I want my classrooms to be places where students can reach hard mathematics, not be turned away from it. Much of my teaching is service teaching, the courses a mathematics department depends on, and I have learned to meet students where they actually are and build a clear path from there to where they need to go, without lowering the bar along the way. I hold that bar with structure rather than ease: clear expectations, demanding work, and the scaffolding and support that let students rise to a challenge instead of being defeated by it. And I try to keep learning as I teach, building in ways for students to reflect on their own thinking and for me to hear what is working and what is not, so that the course can adjust to the people in it. I have made mistakes, redesigned courses, and changed my mind, and I think that willingness to revise is an essential part of my teaching. With every course I teach, I strive to bring more structure, more clarity, and fairer grading.
Spring 2026
Teaching
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MATH340 (Numerical Analysis)
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MATH251 (Calculus I)
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MATH110 (Essentials of College Algebra II)
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MATH110Lab
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MATH100Lab
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MW 10 AM - 12 PM, 2 - 3 PM
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F 10 AM - 12 PM, 1 - 3 PM
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By Appointment (Email: sbandyo5@utm.edu)
Office Hours
Office
Latimer Smith Building, LS 360
Teaching Service Classes
Service courses are the heart of a mathematics department. They carry our largest enrollments, and for many students they are the only college mathematics they will ever take. They are also hard to teach well, and learning to teach them well has been the central project of my teaching career.
I started out teaching service courses as a graduate student at UNC Greensboro. I was the instructor of record, but the department gave us a developed Canvas shell and a set syllabus, so my job was mostly to prepare each lecture, deliver it, and grade. I leaned heavily on the course coordinators and did not yet have a chance to design a course myself. I first heard the term "DFW rate" at UNCG, though at the time I did not understand what it really meant for a department. In my last semester there, Dr. Igor Erovenko assigned me MAT 184 with no developed shell, just a syllabus. It was my first time building a course from scratch, and it taught me how much about course design I had yet to learn. The teaching itself went fine, and I gave students the color-coded notes I made on my iPad, but I came away knowing I needed to understand the whole structure of a course, not just its lectures.
When I joined UT Martin, I again borrowed materials and Canvas shells from colleagues and kept handing out my color-coded notes. Over time I noticed how much this generation of students relies on Canvas to know what is due and what is coming. In summer 2024 I sat down and learned Canvas properly, and I started asking myself a series of questions about each course I teach. The answers became the changes below.
UT Martin
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MATH 110 — Essentials of College Algebra II · [SP26, SP24 (Two Sections)]
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MATH 140 — Precalculus / College Algebra · [SP24, FA24, FA25 (Two Sections)]
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MATH 251 — Calculus I · [FA23 (Two Sections), SP25, FA24, SP26]
UNC Greensboro
Click on a semester to view student evaluations for that course.
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Where are my students coming from, and where do they need to go? I learned the prerequisites for each course I teach and the courses students take afterward, and I asked whether my class actually serves that path. To make the structure visible to students, I rebuilt my Canvas shells so that homework due dates, exam dates and topics, and a weekly agenda announcement are always posted and easy to find.
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Are my expectations clear? I rewrote the syllabi for all of my courses with explicit policies on cell phones, class engagement, and office hours, so that students know from day one what the course asks of them.
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Am I being resourceful enough? I assign a lot of homework, and hard homework. To support it, I make homework help videos and tailor my lectures so that students leave class able to do the assigned problems. In my Spring 2026 MATH 110 sections I also restructured my course notes day by day rather than section by section, with five to six homework problems at the end of each day's notes. When a quiz or exam approaches, I can tell students exactly what to study ("review Days 4 through 6"), which turns a vague instruction into a concrete, manageable task. Students responded well to the clarity. I plan on implementing it in all my service classes going forward.
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How do students learn from their mistakes? I give written solutions to every exam and quiz, and I hold in-person exam corrections in office hours where students rework missed problems to recover points. Starting fall 2026, I am adding a general feedback template that lists the mistakes I see most often on each quiz or exam and posts them to Canvas afterward.
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What do my students need that I am not seeing? Before each exam I give a short reflection quiz asking which topics they want me to review. Each month I give a longer reflection quiz asking what is going well, what is not, and how both they and I can do better.
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Specific steps to address the DFW rate. A monthly grade notecard handed to each student in person, with their weakest category flagged and a direct offer of next steps. The monthly reflection quiz, which asks what students want reviewed and what they think they need to do to succeed on the next exam. In-person exam corrections, where students redo missed problems in office hours to recover up to 10 to 15 points.
Teaching style: Demonstrate, practice, circulate, advance
Homework style: Low-stakes, participation, extra practice
Resources
MATH251 - Calculus I Videos
In the past I prepared color-coded handwritten notes on my iPad. I am now in the process of digitizing them in LaTeX; the linked Overleaf notes are a work in progress, and some courses are not yet complete. I update them as needed. If you have questions, concerns, comments feel free to email sbandyo5@utm.edu.
Upper-Division & Major Courses
My upper-division teaching is shaped by a challenge that is structural at UT Martin: these courses are genuinely heterogeneous. Several of them do not have a proof-based course as a prerequisite, so students arrive ready to compute but often without formal experience writing proofs, even when the mathematics calls for them. The rooms are mixed in other ways too. In Numerical Analysis I have taught students who have completed Differential Equations alongside students who have not, in the same section. Differential Equations brings together engineering majors and mathematics majors who need different things from the same material. Applied Mathematics I and II add a third population: engineering majors, mathematics majors, and mathematics education majors, each with a different reason the material matters to them, the future teachers among them needing not only to use the mathematics but eventually to explain it.
The constant question in these courses is how to hold the rigor while genuinely reaching everyone in the room. Coming from years of teaching service courses, I know how easily the instinct to support can become doing too much of the thinking for students, and upper-division work requires the discipline to let students struggle productively while still feeling supported. My aim is to convince students that abstraction and clarity are not opposites, and that being challenged and being supported are not either. The practices below are how I work toward that.
UT Martin
Click on a semester to view student evaluations for that course.
I start with discovery before formalism. Before introducing the machinery, I give students problems they can attempt with what they already have. In an optimization unit, for example, I ask them to find the maximum area by trying numbers and pushing as high as they can by hand before any calculus enters. They feel the problem before they meet the method. Because everyone can start by experimenting, this gives a heterogeneous room a common entry point, regardless of how prepared each student is.
I quiz for understanding, not just computation. Alongside problem-solving, I use metacognitive questions: why did this approach fail to solve this type of differential equation, why can Newton's method fail for certain initial guesses, why might we choose one model selection criterion over another. These questions push students past executing a procedure toward understanding why it works, when it breaks, and how to reason about it. This is how I build depth and a habit of logical thinking, especially for the students who are ready to be stretched further.
I model struggle and mistakes on purpose. I make errors and work through being stuck in front of the class, so students see that getting stuck and making mistakes are a normal part of doing mathematics. My goal is for them to feel safe enough to try, which matters most in courses where the material is unfamiliar and the temptation is to give up rather than risk being wrong.
Every course includes a project with a communication component. In each upper-division course students complete a project, individual or group, where they explain their work verbally, in writing, or through code. Whatever their major and whatever career they are headed for, communication is a skill they will need, and it is the one thing my engineering, mathematics, and mathematics education students all have in common reason to develop. The projects give a mixed room a shared and transferable goal.
I assign hard homework and support it fully. My homework is demanding, and my exams are drawn from it. Students have time and resources to complete it, and for every assignment I provide written solutions and video walkthroughs. The bar is high, but so is the support: the hard practice is the preparation, and effort on the homework is what carries students through the exams.
Teaching style: Explore, formalize, struggle, extend
Homework style: Graded, challenging, independent
Resources
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MATH330 (Notes, Syllabus)
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MATH451-452 (Notes, Syllabus)
MATH330 - DE Videos
Pedagogy
For years I have thought about how to make my classes more engaging and worth showing up for. My guiding idea is that the techniques I use should build the skills students will actually need after they leave my classroom, whatever their major or career: collaboration, communication, and the habit of thinking about their own thinking. The methods below are chosen with that purpose in mind.
Active learning, narrowed to what works. Through Project NExT I learned a wide range of active-learning techniques, from think-pair-share and jigsaw to scavenger hunts, entry and exit tickets, and tools like Padlet. Early on I tried to use many of them. My department chair gave me advice I have come to value: choose one or two and do them well rather than spreading thin. Over time I narrowed to the approaches that genuinely work in my rooms. Students regularly work with a neighbor, and in Differential Equations I use jigsaw activities to build real group work. My aim with these is not novelty for its own sake but collaboration, which is a skill students will need in nearly any profession.
Attention and community: the two-minute break. After about twenty minutes of teaching, I give students a two-minute break to simply talk with the people around them. They can chat, check their phones, watch something together. It sounds small, but it does two things deliberately: it respects the limits of sustained attention, so the next stretch of class lands better, and it builds the sense of community that makes students comfortable speaking up and working together. A class where students know one another is a class where more of them are willing to try.
Assessment as learning, not just measurement. I use several grading approaches designed to deepen understanding rather than only score it.
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In one, students write a problem on a blank page and pass it to a neighbor, who solves it; a third student then reviews the solution and gives feedback. In a single exercise they practice creating, solving, and critiquing mathematics, and they learn that giving good feedback is its own skill.
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I also periodically let students create problems for their own exams, modeled on the homework. Designing a fair, solvable problem requires understanding the material more deeply than answering one does.
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The approach students respond to most is one I use to prepare them for multiple-choice finals. I ask them to produce wrong answers, scored inversely: a completely wrong answer earns full points, a partly wrong one fewer, and an answer almost identical to the correct one earns the least, with a fully correct answer earning none. For each wrong answer, students have to explain why it is wrong. Students enjoy it, and it does something I find important: it forces them to recognize the mistakes we often make without realizing we are making them. Understanding why an answer is wrong is frequently harder, and more revealing, than producing a right one.
PBL in MATH451
When I designed MATH 451, Mathematical Modeling, I wanted students to do more than memorize algorithms. Modeling lives at the intersection of mathematical reasoning and real-world problem solving, and a lecture-and-exam format felt like a contradiction: how do you teach students to handle open-ended problems with closed-ended tests? So I built the course around projects. Students learned regression, linear programming, and optimization, then applied them to realistic scenarios and presented their findings the way an analyst would to a client.
The idea was sound. The execution taught me more than I expected.
What worked. Students responded to the project format. They told me it gave them applicable knowledge of the subject and helped them understand the mathematics in ways traditional homework could not. The sample projects and structured worksheets became anchors they returned to. Project-based learning created a different kind of energy: students were engaged because they were invested, and they wanted to get the math right because it mattered in a context they could see.
What I learned. Enthusiasm for a teaching philosophy is not a substitute for the scaffolding that makes it work. Students needed to know exactly how they would be evaluated, what a strong project looked like, and how each week's instruction connected to their work. When those structures were missing or shifted mid-semester, the uncertainty undermined the very engagement I was building. In project-based learning, transparency is not optional: a rubric from Day 1, a sample to aim at, a schedule that holds steady. These are the infrastructure that lets open-ended work succeed. I also learned that grading varied, original projects requires particular care, with rubrics tailored to each project's content and specific feedback, so every student understands not just their score but why they earned it.
Where I am headed. I am redesigning MATH 451 with these lessons at the center. The project format stays; it is right for this material and this student population, which includes secondary mathematics education majors who will carry these experiences into their own classrooms. The changes are structural: each project cycle will follow a consistent rhythm of instruction, practice, written submission, and presentation, with a detailed rubric specific to that project. Students will know the full schedule from the first day, and grading will separate mathematical content from presentation delivery, so a student's command of the mathematics is never obscured by their comfort at the front of a room. Teaching this course to future teachers makes the stakes double: every choice I make about scaffolding, assessment, and feedback is itself a lesson in pedagogy. Project-based learning is hard to do well, but I am convinced it is worth the effort, for my students and for the classrooms they will someday lead.