Goodbye Gaussian

I'm taking a break from my series on analytical techniques as the new fall semester commences. This is because I'll be studying Molecular Spectroscopy with Dr. Charles Wurrey here at the University of Missouri-Kansas City, and the next two techniques I hope to cover, Raman Spectroscopy and Fourier-Transform Infrared Spectroscopy, will be discussed in great detail within that environment. I think it will be best if I hold off posting on those methodologies until after I have the chance to study their intricacies with my professor.

That being said, given that the new semester is upon us, I want to get back into discussing relevant topics pertaining to student success at the collegiate level. And one way I want to do that is by examining the following graph.


As a Graduate Teaching Assistant, one of the tasks I'm given responsibility over is administering and grading final exams for my sections. Now, pertaining to FERPA regulations I'm not going to mention exactly which section(s) of lab are represented here, but note that I find that the trends I'm about to demonstrate herein are relatively applicable over all the courses I've taught so far while at the university level. The red dots are raw data points, and the pink line shown is my rough attempt to functionalize the data via p(x) without using a piece-wise interpolating polynomial.

This pink line is what I want to draw your attention to, specifically due to the components I utilized to generate the final function that you see. In order to functionalize the data set the way I did, I used a linear combination of both a Gaussian and a Lorentzian distribution function, shown below by the curves blue and green, respectfully.


The ability to demonstrate this data set as a linear combination of two distribution curves is something that worries me as an educator. It use to be the case that a simple Gaussian would represent the normalized distribution of graded elements like final exam scores, where select students show above average proficiency, most students demonstrate average proficiency, and some students simply struggle. This may sound worrying at first but I believe that this type of distribution is good, in that it enables the teacher to take the next, more critical step in education and push his or her students to not just reach the threshold for proficiency, but to push beyond that and ultimately grow.

This bimodal distribution on the other hand presents us who are tasked to teach with quite the dilemma - on one hand, a significant portion of our class is learning, engaging, and growing with the material we teach; on the other, a significant portion of the class is not succeeding in doing so. This distribution also implies that to a certain extent, the cause for this function output lies beyond what is in our ability as educators to control. If as an educator I can be considered a constant for each individual in this function, then my input as a teacher is having a great positive effect for one distributive set, and little to no effect on the other. And if I try to engage the class as a whole in a more challenging way so to push for growth, what ends up happening is that the efforts on my part ultimately drive the two distribution curves apart, and not uniformly forward as desired.

I don't yet know the solution to solving this bimodal distribution problem. I can however talk about the differences in individuality and culture between the students of these two sets, in the hopes that those reading this can use the information herein to push oneself to be in the former higher set, and not the latter lower set.

Firstly, and probably most importantly, I find that students who are in the former distribution set are students who show up. Not only in a physical sense of being present in class, but mentally present as well - listening intently, taking notes, asking questions, and engaging with the lecture and teacher. Comparatively those in the latter set may have physically checked into the classroom, but mentally establish their domain on social media or in microcosms not relevant to what's being taught.

Secondly, students in the former distribution set tend to be those who engage with an intent to understand. They do so by coming to talk one-on-one outside of lecture, and during office hours. And often it's in this environment where I as an instructor get the greatest capacity to engage back - the dynamic is no longer one who lectures and one who receives; it's that of two gladiators together in the arena, facing a common foe that need be vanquished. And I find it almost funny, how these students, who probably don't need my extra help, are the ones showing up anyways. Their willingness to engage isn't just about an aversion from struggle; it stems from a desire to engage and truly understand. I rarely find students of the latter set who enter this arena, daring greatly.

Finally, the students who are in the former distribution set tend to be the ones who connect. They do this in two ways: they connect with other students in their distribution set, and they connect with me as the instructor. They establish systems of support throughout their academic identity and maximize those connections to achieve maximal growth. Cliche quotes like "who you surround yourself with, you become" and "bad company corrupts good character" really do ring true when it comes to who you are and how you carry yourself through academia. Students of one distribution set or the other tend to keep the company of those within their distribution, so be active in seeking out and connecting to the best of those around you.

Show up, engage, and connect. If I could recommend any piece of advice to my incoming students it would be these. University studies are the pinnacle of your educational path, designed to expose you to new ideas, show you new ways to think, and open new paths for you to follow. It's hard, but most certainly doable. It's challenging, but conquering the challenge yields to you the opportunities that dreams are made of.

Hopefully as semesters wax and wane we might find ourselves back in an environment that fosters that next step in education, where we can push past proficiency and move into a realm of growth. But until then, it may be goodbye to the Gaussian.

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