# 2022 TCM Presentations

Laurie Rubel, PhD, University of Haifa

Keynote Address: Mathematics, Place, and Power: Teaching Mathematics for Spatial Justice

Laurie will share ideas about place/space in education and how place is taken up in mathematics education. She will consider the question of how place/space are related to justice and will explore potential directions for teaching mathematics for spatial justice. Examples from four thematic categories: geographies and opportunities, mapping, mobility, and land relations will be shared.

Tamar Avineri, NCSSM

Is This Really Logical? Analyzing Logical Statements and Argument Validity

For this active learning session, we will focus on mathematical logic and argument validity. We will spend the majority of our time working collaboratively on tasks pertaining to these topics, and participants will walk away with resources they can implement in their classrooms. These topics can be found in the North Carolina Discrete Mathematics for Computer Science course, which launched in Fall 2020, but participants outside of North Carolina are very much encouraged to attend as well! Some of the shared activities make for great math club or recreational math activities!

Dr. Kevin Bartkovich, Phillips Exeter Academy

Mastery-Based Assessment in Algebra I

In the Fall term of 2021, a pilot program at Phillips Exeter Academy challenged the status quo of traditional grading in the 9th grade Algebra I classes. Weekly assessments were graded on a mastery basis with individualized reassessments for learning objectives not yet mastered. The success of the pilot makes us eager to expand the project into other classes next year. In this presentation we will discuss the rubric used for marking assessments, assignment of grades at the end of the term, handling reassessments, equity in grading, and strategies to keep from deconstructing the course into a set of disconnected objectives. The learning objectives matrix will be shared, as will case studies of some individual students.

Christine Belledin, NCSSM

The Art of Lines and Circles

In this session we will explore ways that we can use families of lines and circles to create interesting patterns and beautiful images. We will use Geogebra activities to explore modular multiplication on circles and ways to create cardioids and other interesting curves and patterns.

Chris Bolognese, Columbus Academy

Positioning Students as Problem-Posers

We frequently talk about how students should be problem-solvers. But often, the problems students are asked to solve are already created. In this session, we will explore how to support students as they generate and solve their own problems.

Floyd Bullard, PhD, NCSSM

In and Out of Sync: Using Real World Contexts to Help Students Appreciate and Understand a Trigonometric Identity

What do school bus windshield wipers, an exoplanetary system, and an out-of-tune piano all have in common? They all involve periodic functions that go in and out of sync with one another. In this session we'll see how these (and other) phenomena can be used to motivate the study of trigonometric identities involving sums of sine functions. Participants will leave with one classroom-ready activity--and they may never again experience a sidewalk the same way.

Michelle Cirillo, PhD, University of Delaware

Thought Tools for Mathematical Modeling: Strategies and Tasks for Teaching Modeling Competencies

Mathematical modeling is an important mathematical process that has the potential to engage and motivate students as well as support the development of mathematical agency (see, e.g., NCTM, 2018). However, a lack of curricular resources and teacher development in this area have proven to be obstacles in teaching this increasingly important process. To make progress on this issue, a set of research-based Thought Tools and corresponding tasks that support teachers to develop, in students, competencies for modeling will be presented. Competencies that ultimately support full modeling instruction, such as identifying factors, making assumptions, and choosing mathematical objects, will be explored. Attendees will leave with classroom-ready tasks and further ideas for developing their own tasks.

Diana Davis, Phillips Exeter Academy

A Discussion-Based Math Class With a Problem-Centered Curriculum

I'm passionate about classrooms where students discuss mathematics with each other. I'll explain how to create a classroom like this, and how to construct a curriculum that makes it happen. In addition to explanations, I'll give lots of examples and show lots of pictures. If you're interested, you can read about this in advance in this manual that I wrote: https://dianadavis.github.io/davis-how-to-write-a-pbc.pdf

Cheryl Gann, NCSSM

Fractals & Iteration: From Middle School to High School*

Iteration and recursion are powerful tools that show up in math and related fields. In this session, we will explore fractals and iteration through hands-on activities and using technology. We will see how these topics can be shared with students at different places in their mathematical journey.

*This session will be co-presented with Katherine Lavine

Mahmoud Harding, NCSSM

A 2-Ton Problem: Using Hippos to Increase Student Choice

In this session, participants will examine a model-building activity through the lens of student choice. This activity will allow participants to analyze the hippopotamus crisis caused by Pablo Escobar and his four hippos. Participants will engage with data analysis, exponential functions, and a discussion about how student choice affects modeling.

Shelly M. Jones, PhD, Central Connecticut State Univ.

#Representationmatters: Strategies to Develop Students’ Positive Math Identities

Getting students to believe in their ability to do mathematics and helping them to see how math can play a powerful role in their lives is at the center of math identity work. This session will focus on how to use the stories of diverse mathematicians to broaden students’ views on who can do mathematics and for what reason. There is a lesson in each story – come and hear our stories and tell yours.

Nick Koberstein, NumWorks

Exploring the IDEAL Problem Solving Model: The NumWorks Story

One of the greatest skills we can teach our students is problem solving. But solving problems is more than just coming up with solutions. Using the IDEAL problem-solving model, NumWorks sought to create a math tool that is easier to use. We will explore the lessons learned from the NumWorks experience that we can bring into our classrooms.

Ron Lancaster, University of Toronto

Solving optimization problems using mathematical, mechanical and physical models

In this workshop we will explore how mechanical and physical models can support students when they solve optimization problems using mathematical models. Mechanical and physical models can deepen students' understanding of the problems they are solving; they allow students to tinker with the conditions of the problems, and they provide students with evidence of whether or not their mathematical solution is on the right track. These models also invite students to explore the physics principles behind the models and can facilitate conversations between mathematics and physics teachers leading to future collaborations.

Katherine Lavine, The Expedition School

Fractals & Iteration: From Middle School to High School*

Iteration and recursion are powerful tools that show up in math and related fields. In this session, we will explore fractals and iteration through hands-on activities and using technology. We will see how these topics can be shared with students at different places in their mathematical journey.

*This session will be co-presented with Cheryl Gann and the video may be found under Ms. Gann's name.

Steve Phelps, Instructional Technology Coach and Mathematics Coach

What-If-Not Completing the Square

What if we changed the traditional completing the square algorithm? What if we decide to not "take half the middle term, square it, and add it to both sides" and (instead) try adding something else? Let's explore what happens when we try to complete the square (or cube) in different ways by using GeoGebra to examine the unexpected patterns in the graphs of these completed squares or cubes.

Ryan Pietropaolo, NCSSM

Solving My Favorite Differential Equation problem: The Snowplow

We will tackle a classic problem that provides little background information and initially seems impossible. With closer inspection, we can extract the necessary equations which, when coupled with a little integration and creative grouping, can be used to solve this riddle-like challenge. The solution uses a related rates approach, making this problem suitable for any student from AB Calculus to Differential Equations.

Ginger Rhodes, University of North Carolina Wilmington

Finding Treasure with GeoGebra

We will explore the classic and engaging treasure-hunt geometry problem using several strategies, including exploring the problem through GeoGebra. The dynamic software provides insights that are difficult to see with traditional paper and pencil strategies. We will discuss various solutions to the problem and make connections to state standards.

Amber E. Smith, NCSSM

Hi Ho! Cherry-O: A Simulation Activity Using Python and Data Science

Hi-Ho-Cherry-O is a classic children's game that can last anywhere from 3 turns to over 100 turns. Depending on where the spinner lands, the players will either add cherries to the bucket and get closer to winning, or put cherries back on their tree. Using Python and Data Science, we will simulate Hi-Ho-Cherry-O games and determine the answer to the question, on average, how many turns does a Hi-Ho-Cherry-O game last?

Dan Teague, NCSSM

What do you know if you know the solution to a differential equation? A Calculus Investigation

This session will compare the solution to a differential equation with the results of simulations of the process the differential equation describes. Examples will be the classic S-I infectious disease model (which leads to the logistic function) and some modern network models that have easy AP Calculus level differential equation representations. Teachers will have access to the simulations created in Netlogo for use with their classes (Netlogo is free, cross-platform programing language).

Verónica Vázquez , NCSSM

Upgrade Your Assessments! Strategies and Tools to Make Tests More Meaningful

Explore some fun and easy strategies for low stakes formative assessment, creative ways to use ipsative assessment (and why you want to), and how to leverage the power of Gradescope to quickly give students specific feedback they can use to improve their skills.