Math and Power: My 2021 Teaching Statement

I wrote this teaching narrative as part of my portfolio for promotion to professor at Bridgewater State University in 2021. I’m sharing it here in case it helps the interested reader of this blog to better understand the ways I think about and approach teaching (at least since 2014, as far back as my portfolio needed to go).

Disclaimer: Everyone’s teaching narrative is different, not least because of the context in which it is written. Mine is reflective of both (a) my position as a faculty member at a teaching-focused primarily-undergraduate institution with a social justice mission; and (b) my limited amount of actual classroom teaching relative to my colleagues, since I have always held simultaneous administrative roles at the university. Your needs and contexts will vary! And… if I had had more time, I probably would have written a shorter version.

My Teaching Narrative

While I began my teaching at BSU with a primary commitment to teaching and coordinating developmental math courses, I have throughout my time been fortunate to have opportunities to teach a broad range of courses and students, from academically-vulnerable first-year students taking non-credit math courses, to graduate-school-bound senior math majors, and everything in between. Each group of students brings with it a unique set of experiences, goals, advantages, and challenges — and my consistent habit of innovating and experimenting in my teaching is, I believe, a reflection of my efforts to teach in ways that are more than just effective, but address the unique needs of the students in the room.

No educator steps into a classroom alone, nor do they bring only themselves to the task. As the constructivist D. Bob Gowin writes in the opening lines of his book Educating, we always “begin in the middle.” Not only do students carry with them sometimes-helpful, sometimes-imperfect content knowledge from their previous courses atop which to build new knowledge, we as teachers also carry with us the momentum of our own experiences and habits both as teachers and learners, which in turn have been inevitably shaped by the norms and customs of our discipline’s habits of, and beliefs about, teaching. 

First, do no harm. In mathematics, our students know — even when we do not — that those norms, customs, and habits have not always served all students well, nor equitably. Math is a subject whose truths both have power, and often serve power. Across status hierarchies of any scale, from that between a third-grade student and her teacher to that between the Black community in the U.S. and their elected government, math has an unfortunate history of being wielded by the powerful to exploit and exclude the powerless. So while a teacher’s dismissive comment about a third-grader’s math ability and a sophisticated algorithm that gerrymanders legislative districts to dilute the voting power of a minoritized group may be quite different in degree, they are not all that different in kind.

Math is a subject whose truths both have power, and often serve power.

Because Bridgewater is a place with a long history of teacher preparation and educational leadership, it is only natural to me that understanding and redressing the painful parts of the legacy that math and math education has created in our country should be a responsibility that our faculty, and especially a faculty in the department chairperson’s seat, must take seriously. Fortunately, whether you ask a student what led them to embrace mathematics for themselves or you ask them what drove them away from mathematics — whether you ask when they first felt included, or when they first felt excluded — the answer is almost always the same. 

It starts with one teacher.

Everyone who purports to teach math, therefore, should feel the weight of that responsibility. What I do with my students not only has the power to shape their cognitive capacities, it also has the power to shape their self-concept, and their conception of their place in the mathematical world and beyond. And it is not a given that those changes will be for the better.

In the past few years I have recommitted myself to examining my teaching practices through the lens of not only what will make my students learn more, but what will make more of my students learn. What can I do to expand access to mathematics across the barriers faced by many of our students? What can I do to make myself a teaching resource not only for my students but for students beyond my courses, even beyond my institution? And what can I do within my sphere of influence to dismantle some of the historical practices of mathematics teaching that might otherwise interfere with the learning and success of all of my students?

In the narratives below, I’ll discuss the contexts and approaches with which I’ve taught my courses over the past few years at BSU, and highlight how they reflect the evolution of my practice in several important ways.

Growth-Focused Grading

The first is growth-focused grading. Without a doubt the most profound change I have made to my teaching practice in my career was my complete shift in the spring of 2017 away from the historical practice of tying students’ grades to an average of their performances on the tasks I set for them, and instead tying them to the sum of the learning outcomes that the totality of their work demonstrates they have mastered. This approach, which in various implementations is called standards-based, mastery-based, or specifications-based grading, mitigates the adversarial power dynamic between student and teacher created by points-based grades.

Does the way I assign students grades align with the rest of my teaching philosophy?

Grades determined by average scores on timed, single-shot tasks focus student attention on performance more than learning; points grades are often are determined by imprecise and nontransparent means (rubric scoring is rarely used in grading mathematics, leaving students to wonder why their work merited 6 points out of 10, rather than 7); and, especially crucially for online teaching, single-shot grades increase students’ incentives toward academic dishonesty (a student who’s not yet comfortable with the material may decide the risk of being caught cheating is lower than the risk of submitting work that accurately reflects their current understanding and being stuck with a low test grade). Common traditional-grading practices intended to lessen its deleterious effects on student outcomes and student mental health, such as dropping lowest scores, offering extra credit, or diluting grades with data such as attendance which are not evidence of student learning, are band-aids at best and can be inequitable at worst. (For example, students whose grades are already high are more likely to take advantage of opportunities for “extra credit” than students whose grades are low.)

The path toward growth-focused grading begins with some often-unexamined questions. Why do we grade? What do our grades mean to us? To students? To external constituencies (employers, graduate admissions officers, scholarship reviewers)? What do we want them to mean? And most importantly, does the way I assign students grades align with the rest of my teaching philosophy?

In my case, it was the latter question that caused me to change my practices. I had always taken pride in experimenting with evidence-based and innovative ways of teaching — incorporating active and project-based learning, flipping the classroom, using inquiry-based techniques — all of which align with my desire to decentralize the authority among me and my students to hold space for their agency, their creativity, and their diversity. But I had been assigning grades “the way it’s always been done”: by making quick, subjective, and to students often arbitrary, judgments assigning points to their performances and then averaging the results using category weights that I’d chosen just as arbitrarily. My pedagogy was built around honoring my students’ individual voices and processes, but my grading was anything but.

I had first learned about growth-focused grading approaches in 2016 through math faculty colleagues at Grand Valley State University, one of whom, Robert Talbert, had written the book Flipped Learning that had been influential for me in using flipped classrooms years earlier. Working with and learning from him and a small group of other math faculty across higher education in a small Slack group, I resolved to implement one such approach (standards-based and specifications grading) in my Spring 2017 course, MATH 401 Introduction to Real Analysis. I selected this course in particular because of its reputation among math majors — both at BSU and elsewhere — as among the most challenging required courses an undergraduate will encounter. It was also a new prep for me at BSU, though I had taught the course at a previous institution. If changing my grading could help ease student anxiety and place their focus on learning, I reasoned, there would be no better test case than this course to try it.

I laid out a set of 15 learning goals (“standards”) for the course, consisting of 9 essential “core” standards that must be mastered to earn a grade of “C” and 6 additional standards whose mastery would count toward grades in the A/B range. Students “master” a standard when I assess that their work provides evidence that no further instruction is needed on the topic; until then, they receive opportunities — sometimes during class, sometimes outside of class — to revise their previous work and re-attempt to demonstrate mastery. And at no time would their poor performances hurt their grade: the only permanent marks in their gradebook are ones that confer full credit for mastering a standard. Every other mark is a “not yet.”

I used the same quizzes-and-exams regimen that I would have used in previous semesters; I only changed how they, and I, interacted with them. Instead of assigning points, I assigned a mark (E, M, R, N) indicating whether their work shows they’ve (M)et the standard, or done so (E)xceptionally well; or whether they should (R)evisit the standard at a later opportunity. I also gave students feedback on their work to help them improve – as I always had tried to do when marking student work – but this time with the knowledge that they were more likely to read it and heed it because they knew there would be more chances to get it right. What’s more, they knew their unfinished learning would not be held against them because they hadn’t fully absorbed a topic by the time they were first tested on it. This freed them up to take risks with their in-progress understanding, knowing that if it paid off there would be credit and if not, there would be feedback and another chance.

I felt the change on the first day of the semester, and not least because my students told me so. Not only did it succeed over the semester in shifting my conversations with students away from grades, points, and assignments and toward learning, progress, and the course material itself; it also transformed my experience of grading student work from a somewhat-aimless process of deciding point values to a much clearer assessment: would I say that the person who submitted this work really has learned this topic? Or does it show a need for further instruction and review? If the latter, what feedback can I give that would most point them in the right direction?

[Students] knew their unfinished learning would not be held against them.

The change in dynamic, while it always takes students a few weeks to adapt to (and, in some cases, believe), was so positive that I have implemented it across all my teaching since then, with some tweaks every semester as always, as I learn what works best for each course context. I believe my students are learning better and with less assessment anxiety as a result. My grade distributions, meanwhile, have not inflated: if anything, I am assigning somewhat more grades in the C range and lower than before. But I know now, and my students do too, that those grades do not reflect poor performance as much as they reflect missed opportunities to reflect, revise, and improve upon the topics they had not yet mastered.

Since then, there has been a renewed scholarly conversation about growth-focused grading, both in higher education and in the K-12 sector, for many of the reasons that led me to the practice. The small Slack group where I first developed my approach has blossomed into a nationwide network of educators, most of them in STEM disciplines, that will hold its third annual Grading Conference later this academic year. Just last summer I had my first experience of a student who was not taken by surprise by my approach to grading, because she had had a great experience with her biology professor at a previous institution who did the same. I’m proud of the way this practice is creating new critical, learning-focused, and justice-focused conversations among faculty about grades, and creating more positive, humane learning experiences for students, and I’m excited to see the impact of its increasing adoption by faculty across the K-16 spectrum in the coming years.

“The Multimedia Professor”: My Open Educational Resources

A second significant change to my teaching practice during the review period has been my commitment to adopt and use low-cost and no-cost educational materials in every course I teach. The open educational resources (OER) movement in higher education gained a significant amount of traction during these years, and for me it “clicked” when I became familiar with the work of Plymouth State University English professor Robin DeRosa. When she presented at an Office of Teaching & Learning seminar showing how her teaching is not just about “free books for students” but embodies a wider philosophy of student co-creation, remixing and reinterpreting these open resources and creating new, public anthologies of literature with them — and that this kind of open, public scholarship epitomizes the value and mission of public higher education — I was hooked.

I had never been overfond of the textbooks I assigned in my courses for students to buy and read. In part this was likely because I was not using the texts to their fullest potential, but in part it was because I usually ended up creating and drawing from resources of my own: sometimes written notes, sometimes interactive applets, and sometimes – especially as I began to use flipped-classroom approaches – instructional videos. As a result, when I reflected on my habit of using commercial texts, I found it very difficult to justify the expense they shifted onto my students — especially students in developmental math, who are not only not earning college credits for their investment but are also disproportionately first-generation and Pell-grant eligible students. The cost of college already burdens those students regressively; by adding the costs of textbooks that I wasn’t using effectively, whose information is freely available elsewhere, and which students would have no reason to retain beyond the end of the semester, I was complicit in adding to that burden for my students.

This kind of open, public scholarship epitomizes the value and mission of public higher education.

Beginning in mid-2016, I phased in open educational resources in almost all my courses. And, in the courses that I helped to coordinate in the department, worked with faculty colleagues to identify OER options that they could review and adapt in their sections as well. As I was leaving my Math Services role, I worked with my successor to adopt the low-cost Knewton Alta platform across the MATH 090 and 095 developmental courses that remains in use today. As Chair I’ve also supported colleagues doing the same work with the courses they coordinate, and this year the high-enrollment MATH 105, MATH 122, and MATH 132 courses all have well-developed OER options selected by their coordinators and available to instructors across all sections. I’ve connected with colleagues across the country authoring dynamic, multimedia-enhanced math OERs through the “PreTeXt” platform, and used that platform to author and share a number of resources of my own for the courses I’ve taught.

This work has also helped me to see my teaching work in a new light. In my previous portfolio I spoke to my creation of a full course of flipped-classroom videos when I first taught MATH 302 Abstract Algebra II in 2013, and my public sharing of those videos via a YouTube playlist. Learning more about OER and open pedagogy has helped me to frame that work as a kind of public scholarship. It’s given me the incentive to continue and expand those efforts as a result.

Now, I share the videos I create in the process of teaching almost every course, and in 2019 I created and shared another full video course, MATH 301 Abstract Algebra I, to accompany my earlier work on its second-semester followup. The 77 videos, totalling nearly 15 hours, in this course have since been viewed more than 53,000 times by viewers worldwide. Across my YouTube channel, populated entirely by educational math and quantitative literacy content, my videos are viewed on average 700 times per day. In the first three months of the COVID-19 pandemic, my videos were accessed by more than 30,000 unique viewers as remote-learning made access to open content from a luxury into a near-necessity for both instructors and students around the world.

When the whole world had to pivot to using the internet for teaching and learning, I was in large part already there.

My engagement in this online teaching and content generation work also meant that when the whole world had to pivot to using the internet for teaching and learning, I was in large part already there. As an extension of my video creation, I had begun in 2018 to offer my students some additional office hours and review sessions via streaming video, at first using the public Twitch platform to make these sessions viewable both live and pre-recorded to anyone on the internet. I experimented with this practice for several semesters before my Fall 2019 sabbatical, and could not have known how valuable that preparation would be when live-stream teaching and learning became the norm in 2020. Especially early in the pandemic, I found myself being regularly contacted by educators – some of whom I’d never met but were familiar with my online teaching presence – for assistance in locating and training colleagues on tools to facilitate live synchronous teaching. I created and shared instructional handouts, videos, and blog posts in an attempt to reach whomever my experience could help (beginning, of course, with my BSU faculty colleagues in the department). 

To Robin DeRosa’s point, this is the kind of public scholarship, public teaching, public faculty-to-faculty support, and public engagement that I believe highlights the value and the mission of an institution of public higher education. The idea that one’s own teaching can positively impact not only their own students, but students and teachers they might never meet: that should put a smile on anyone’s face.

Experimenting at Scale

Finally, my desire to experiment and innovate in my teaching — and my commitment to improving BSU’s first-year math experience, from placement through the first semester — have involved me in several exciting pilot programs over the years. Each was an opportunity not only to test out new instructional models for these first-year courses, but also to expand my own base of knowledge and practice for teaching this often-vulnerable group of students transitioning into their first semester of college.

During the review period of this portfolio, all of these pilots have involved the MATH 105 Mathematical Thought & Practice course. I had served the math department as course coordinator in 2013-2014 and, as part of that work, collaborated on the articulation of common learning outcomes and development of shared sets of materials and available online homework sets to support the instructors of this multi-section course that, at the time, was the largest single math course in BSU’s Core Curriculum. It’s also a course whose math objectives are more broad than deep, as its goal is to engage students intending on majoring in humanities and fine arts disciplines with what may be, for them, the last mathematics course they will be required to take in their educational life. As such, the course does not typically employ much computation or algebraic manipulation — even though students are required via the placement process to demonstrate fluent algebra skill to satisfy its prerequisite. 

This seeming misalignment has made the MATH 105 course a frequent target of reimagination. Most recently, in the 2020-2021 academic year the math department designed a pilot study, encouraged by placement policy changes at the Department of Higher Education, to offer first-year students placement into the course on the basis of their high school grade point average, with an additional corequisite hour of instructional time for students whose math placement scores would otherwise have assigned them to the non-credit prerequisite. That pilot study, which also included the MATH 110 Elementary Statistics course, is under way in Fall 2021 and has allowed 100 students in the 2021 first-year class to access credit-bearing mathematics in their first semester who would not otherwise have had the opportunity.

The previous experiments with MATH 105 during these years were twofold, and both happened to take place in the same semester, Fall 2014. 

One of these was a project led by then-Dean Paula Krebs in the College of Humanities and Social Sciences that sought to create linked-learning community cohorts among first-year students. In this program, cohorts of first-year students would register for a linked pair of first-year courses appropriate for their major, and the instructors of the linked sections would collaborate across disciplines to align and find connections between the material of their courses and create some shared assignments and co-curricular experiences to promote integrative learning for their students.

My role in this project was as instructor for a section of MATH 105 that was linked to a section of PHIL 111 Foundations of Logical Reasoning, taught by Dr. Laura McAlinden. Through our collaborations in this program, she and I quickly came to realize that our two courses in fact shared a large number of common goals and even covered many common topics (MATH 105 has a significant unit on logic and assessing logical arguments). However, the terminology, notation, and language we each used for these common topics was quite different. This was the kind of mutual understanding that might never have occurred outside of this kind of collaboration, and it equipped both of us to talk across disciplines and use the other’s vocabulary in the classroom to reinforce as common the ideas that students would otherwise have found disconnected or confusing. The experience was particularly helpful for me in future conversations about MATH 105 and PHIL 111 in particular, and about the BSU Core Curriculum’s skill goals in general when these were the subject of review and proposed revisions from 2016-2018.

The other significant pilot during this same semester represented an early iteration of this year’s high school GPA placement pilot. In Fall 2014, working with my colleague and then-Chair Dr. Becky Metcalf and with staff and advisers in the Academic Achievement Center, the math department offered placement into MATH 105 to a group of 50 incoming first-year students who met a minimum overall high school GPA criterion but whose math placement exam scores were marginally lower than the minimum for MATH 105 placement. These students were permitted to enroll in any available section of MATH 105 in the fall, but required to take a one-credit experimental corequisite course entitled MATH 123 Strategies for Math Success, that met over three weekly contact hours. 

The aim of the MATH 123 course was twofold. Half of students’ time in this corequisite support was devoted to a instructor-guided yet self-paced review of algebra topics such as they would otherwise studied in the non-credit MATH 090 course. The other half was participation in a self-regulated learning (SRL) curriculum in which students learned and practiced explicit strategies for academic success such as study session strategies, note-taking, time management, test anxiety management, basic research and presentation skills, and other elements of so-called “college knowledge.” A heavy emphasis in the SRL curriculum was placed on metacognition and reflection strategies to increase students’ awareness of, and accurate assessment of, their level of understanding of a course’s material and their need for additional practice. 

Less bound by the particulars of math content, it gave me the ability to interact with students on a more holistic level and blend advising and coaching qualities.

I designed and was the classroom facilitator for this segment of the MATH 123 course, and being less previously familiar with teaching these kinds of college-success courses this involved a large investment of my research and time. It ultimately became one of the highlights of my teaching life during these years, however: being less bound by the particulars of math content, it gave me the ability to interact with the students on a more holistic level and blend advising and coaching qualities with the instruction. The activities I developed and collected into a student notebook for this course would also be ones I would borrow from frequently in my other courses over the coming years, and the self-regulated learning framework reflected in them has become a lens through which I now understand my teaching, advising, and student support more generally.

Conclusion

Teaching, learning about teaching, thinking about teaching, supporting others’ teaching: these are the things that have always consumed the majority of my mental energy since my first full-time semester of teaching in 2006. It should be no surprise, therefore, that this has had ripple effects out into my scholarship and my professional activities both on our campus and beyond. Indeed, nearly every achievement in my portfolio can be traced back to my commitment to both being a better teacher, and encouraging others to do so.

And I could not have accomplished all this on my own. Being a faculty member at Bridgewater State University has uniquely situated me among a community of teacher-scholars who are at least as committed to that mission to improve education as I am, and so much of what has made me a better teacher, I have learned from my colleagues at this institution. And while my unusually high level of professional service has limited my teaching assignments in quantity, they have not been limited in quality. The experiences I have had in my service roles, whether through the Academic Achievement Center, through faculty development leadership, or as Chair, have allowed me both to continue to learn and grow in my teaching, and also — perhaps even more importantly to me — to contribute to my colleagues’ growth as teachers, and so to contribute to the success of so many more students than I could ever have in my own classrooms. 

It starts with one teacher. And both following and leading by example, I want to help us all to be that teacher, whether for hundreds of students or for just one.

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