A Journey Through Linear Algebra: Insights and Lessons

For many, the experience of encountering and grappling with linear algebra can be transformative—or in some cases, life-changing in the worst way. This is a story that amuses me, and I hope it will also entertain and inspire you. When I was in school, linear algebra was a required subject of my program, yet the term itself was a mystery to me. Despite this, I approached the course with the unreasonable hope that it wouldn't be too challenging and that it would be a breeze.

Challenges in Learning Linear Algebra

Little did I know that this was to be a challenging journey. The professor started each class by writing on the board, seemingly arbitrary content that made no sense to me at all. The struggle to understand the material soon translated into a behavioral and emotional cascade that is all too familiar to anyone who has ever found themselves in a similarly frustrating academic situation. Just like the students I now teach, I started to personalize everything, questioning whether the teacher liked me and whether I was doing well enough. My ability to take good notes, ask insightful questions, and study effectively took a hit as I began to doubt the relevance of the material to my life.

Overcoming Obstacles: A Personal Turkey

The situation came to a head one evening. After class, I realized that I had left my textbook behind in the lecture hall, which was now locked until the next day. The campus bookstore, where all required texts were sold, was open late. On impulse, I bought another copy for what seemed like an exorbitant price—$1996. This experience highlighted not only my struggle to keep up with the coursework but also the significant financial burden such a situation could impose.

Despite the immense challenge, I managed to pull off a surprising A in the class. My success was not based on a deep understanding of the material but on sheer determination and resourcefulness. Years later, I've never needed the subject in my professional life, but I believe I gained something more profound.

The Spectrum of Mathematical Ability

Mathematics, it seems, can be dissected into two distinct types of ability. There's the genuine mathematical talent, which I possess to some extent, enabling me to grasp and discuss the issues that math effectively addresses. On the other hand, there's the knack for achieving success in math classes, a quality I gained but which didn't necessarily translate into understanding the pure concepts. If I had to teach linear algebra, my approach would likely mirror the ineffective learning environment in which I found myself as a student. The subject would be presented as a series of magic potions, with steps taken that result in the correct answers, but without any clear rationale for why they are correct.

There is a spectrum of math classes, mirroring this. At one end, you have teachers who genuinely understand the material and strive to help students grasp it, leading to a deeper understanding among the brighter students. At the other end, there are those who either lack the necessary understanding or consider it unimportant, focusing instead on quick outcomes. This often leads to bad students shutting down intellectually.

Reflections on Math Education

Maybe this is why math is perceived as a misery by so many. The quality of teaching plays a crucial role in how students perceive and engage with the subject. A bad class can be a catalyst for a long-term aversion to math, and good classes that follow can be a refreshing change. This divide in teaching quality can create a lasting impact on students, affecting their attitude towards not just math but potentially other subjects as well.

Reflecting on my journey through linear algebra, I've learned that the path to academic success can involve more than just understanding the subject matter. It often requires a combination of personal determination, resourcefulness, and the ability to adapt to challenging teaching methods. These are valuable lessons in themselves, applicable far beyond the realm of mathematics.

Mathematics, whether taught well or poorly, has the power to shape our intellectual capabilities and attitudes towards learning. As educators and learners, we should strive for the former to foster a love for knowledge and a deeper understanding of the world around us.