply do not think that these stereotypes ring true—struggling to learn a math concept isn’t an indication that you are ontologically predisposed to failing at math; it simply means that you are finding your footing in your learning.

Finally, most schools lack a robust math curriculum that is adaptable to a variety of different learning styles. Too often, instruction focuses on memorizing formulas and following rigid procedures rather than fostering a deeper understanding of mathematical concepts. Many students learn to plug numbers into equations without fully grasping why those equations work; they are left on their own to discover the nuance that is inherent in any mathematical concept. Given this, most students have a surface-level understanding but struggle to make sophisticated connections, employ critical thinking, and adapt concepts to new formats.

I like to tell students that math isn’t about formulas and rules (though these things are important!)—it’s about objects that you apply a certain kind of thinking onto. It is a form of applied logic. Seen this way, math is a way of thinking that intersects with creativity, history, and problem-solving, not a cold, abstract subject.

A: The first step toward becoming a better test-taker in math is identifying the source of your struggle: Do you lack foundational knowledge? Do you make silly mistakes? Does test taking anxiety make you freeze? It can be difficult for high school students to be self-aware about their weaknesses so in my role as a tutor, I spend a lot of time asking the right questions to help students self-reflect and think critically about why they are struggling.

Often, the key is to work backwards—if you’re a junior or senior, go back and assess whether you understand the sophomore year concepts that build up to the topics you’re currently wrestling with.

Once students recognize their specific challenges, they should take a comprehensive approach to studying. Instead of reviewing math in a general sense, I help my students create a detailed breakdown of topics and subtopics, ensuring they can study and understand how different ideas relate to each other. I ask them to consider things like: What is everything you know about this concept? In what ways have you seen it appear?

As we prepare for tests, I encourage students to focus more on the process rather than the answers—if you can’t correctly write out the process you took to arrive at your answer, it’s a good sign that you don’t fully understand the concept itself; you may just recognize the question format.

At the end of the day, mastering basic concepts comes down to finding a method or thought-process that makes sense to the student through practice and repetition. There is almost always more than one way to arrive at an answer, and what works for one student may seem unintelligible to another. The biggest part of my job is identifying and pre-empting knowledge gaps so that they don’t become problems in the future. I might explain something three times in three different ways, continually going back to basics, to ensure that I am breaking down the concept in a way that makes sense to the individual student I’m working with.

A: If you know where to look, you can find math anywhere. Math isn’t confined to textbooks and equations; it plays a role in everything from music and art to biology and economics. One of the best ways to deepen mathematical understanding is to cultivate curiosity. Seeking out real-world applications can make learning more engaging and meaningful—how you choose to do that will depend on your own interests and passions.

For instance, I watch YouTube videos of people solving problems for fun. If that’s not for you, perhaps exploring mathematical puzzles or reading about the history of math could help you deepen your math knowledge and see the subject in a new light.

Struggling with math doesn’t mean a STEM degree is out of reach. Math is just one component of STEM fields, and students can often tailor their academic path to align with their strengths. While some STEM disciplines require intensive math coursework, others, such as environmental science or certain branches of biology, rely more on data analysis than advanced mathematics. Even in fields that require math, understanding concepts within a specific context can make them more accessible.

A student who struggles with abstract algebra, for example, might find mathematical applications in physics or engineering easier to grasp because they can see how the numbers relate to real-world problems. Lastly, students should be sure to pursue a discipline that aligns with their skill set. If you struggle with complex math concepts, physics may not be the ideal path for you, but engineering could offer you an inroad in a subject that interests you with more of an applied—rather than theoretical—mathematical focus.

A: Yes, Command Education offers subject tutoring in math. One of the most valuable aspects of working with a tutor is learning to identify subtle knowledge gaps that might not be obvious to students or even their teachers. For math—perhaps more than any other subject—one-on-one tutoring is critical both for recognizing missing links in students’ understanding and for finding targeted ways to adapt complex ideas to a student’s particular learning style.

One of my greatest strengths as a tutor is in finding creative ways to communicate math concepts to students of all different abilities—do they like questions? Do they want to practice together or alone? Some students like to see that math is formulaic and follows clear, simple steps, while others respond best to conceptual thinking or illustrations using practical examples. Discovering and adapting to these learning styles isn’t easily possible for teachers in a classroom full of students, but it is possible in one-on-one tutoring sessions.

A: Our Senior Tutors have a strong understanding of most schools’ math curricula and can therefore find ways to supplement students’ in-class learning with one-on-one support. The way many schools teach is very complicated and doesn’t break concepts down so that students can see the connections between them; this method works for advanced students, but those who struggle need to hear their instructor spell out these connections in order to understand them. That’s exactly what we do for students.

Because I understand what most students are being taught in the classroom, I can target my teaching to the knowledge gaps I typically see students struggle with or employ alternative teaching modalities that I anticipate students have not encountered in traditional curricula. Students need personalized guidance to understand the how and the why of a given mathematical concept, rather than the same formulas-based instruction they often receive in the classroom.

The best way to practice math equations is to write them yourself, so I never provide tutoring instructions via PowerPoint. Instead, I focus on crafting well-designed practice problems that bridge the gap between theory and application, helping students grasp nuances they might not have noticed otherwise.

Finally, I strive to de-formalize math for students, turning it into a puzzle or game in order to make the subject feel less intimidating. The ultimate goal of our tutoring is to ensure that students don’t just memorize formulas, but actually understand the reasoning behind them.

By making math instruction more personalized, accessible, and engaging, we help students build a strong conceptual foundation so that they can build toward more advanced math and execute confidently under pressure—whether standardized tests, an AP Calculus exam, or a collegiate math course.