By Nicholas Long, Stephen F. Austin State University
In one of life’s weird coincidences, when I moved to a small town in East Texas to start my academic career at Stephen F. Austin State University (SFA) ten years ago, I didn’t know that I would be working with someone from my high school graduating class of about 150 people. Through that small quirk of life, I met a lot of the art faculty and local artists in the Nacogdoches area. I love that I get to hang out with artists and art educators. They are really cool people and they MAKE THINGS. Things that people want to look at, things that people want to discuss, and sometimes, things that people even buy.
The idea I want us all to consider is: “How do we grow and improve the culture of making and improving things for our teaching?” When I say things for our teaching, I mean much more than just textbooks and notes for lecture; I mean software and technology that adds meaning and value for our students; I mean activities that can change the attitudes, habits, and practices of our students; I mean the many other materials and resources that will transform students and mathematics classrooms. While I will cite some examples below of projects and resources that I think are doing good things, I genuinely think we need to not compartmentalize these practices, but make them part of what we as a community do.
The Teacher as Artist
Anyone who knows me and has seen me since last May knows all about my most recent project because I can’t contain my excitement for it. My SFA colleague Jeremy Becnel and I spent the summer of 2017 building an app that uses a Google Cardboard viewer and a smart phone to allow the user to visualize the concepts of multi-variable calculus in a virtual reality (VR) setting. You can see more about what we have accomplished and where we are going with this project here. It has been a frustrating, wonderful, humbling, and exhilarating process. Jeremy has taught me a lot about writing good code for software so that we have less of this kind of thing:
I could spend the next ten thousand words just talking about the problems and solutions, both great and terrible, we encountered so far on this project, but I am saving that for a grant proposal.
By far, the thing I have liked most about this project is the opportunity to make something that I think is beautiful and interesting and useful and new. While I like thinking about traditional mathematical research questions, I struggle with that type of work. Not just because mathematical research is hard, but I sometimes feel like I’m doing it because someone told me I need to do this type of work to advance to the next level. There is tremendous value gained by pushing through the struggles of understanding and expanding the frontiers of mathematical knowledge, but I bet I talk to more people in a month about my virtual reality project than I ever have about my research in dynamical systems. Those conversations about virtual reality and the process of making things has been a breath of fresh air for my career and my enthusiasm for my work. It certainly helps that this project lets me draw pictures and see patterns (i.e., do mathematics) in an immersive environment that seems to be of broad interest to a mainstream audience.
I love having something that I can show other people that leads to a discussion like the ones I enjoy having with artists. I usually get asked something along the lines of “How did you make that?” or “How are your students using this?” When I meet an artist for the first time, I usually ask similar questions like “What does your creative process look like?”, “How do you decide when a piece of work is done?”, or “When you look at art, how do you evaluate it?” I have discovered that artists make pieces for lots of different reasons and with different motivations. Having created a tool for teaching, and being on the receiving end of these types of questions, makes me feel like more of an artist than my traditional research has. In other words, the value of making things is not only the creation of the product but also the discussion that is prompted by the process of making and evaluating the product.
Sharing the Art in Teaching
When I reflect on the VR project, I think that there were a few things that were vital to the early successes we have had. First, we had a clear vision of what we wanted the product to look like and what we wanted the materials to do. It is so easy to get caught up in the minutia of making something that you forget about its purpose and audience. Second, there were some tools available that helped bring down both the cognitive and technological hurdles. (Thanks Unity, Unity Development Community, and Google VR!) Third, it built upon the habit I had long been practicing of making things of my own for teaching. Those things were often terrible at first. Some of them came from half-baked ideas and others came out of a curiosity for whether I could even do the thing. Some of these terrible things I made showed me how to make things better, more useful, or more aesthetically pleasing. Depending on how urgently busy I felt at the time, I would modify the stuff that I was making. Lastly, we had time to wander. Let me be more specific. One of The Five Elements of Effective Thinking by Burger and Starbird is to follow the flow of ideas, for better or worse. This was our unstated motto for the first month of development in the VR project. I found how wonderful it was just to explore what you can create and how polished you can make it.
Over the past few years I have become more active in the Inquiry Based Learning (IBL) community and in my work with Project NExT in the Texas Section and at the national level. Both endeavors have been very useful for me as an individual, but more importantly, they are both building communities and improving the cultural practices of our profession. Stan Yoshinobu gave a great talk at MathFest on “The Next 20 Years: Moonshot Challenges in Post-Secondary Math Education and IBL.” Stan also outlined goals and steps to reach those goals, as well as ways to build groups to address these steps. One of the most appealing aspects of the “big tent IBL” that Stan talks about is the idea of transforming students from users of information into creators of information. A great strength of the Project NExT groups is the ability to expose new faculty to ideas and resources that can help them evaluate what their role is in the classroom, in their departments, in our profession, and in an increasing complex and demanding world. Further, Project NExT offers a community of continuing support for faculty to strive to become the best versions of themselves.
Currently, there is a lot of work, both in academia and in the larger world, on identifying and dismantling barriers to progress in education (and society in general) that are arbitrary, hidden, or intentionally obstructive. For instance, the cost of textbooks and software is certainly an obstacle, but it’s one our mathematical community has been working to remove. We have many tools now that make publishing and sharing resources incredibly easy. As a community, we have made great tutorials on using open source, freely available mathematical software like Sage. Projects like the AIM Open Textbook Initiative have started to centralize and vet valuable resources. Projects like UTMOST are aimed at growing both the community and the tools for open source textbooks. We need to continue to examine the hidden and arbitrary barriers and costs of building great resources for teaching, as these projects do.
Just as we try to model good behaviors and practices for our students, we should make sure we are modeling good behaviors and practices for our new faculty. Do we value and support making quality materials for teaching in a comparable way to the way we value and support quality research? Further, I think we must minimize the “tyranny of the urgent” on new faculty to allow them to think bigger about their goals for teaching and making things for their teaching. Urgency is the antithesis of strategy, and we must properly harness the energy, ideas, and enthusiasm of our new faculty for teaching. Good management and administration allow all of us to flourish in all aspects of our jobs.
For example, many departments are able to offer teaching load reductions during the first year to allow new hires to adjust to new expectations. I have benefitted from this kind of accommodation for the purposes of research as well. Unfortunately, the support resources for building curricular materials can be spotty at a local level. Larger scale projects involving the making of teaching things, like UTMOST and WebWork, have received support from places like NSF and MAA. These big projects had to start as small projects and without some local support, they could not have grown to what they are now. We should be pushing for more resources at both the local and national levels for support to build things related to teaching. It is also imperative to increase the collaborations between mathematics and mathematics education faculty to build, measure, and improve upon the things we make for our teaching. Building these connections should be an explicit part of the many existing faculty communities like Project NExT and should be considered through many regional organizations like MAA and AMS Sections.
Francis Su’s 2017 MAA Retiring Presidential Address “Mathematics for Human Flourishing” does a wonderful job of talking about doing math as a truly human endeavor. “A Mathematician’s Lament” by Paul Lockhart is an insightful essay contrasting the way teaching comes through to students across disciplines. Lockhart’s work even cites G.H. Hardy’s description of mathematics as art:
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
Both Lockhart’s and Su’s pieces examine aspects of the culture of teaching mathematics and the culture of who should do (make) mathematics, respectively. I have been thinking a lot about how I make things for my teaching, how much of this making is an individual practice and how much of it comes from the culture of teaching in mathematics. There is a truism from business management “Culture eats strategy for breakfast.” Culture is a representation of what “we” do. Strategic planning and vision statements come and go, sometimes at mind boggling speed, but people (mathematicians are people too…) are loyal to culture and not to strategies. Culture is about the expectations and corresponding accountability for all in a community. And I hope that we can find a way to grow our culture of making remarkable things for our students and their learning environment as pervasive and encompassing as the culture making of art is for artists.