TCM 2026 Sessions

Check this page frequently as we continue to add our 2026 session titles and descriptions!

The Sound of sin(x)

Christine Belledin, NCSSM - Durham

In this session, I will share one of my students' favorite trigonometry activities. We will begin by expanding our undertanding of transformations by exploring what happens when the amplitude of a sine wave is not constant. We will then use this to investigate sums of sound waves, particularly frequency beats - rhythmic pulses of loudness that occur when two sound waves with a small difference in frequency are played together. Through this process, we will discover and appreciate a "new" trigonometric identity.

Simulation Based Inference - Hands-on Tools for Hypothesis Testing and Confidence Intervals

Taylor Gibson, NCSSM - Durham

In this interactive session, participants will explore both physical and digital simulation tools for teaching inference concepts in introductory statistics. Using hands-on materials like sampling paddles alongside coding environments and interactive websites, we'll build intuitive understanding of hypothesis testing and the construction of confidence intervals for prediction. Attendees will experience these activities as learners, discuss the pedagogical principles behind them, and leave with several classroom-ready simulations and lesson materials adaptable for various levels of technology access.

Coloring Knots and Systems of Equations

Jason Joseph, PhD - NCSSM Morganton

This talk will give a brief introduction to knot theory and focus mainly on knot colorings as a means to distinguish knots. After an initial combinatorial take (actually coloring knots), we will recast knot colorings as solutions to systems of linear equations. This can be used as a fun enrichment activity and other topics can be built in at various levels, such as solving systems of equations, linear algebra, modular arithmetic, and group theory.

IFAT First You Don't Succeed...Using Multiple Choice to Spark Debate and Activate Peer-to-Peer Instruction

Michael Lavigne, PhD - NCSSM Durham

Multiple-choice questions have a bad reputation in math education—often dismissed as instruments of rote assessment. In this session, I argue that, when used strategically, they can do the opposite: surface misconceptions, invite debate, and make reasoning visible.

Drawing on classroom practices from NCSSM, I will share three techniques that use multiple-choice or binary-response formats as vehicles for rich mathematical thinking:

1. Mathmatize – A clicker-question platform that allows students to submit symbolic answers in real time. This lets instructors visualize diverse reasoning paths and use disagreement as a springboard for whole-class discussion.

2. IFAT (Instant Feedback Assessment Tool) Quizzes – Scratch-off group quizzes that turn assessment into collaborative argument. Students must persuade one another before committing to an answer, and immediate feedback turns errors into moments of shared reasoning.

3. True/False Rodeo – A low-tech classroom routine where students take a stance on a list of mathematical claims, then defend, revise, and refine their thinking through structured debate.

Each format reframes multiple-choice questions as opportunities for metacognition and collective sense-making. Participants will leave with practical examples, design principles, and adaptable templates for using multiple-choice tasks to teach reasoning rather than just test it.

Orchestrating Modeling: An Analysis of Teacher Moves in the Modeling Classroom

Ashley Loftis, PhD - NCSSM Durham

In this interactive session, participants will engage in a mathematical modeling task centered on minimizing total road length and analyze classroom videos of teachers facilitating the same task with students. Discussion will focus on identifying and reflecting on teacher moves, exploring how they connect to phases of the modeling cycle, and how they promote perseverance, collaboration, and deep reasoning while supporting productive struggle and maintaining high cognitive demand.

Artspace

Samantha Moore - NCSSM Morganton, TCM Coordinator

Have you ever been interested in exploring the intersection of mathematics and art in your classroom, but been unsure how to do so? If so, this session is for you! We will have three mathematical art projects as well as ideas about how to integrate them into your classes. The math topics tied to the projects will range from math 3 to graph theory. This is a hands on session, so you will get to make your own art pieces while exchanging ideas with your fellow attendees!

Taxicab Geometry for Enrichment

Ryan Pietropaolo - NCSSM Durham

Is Euclidean geometry for the birds? On a Euclidean plane, distance is “as the crow flies,” but most of us are not crows! This understanding of distance isn’t really applicable to the urban built environments that we are most familiar with in our immediate surroundings. What if distance was defined differently? In this session we will learn about taxicab geometry to enrich students’ understanding of Euclidean geometry. In taxicab geometry, the distance between two points is defined as the horizontal plus the vertical distance between them. Under these conditions, what does a circle look like? What is the value of pi? Learn the answers to these questions and more and leave prepared to surprise your students with taxicab geometry!

What I Learned About Teaching Math From Teaching Flying

Philip Rash - NCSSM Durham

How is teaching someone how to fly an airplane similar to teaching someone mathematics? As I've discovered over the past several years, they have more in common than you might realize. In this session I'll briefly overview the process involved in earning a pilot certificate and share some reflections on the similarities between flight instruction and teaching mathematics. While I’ll have multiple examples and experiences to share, I look forward to hearing ideas from session participants as well!

Introduction to Modeling with Lab Based Calculus, and

Taking Modeling with Lab Based Calculus to the Next Level

Ryan Severance - NCSSM Durham

Introduction to Modeling with Lab Based Calculus

Students are naturally curious individuals, but how can we enhance their curiosity and sense of wonder of mathematics in the classroom? In our program we have structured our calculus curriculum to be centered around a lab based approach to learning. This approach invites the students to work in tandem with the instructors to build ideas, recognize patterns, model real world scenarios, and communicate their thinking.

Taking Modeling with Lab Based Calculus to the next level

Once you have introduced Modeling and labs into your Calculus courses, you should begin to ask where we can go from here. During this session we will look at a couple of our more open ended investigations and one that can also be used in a Differential Equations course. This approach continues to invite the students to work in tandem with the instructors to build ideas, recognize patterns, model real world scenarios, and communicate their thinking.

Taxicab Geometry for Enrichment

Veronica Vazquez Zamora- NCSSM Durham

Is Euclidean geometry for the birds? On a Euclidean plane, distance is “as the crow flies,” but most of us are not crows! This understanding of distance isn’t really applicable to the urban built environments that we are most familiar with in our immediate surroundings. What if distance was defined differently? In this session we will learn about taxicab geometry to enrich students’ understanding of Euclidean geometry. In taxicab geometry, the distance between two points is defined as the horizontal plus the vertical distance between them. Under these conditions, what does a circle look like? What is the value of pi? Learn the answers to these questions and more and leave prepared to surprise your students with taxicab geometry!