Anyone who has interacted enough with the education system of a university that houses greek life eventually finds out about ‘test vaults.’ I first found out about these when hanging out in the attic of a fraternity waiting for a friend to finish an assignment so that we could get on with our Friday night. Passing the time, I started snooping around various drawers and cabinets that littered the space, and I eventually found a filing cabinet full of tests. I asked my friend about this, and he explained that the fraternity stored all of their tests so that later members can use them to pass their classes. Of course my first reaction was to think of how unfair this was to me - and this indignant attitude only grew as I learned how widespread this practice was among greek houses. However, after spending some time on the other side of classroom as an instructor and reflecting on education through the lens of equity, my perspective has gained some nuance.

This practice didn’t just mean that myself and other students were at a disadvantage because some of our classmates had access to test answers. These test vaults were available to a very specific kind of person, namely one who has the generational support and financial resources to enter through the gate-kept doors of greek life. This poses a serious equity problem: for example, a first generation student will not have the sort of impetus and support to enter into greek life as a student who comes from a ‘greek’ family. Hence, the unfairness of the test vaults isn’t distributed randomly: there is a built-in disadvantage towards first-generation students.

If I really wanted to convince you that this is the case, this is where I would start citing statistics. However, my goal isn’t to prove that test vaults are a source of inequity in the university education system, rather it is to demonstrate an example of how institutional inequity can arise and function. Greek life has already been the subject of much scrutiny, as any google search will reveal. Instead, I would like to continue by pointing out a possibly lesser known source of inequity in education - specifically in mathematics.

This semester, I taught Calculus I. With the worst of quarantine life behind us and some more experience enforcing classroom attendance, I was able to implement much more group work and classroom interaction than my previous teaching assignments. This allowed me to get a much closer look at my students work habits. While they worked on practice problems, I would walk around the classroom offering assisstance when needed, but otherwise observing how my students were approaching the assignment. Around the section on implicit differentiation, I started to notice a slight dichotomy in my class: some students knew about and used computer algebra systems (CAS), and others did not.

What I mean by CAS are websites like Symbolab and WolframAlpha. These websites, among others, allow students to input virtually any standard question from all sub-400 level math course and receive a correct answer sometimes with calculation steps. If you are a student who is savvy in one such CAS, you are clearly going to have an advantage over those who don’t. This is where the equity step happens. We ask, “what kind of student knows of and can use a CAS?” If it is random chance, then it is not much of an equity issue. However, I don’t think that is the case here. Consider the first equity example. Just as test answers can be passed down through a large, structured community like a greek house, use of platforms like WolframAlpha can be passed down as well. What is different about the latter situation is that it doesn’t need an organized structure to pass it down, like tests do. Instead, I believe that knowledge of CAS is more accessible to students involved in communities where survival tips for their education are commonly passed around. This leads me to suspect that types of students which struggle to integrate into university communities will have less access to CAS. This applies similarly to first generation students as previously discussed, but more broadly I think it also applies to non-traditional students and students of marginalized communities, especially at universities with low diversity and few initiatives to support these students.

This is where a math-ed researcher comes in and performs qualitative research using surveys and interviews to come to a more precise conclusion than my musings can. I am not a math-ed researcher, so the best I can do is assume my hypothesis and give some possible solutions to this source of inequity.

One approach is to address the inequity directly. Recently at Colorado State University, some undergraduate math students have built a community called ‘Inflection Point’ designed to be a space of support and learning for students of color and first generation students. Bringing information about CAS to this group in the form of a presentation or an interactive learning session could help address this inequity.

More broadly, a freshman orientation for all students on degree tracks that would benefit from knowledge about CAS could be implemented to ensure that everyone is clued in. Unfortunately, both of these approaches come with a problem: knowledge of CAS can be abused, so how do we ensure responsible use.

What does responsible use of a CAS in a math class even look like? Something that makes this hard to define is that it is going to vary with respect to which class is being taken. Using WolframAlpha to compute the integral of cos(x)sin(x) without a single thought to the underlying process has very different implications for Calc I than Differential Equations. In Calc I, it is key to the learning process to work out the integral by hand, and to gain experience manipulating the symbols of calculus. In Differential Equations, the learning goals are different. You are assumed to know how to solve such an integral, and the learning is instead focused on the technique for solving separable equations, for example. I would argue that using a CAS as described is not resonsbile use in Calc I, but could be responsible in differential equations.

Successfully communicating this difference and enforcing responsible use are challenges that need more attention before one of the described solutions could be implemented. One consideration is the use of creative, conceptual questions like the following: ![[calcproblem.png]]

This question challenges students understanding of derivative rules, while avoiding being solved without effort through a CAS.

As mathematics and computer science become more intertwined, we have to reflect on education practice that may be archaic. Avoiding the discussion of CAS in the classroom not only could enforce inequities, but also demonstrates a blindness to the changing realities of mathematics in practice. Very few integrals get solved by hand outside of classrooms, integration bees, and the Math GRE. Insteadm modern engineers and even mathematicians typically rely on CAS to solve or approximate their integrals (I certainly do). My hope is that the potential inequity underlying CAS in mathematics education is investigated and considered more by instructors and researchers, and that the outcome is a more modern and supportive mathematics experience for all students.