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.

Introducing (and Assessing!) the Normal Distribution

Lydia Allen Hall - Walter M. Williams High School

How do your students first experience normally distributed data in a statistics course? And how do you know if they “get it?” We will begin this session with an activity that introduces students to the normal distribution through interactive data collection. Then, we will explore both traditional and non-traditional assessment strategies to gauge and deepen students’ procedural fluency with and conceptual understanding of the normal distribution.

Thematic Learning in Secondary Mathematics

Jeff Ibbotson, PhD - Phillips Exeter Academy

Mathematics is more than just a "random" collection of problems (although students don't always see it that way!). I want to make a case for deep ideas that haunt our field of study by looking specifically at the Pythagorean Theorem and its extensions. Is it about orthogonality? Or distance? Or some other measure? Or something else? Pappus's extension points to different uses in antiquity and there is good reason to assume it functioned as part of a solution to the problem of quadratures. Even more than this it leads indirectly to the creation of new types of numbers (complex numbers, quaternions). I will present a number of proofs of the result as well as showing how it unifies Euclidean, Elliptic and Hyperbolic geometries.

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.

As You Rearrange It: Much Ado About Counting

Ben Kafoglis - The Packer Collegiate Institute

Co-presenting with Sameer Shah

Combinations and permutations? Pshaw! We kicked both to the curb when teaching combinatorics. We created a framework where students don’t see any difference between combinations problems and permutation problems. To our kids, they are the exact same kind of problem. And our students use this framework to solve more complex problems with ease.

Our approach makes more sense to kids, builds deeper conceptual understanding, and is more powerful as a problem solving tool than combinations and permutations. It’s become the unit that we most look forward to because it’s filled with so many “WAIT… WAIT… ARE YOU KIDDING?!” moments that we teachers live for. We are excited to share this framework with you. And, as time allows, we will showcase as many of the cool things we’ve gotten kids to think about using this framework as we can, such as investigating hypercubes and expansions of expressions beyond binomials. As the famous adage goes, "There are more things in heaven and earth, Horatio, than are dreamt of in your combinatorics."

Developing a Mathematical Eye: A Practical Guide to Inquiry-Based Walks

Ron Lancaster - Mathematics Consultant

Imagine students going on a math walk to make measurements, collect data, observe how things change, and notice the little things we often overlook. Picture them answering mathematical questions related to what they encounter as well as posing their own questions based on what catches their eye and sparks their curiosity.

This is what a math walk is all about: learning to slow down, be curious, and develop a mathematical eye to find and photograph where math lives. Whether on the campus of your school, in a park, at a shopping mall, or in a museum, math walks can be done almost anywhere. All you need is an imagination.

NOTE: We will also be doing a math walk on-site during this session so please wear comfortable shoes and be ready to explore and engage with the environment around you!

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.

Exploring Our Vision for Mathematics Instruction in a Rapidly Advancing Technological World

Allison McCulloch - UNC - Charlotte, North Carolina Collaborative for Mathematics Learning (NC2ML)

Technology has the potential to expand what is possible in mathematics instruction, but only when guided by a clear instructional vision. This session invites participants to explore how technology-enhanced mathematics tasks can position students as doers of mathematics. Together, we will examine what it means to enact high-quality mathematics instruction in a rapidly advancing technological world.

Participants will engage in technology-enhanced mathematics tasks and analyze video of students engaged in such tasks. These shared experiences will serve as a basis for examining how instructional choices shape what students notice, wonder about, and come to understand mathematically. Rather than focusing on specific tools, this session emphasizes the instructional vision that guides their use and remains relevant as new technologies continue to emerge.

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!

Differentiated Learning Through Tiered Projects

Brian Sea - NCSSM Morganton

Half the class is finished within ten minutes and bored, while the other half is diligently working to understand the material. How do we maintain high expectations for all students while acknowledging vastly different starting points without doubling your prep time? This presentation demonstrates using Tiered Projects to keep students engaged while giving others the space needed to understand material. It is part explanation (“Here’s what it is”), part modeling (“Here’s how I do it”), and part kinesthetic (“Here’s what it feels like”). While this presentation focuses on Computer Science, hopefully, it will be a conversation starter for “What does it look like in your course?” Come be a student and learn a bit of Computer Science while having some fun!

As You Rearrange It: Much Ado About Counting

Sameer Shah - The Packer Collegiate Institute

Co-presenting with Ben Kafoglis

Combinations and permutations? Pshaw! We kicked both to the curb when teaching combinatorics. We created a framework where students don’t see any difference between combinations problems and permutation problems. To our kids, they are the exact same kind of problem. And our students use this framework to solve more complex problems with ease.

Our approach makes more sense to kids, builds deeper conceptual understanding, and is more powerful as a problem solving tool than combinations and permutations. It’s become the unit that we most look forward to because it’s filled with so many “WAIT… WAIT… ARE YOU KIDDING?!” moments that we teachers live for. We are excited to share this framework with you. And, as time allows, we will showcase as many of the cool things we’ve gotten kids to think about using this framework as we can, such as investigating hypercubes and expansions of expressions beyond binomials. As the famous adage goes, "There are more things in heaven and earth, Horatio, than are dreamt of in your combinatorics."

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!

Letting MP5 Lead the Way: Supporting Student Choice in the Geometry Classroom

Jenny White - Amplify Desmos Math

At its core, Geometry invites curiosity, experimentation, and an opportunity to play – asking us to explore patterns, figures, axioms, and theorems with our minds. But it doesn’t prescribe which tools we are required to use for that exploration. What could a Geometry classroom look like if students chose what tools they used to explore? How might it create a space that allows student brilliance to shine when engaged in problem-based tasks? In this session, you’ll consider what it means for Standard of Mathematical Practice #5 to be on center stage in the Geometry classroom: creating a platform for students to develop strategic competence as they discern which construction tools (digital, paper folding, or compass & straightedge) to use on their exploration.