Editors’ Picks 2019

One of the exciting elements of being the Communications Editor is that I get to connect people with the exciting papers in PRIMUS that I think will impact their professional work for the better. In support of this goal, Taylor & Francis allows us (Jo Ellis-Monaghan, Matt Boelkins, and me) to select 5 papers each year as Editors’ Picks and makes them freely available for download to all without login, without requiring access to the journal.

This blog post is intended to share a little about the 5 categories of Picks and why I am excited about these particular papers. In general, I am excited by papers that push the boundaries of the ways we often think about our work as faculty and challenges us to recommit to being our best. I think it’s also really important that PRIMUS, as the most visible journal that engages mathematics and pedagogy for a readership of mathematicians of all types, supports this broad community; so I’m excited that this collection spans so many of our various subdisciplines and professional responsibilities.

MOST READ: We select a paper that is already highly active in part because this activity is evidence that people are finding this paper useful and compelling. This suggests to me that the subset of people who already had access to this paper, and people who went out of their way to get this paper, believe that this paper needs to be ready by a wider cross-section of our community.

This year, we selected “Infographics and Mathematics: A Mechanism for Effective Learning in the Classroom” by Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, and Victoria V. Polyakova. This paper takes serious several ideas that I think are otherwise under-discussed. Namely, lots of quantitative reasoning happens at the intersection of symbolic, graphical, and visual representations and that working with these representations is engaging for learners. Moreover, building these representations is powerful for learning of concepts and is a key mechanism for learning the more general reasoning skills, but many students only have the experience of trying to read, rather than construct, these representations. Unsurprisingly, this paper also contains some of the most interesting images published in the journal.

SPECIAL ISSUES: Guest Editors do a lot of exciting work in recruiting high quality papers focused on topical themes for PRIMUS, and this year we received a lot of nominations from the editorial board for papers from special issues that they would like to amplify. These individual papers are great, but making them freely available also helps draw readers into the special issue in general.

This year, we selected “Calculus Homework: A Storied Approach” by Judy A. Holdener and Brian D. Jones from the special issue The Creation and Implementation of Effective Homework Assignments. This special issue engages the national conversation about whether homework is the right choice for younger children as well as the critical question of how we in higher education will respond to the changing ways that our students are participating in our institutions. In this context, I am excited to elevate this paper, which focuses on the narrative dimensions of thinking and learning. Over the past few years, I have asked students to articulate the stories of our ideas, and frankly they sometimes respond by asserting that mathematics is just inert facts and cannot have stories. I hope this paper and the others around it lead to a sea change in which all students experience the humanizing aspects of narrative and inquiry in mathematics, especially those students who are shuffled away by our systems from these rich, sense-making experiences.

EDITORS’ CHOICE: I see this category as our opportunity to assert a stronger editorial perspective into the higher education mathematics discussion. Is there an assumption that is taken as axiomatic that we need to reconsider? Are their voices that are not being heard? Where do we need to be pushed a little further out of our comfort zones?

This year, we selected “Student-Created Definitions of Sequence Convergence: A Case Study” by Brian Fisher. I love this paper, as should be clear from how frequently I recommend it on Twitter, and I’m glad we selected it as an Editors’ Pick this year. I often tell my students that mathematics is revisionist history; I mean at least two things by this assertion. First, that when we write mathematical arguments for public engagement, we often hide all of the thinking that went into building it. It’s no wonder that students develop the non-availing belief that if they can’t do a problem correctly in under five minutes something is either wrong with the task or with themselves. Second, we also treat mathematical definitions as though they always existed or were born fully-formed in their current articulations. When working with definitions in research, we know that picking the right definitions (often to make the lemmas easier!) is a key step, and we’ve all had the experience of redefining a concept (for example function) so that our later work with is more general or swaps a hard theorem with an axiom.

One definition is omnipresent in our curricula, especially in Calculus, while also being erased: “approaching” and its formalization as convergence. The history of this concept is much more complex than I knew as an undergraduate (see this piece by Judith Grabiner), but without a working definition, students cannot really reason about limits, continuity, derivatives, et cetera. In this paper, Fisher offers a detailed plan for having students build a meaningful definition for convergence. I use this activity in Calculus I and II, and it was the way I started Real Analysis the last time I taught it. I genuinely believe that all students deserve this kind of experience with definitions, and if (Pre)Calculus is going to be a barrier to other mathematics, I think we need to offer this experience to all students. I also love how Fisher’s paper is serves as a model for translating robust MathEd research agendas into tools that impact pedagogy. I certainly don’t want to assert that all MathEd (or RUME: research on undergraduate mathematics education) should be about these kinds of tools, but as Boyer pointed out more than 20 years ago, there is important scholarship in application of research to solve challenges in our world.

FROM THE ARCHIVES: Similarly to the Editors’ Choice, we select a paper from the Archives, perhaps because it was ahead of it time or has become highly salient again. Is there an idea from which we can learn without having to recreate it from the ground up? I began this job as Communications Editor by tweeting for all of September with the hashtag #PRIMUSArchives on Twitter, identifying papers from which I believe we can keep learning.

This year, we selected “Mathematicians’ and Math Educators’ Views on ‘Doing Mathematics’” by Jim Brandt, Jana Lunt, and Gretchen Rammasch Meilstrup. As you may know, my PhD is in mathematics research, but I do education research now, so I often feel like I have a foot on both paths. There is a long history of tension between mathematics and education researchers, and I am deeply invested in building and mending the bridges between these groups. I think that one of the core reasons for these gaps is that we can hold different visions of our disciplines. This paper brings these ideas to the surface by taking a systematic approach to asking various constituencies what “doing mathematics” means to them. I hope you read this paper and talk with someone from another subdiscipline about the themes that stand out for you both.

NEW AUTHOR: Writing for PRIMUS is different from the writing almost all of us were trained to do, and it takes serious work to learn this new skill, whether the authors are junior faculty or more seasoned colleagues writing about the classroom for the first time. I am very grateful for the work of the editors and reviewers in supporting authors in this learning, but we also want to celebrate authors whose first contribution to PRIMUS is exemplary.

This year, we selected “Dog Treat Ball: An Activity to Introduce Systems of Differential Equations” by Colleen Livingston. I was personally impressed with the way that this paper help readers implement and reflect on applied modeling and mathematical inquiry. This paper is highly accessible for both faculty and their students, and I expect it will have significant impact on the teaching of differential equations. And while I’m firmly in team “cat”, I expect to adapt these ideas the next time I get to teach SIR models in Calculus or other early research experiences for undergraduates.

Please download, read, and discuss these papers, and please help us share these pieces of high quality writing widely! [And as always, MAA members can access all of PRIMUS, and we certainly hope that readers will encourage their institutions to subscribe to and support the journal.]

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