No this isn’t a post about how the best teachers are math teachers although I do love math as it forms the foundation for much of my educational and professional experience. Instead, I want to share the idea of how good teaching can be thought of using a mathematical framework.
In my estimation, the best teachers are always focused on how to maximize the individual potential of each student. Since students have different backgrounds, experience and capabilities, accomplishing this goal is always going to be challenging because of the variables involved.
In fact, as you increase the number of students, n, in a given educational environment, it can be very tempting to focus instruction on just the middle part of the bell curve where most of the students will be. However, this shortchanges those with more advanced skills and those who are still developing. Essentially, the classroom can become exclusively centered on making sure the majority of the students do well.
The challenge for this is that in a given educational environment, we are only in a local maxima. Students as they progress in their knowledge and development will find themselves in an ever changing environment. In an introductory programming class, there may be a small group of students that do extremely well. They find themselves able to speed through the projects and often are able to work independently. When this group moves into a larger group with students who are equally talented, they may suddenly find themselves in the middle or lower part of the bell curve.
Those who were at the lower part of the bell curve may have realized that they are not as talented as those in the middle or upper part of the bell curve so they dedicate themselves to shoring up their weaknesses and getting better. At the conclusion of the introductory programming class, they have moved into the middle part of the bell curve. Now, they realize that if they work hard to develop their skills they will see progress.
Throughout each of these examples, the key insight to realize is that the environment that students are placed within is going to constantly change. While physical constraints place students within a local school, ultimately they will be competing against other talent individuals on a global stage.
That means that while the initial number of students may have been between 20-30 when they were just getting started. Ultimately, their peer group professionally may be in the hundreds, thousands or perhaps even millions. With this realization, it is important that instructors constantly work to influence what we can control. And, that fundamentally is making sure that we always push each student to maximize their individual potential. For some this means that they may rise to the absolute top of the global talent pool for a given skill. In other examples, they may be the best developer or product manager at a leading technology company - a relative maxima. And, still others may become great contributors to the development of a key feature within a broader technology platform.
Each of these roles are important for the broader impact on society. And even more key is that people tend to excel and enjoy what they are good at. The best teachers, mathematically, help students discover their true north and then push them to become the best at their chosen path. Hats off to the great teachers who are doing this important work each and every day. Your impact on society is incalculable. Thank you!