**Morning courses (8 a.m. – 10 a.m.)**

**01 - Foundations of Data Science for High School Students**

**Leader**: Mahmoud Harding, North Carolina School of Science and Mathematics

In this course, we will engage in activities that focus on three core aspects of data science: exploration, inference and prediction. We will learn the basics of the Python programming language along with commands and functions for investigating and graphically displaying data. Throughout the course we will manipulate data sets, plot visualizations, make predictions, and quantify our level of certainty. The course will conclude with participants learning how to design activities that can be distributed to students through Jupyter notebooks.

**02 - Just Five Good Precalculus Labs **

**Leader**: Dan Butler, The Lovett School

Let's spice up our precalculus curriculum with some amazing labs. We will use GeoGebra, the TI-84, hands-on materials and anything else we decide we need to explore some of the concepts of precalculus through great problems, like using “Astronomy” magazine to teach transformations of trigonometric function, using paper folding to show basic trigonometric identities in a meaningful way, and a new look at the classic box problem. We will also take some time to discuss what needs to be in a precalculus course as well as how to fit these spicy problems into an already full curriculum.

**03 - Calculus Before Calculus: Deepening Students' Understanding of and Appreciation for Mathematics **

**Co-Leaders: **Ron Lancaster and Gurpreet Sahmbi, University of Toronto

Takeaways from this course will include strategies so that all middle and high school students can be exposed to topics covered in calculus without actually knowing any formal calculus. Another takeaway will be strategies for using technology and manipulatives that students can use to explore the fundamental ideas of calculus. The purpose of this course is not necessarily to promote the idea that all students should eventually take calculus, but that early exposure to calculus can deepen students' understanding of math and make their learning of math more meaningful with a deeper appreciation.

**04 - Making It Relevant: Algebra I/II (Skew The Script) **

**Leader**: Niki Wells, Skew The Script

We need citizens who can use math to analyze complex issues. So instead of checking the real world at the door, let's invite real issues into our math classes. In this course, we will explore lessons on relevant topics (e.g., voter power, food deserts, electric cars, social media, sports) from the Skew The Script Algebra I/II curriculum. We'll discuss how to use these activities to boost learning, engagement, awareness and critical thinking, all in a non-partisan way. Finally, we will generate strategies for facilitating productive and balanced classroom conversations on such topics.

**05 - Gerrymandering with Math **

**Leader**: Diana Davis, Phillips Exeter Academy

Gerrymandering was an intractable problem for many years, but recently some states have been making progress – thanks to math! In this course, we'll learn how to use modern techniques (the ones that convinced SCOTUS) to detect and measure gerrymandering by solving problems and discussing our solutions. Math tools we'll learn include random walks, graph theory, and outlier analysis, plus all the necessary political background. Come learn the tools to increase fairness, and then teach your students to do the same. A great course for geometry teachers – apply geometry reasoning in a new way!

**06 - Creating and Planning a Diversity, Equity and Inclusivity Unit **

**Leader**: Thomas Hill, Brewster Academy

In this course we will help you search for your starting point for DEI lesson planning. We will be using Learning for Justice's DEI standards that will frame how we look at lesson construction and implementation. We will be looking at high school curricula for examples. One specific case will be exponential population growth and China's one-child policy. We will spend time in group discussions and collaborating to create lessons and unit ideas. You will leave this week having gone through how to build a Diversity, Equity and Inclusivity unit and having had time to work with peers to create your own.

**07 - Using and Building Desmos Activities to Provoke Student Thinking**

**Leader**: Chris Bolognese, Columbus Academy

Desmos is not only a graphing calculator, but an online platform to allow students to explore deep mathematics. This course will explore pre-built Desmos activities for middle and high school grades and allow participants a chance to build their own Desmos activity to use in their classroom. No experience is required with Desmos Activity Builder. Resources will also be provided for more advanced users that want to explore the computational layer.

**08 - Nurturing the Seeds of Calculus in the Middle Grades **

**Co-Leaders:** Laurie Cavey, Boise State University and Tatia Totorica, Boise State University and Boise School District

Using a range of problem-solving strategies, we will explore rates of change and limits, two fundamental ideas in the study of calculus. In particular, we will consider situations involving constant rates of change and how we can support student understanding of related functional representations. With respect to limits, we will consider the infamous 0.9 repeating question (is 0.9 repeating equal to 1?) and other ways middle school students encounter the infinite. Along the way, we’ll examine how these ideas were both intuitively and more formally addressed throughout the history of mathematics.

**09 - Beginning Math Teacher Workshop**

**Leader**: Jessica Schenkel, Porter-Gaud School

This course is designed for teachers in their first five years of teaching. Regardless of your background, this course will provide an opportunity to reflect on past experiences and leave you refreshed and full of ideas for the 2023-24 school year. Jessica will share her experiences, successes and failures as a teacher and department chair in public, day and boarding schools. We will review trends in math education, how to put relevant research to practice, classroom management techniques, curriculum design, and how to create a classroom that supports the development of a growth mindset.

**10 - Early History of Mathematics **

**Leader**: Jeff Ibbotson, Phillips Exeter Academy

This course features an introduction to some of the early history of mathematics. Counting systems and numerals, early quadratic equations, the Pythagorean theorem and the early history of algebra will all be addressed. Learn how the Egyptians multiplied and divided through tables of doubles, how the classical means played a defining role for Greek geometry, and how the ancient Babylonians solved quadratic equations! See Euclid’s early work on prime numbers and learn how to trisect any angle and double any cube.

**Late-morning courses (10:30 a.m. – 12:30 p.m.)**

**11 - Python and the TI 84: Computational Thinking and Coding in Math **

**Leader**: Greta Mills, The Greene School

Coding is a skill that is in high demand for STEM careers. But how does computational thinking connect to the big ideas in math class? By integrating Python into the familiar calculator environment, coding is now more accessible than ever. In this course you will learn how to use Python to challenge your students – and yourself – and enhance your math lessons from algebra through calculus and beyond.

**12 - Making Precalculus Relevant (ATP + Skew the Script) **

**Leader**: Jessica Schenkel, Porter-Gaud School

Do you want to add relevant materials to your precalculus courses? Throughout the week you will go through a series of socially relevant lessons from Skew The Script that you can incorporate into your precalculus course. You will also go through materials from An Alternative to Traditional Precalculus, a website that provides a free, full-year course built around problems/topics that engage teenagers. Check out https://skewthescript.org and https://jschenkelmathstudio.com for a preview of these resources and join this course to gain tools to get students excited about precalculus!

**13 - A Lab Approach to Calculus **

**Leader**: Jess Emory, Phillips Exeter Academy

This course will cover highlights from a year-long calculus class that merges lab investigations with a problem-based curriculum. This program emphasizes qualitative approaches to problem-solving more than symbolic solutions with algebra, while also incorporating writing for understanding, collaboration, and focused spiraling of topics. Some of the labs focus on foundational aspects of calculus, while others delve into calculus-based models (income inequality, probability distributions, the "Tilt-a-Whirl," skydiving). Participants need to bring a tablet or laptop computer.

**14 - Exeter Math 1: A Student-Centered Problem-Based Approach to Algebra 1 **

**Leader**: Julie Van Wright, Phillips Exeter Academy

We'll use the Exeter Math 1 materials to explore problem solving through a Harkness discussion-based format, with the goal of building content with students, rather than for them. We'll discuss ways to empower students to discover, develop and apply general principles and transferable techniques through accessible and contextual problems. Our content spans Algebra 1 topics, including linear relationships, absolute value, quadratics, and a variety of word problems. Come see what Exeter Math is all about, at this introductory level!

**15 - Mathematical Modeling in Algebra 2 and Precalculus **

**Leader: **Christine Belledin, North Carolina School of Science and Mathematics

Mathematical modeling can inspire curiosity in students and allow them to think creatively. We will explore ways to help students navigate the modeling process to work on interesting real-world problems. We will share a selection of students’ favorite problems, with mathematical topics that span from advanced algebra to precalculus. We will also explore how to use Desmos activities and GeoGebra as tools to guide students through modeling problems and to promote exploration and independence.

**16 - Problem Solving in Geometry **

**Leader:** Jeff Ibbotson, Phillips Exeter Academy

An approach to the beautiful subject of Euclidean geometry using the Exeter materials. We will explore the circumcenter, incenter and excenters as well the triangle bisector theorem and Ceva’s intersection results. Along the way we will use technology (GeoGebra and Geometer’s Sketchpad). Tessellations and Polyhedron adventures are also featured! Think you know everything there is to know about the Pythagorean theorem? Think again!

**17 - Mathematically Model Current Real-World Data with Social Implications: Opioids, Climate and More**

**Co-Leaders:** Jeff McCalla, St. Mary's Episcopal School and Tom Reardon, Austintown Fitch High School and Youngstown State University

Analyze, model and interpret real data while creating social awareness of important current issues. Use modeling equations to interpolate, extrapolate interpret data and its consequences. Relevant topics to investigate include opioids, hot car temperature deaths, U.S. debt, COVID, payday loans, plastic straws, Greenland ice mass, burning of fossil fuels, Lambeau Field, sitcoms and more. Learn how to create your own modeling activities. Pre-loaded graphing calculators are provided but data can be used with any graphing technology.

**18 - Fun and Interesting Math Activities that Engage Students **

**Leader: **Ken Collins, Charlotte Latin School

What can we do on a day that is not a normal teaching day? This course will illustrate several activities that can be used as a class warm-up, an enrichment activity, an interesting application, and a way to encourage mathematical imagination. These include patterns, codes, brain teasers, puzzles, games, hexaflexagons, math magic tricks, Pascal’s Triangle, combinatorics, origami, Moebius strips and bands, math challenges and curiosities. These activities apply to both high school and middle school classes.

**19 - Professional Development through Mathematics Teachers' Circles **

**Leader: **Chris Bolognese, Columbus Academy

Since 2006, Mathematics Teachers' Circles (MTCs) have been a growing opportunity for mathematics teachers and mathematicians to come together to explore cool mathematics. With the support of the American Institute of Mathematics, there are now over 150 MTCs across the country. In this course, we will learn about the history and goals of MTCs, play with math through a number of fun and engaging hands-on MTC tasks, and reflect on ways that professional development for mathematics teachers can be enhanced in our local areas.

**20 - Making It Relevant: AP and Non-AP Statistics **

**Leader: **Dashiell Young-Saver, IDEA Public Schools

Together, we'll discuss best practices for teaching statistics, including infusing lessons with data on relevant topics (gerrymandering, college admissions, online dating, sports, etc.). We'll discuss how to use such activities to boost learning, engagement, and critical thinking, all in a non-partisan way.

**Afternoon courses (1:30 p.m. – 3:30 p.m.)**

**21 - Advanced Topics in Data Science for High School Students **

**Leader:** Mahmoud Harding, North Carolina School of Science and Mathematics

In this course we will engage in activities that focus on the core aspects of data wrangling and supervised machine learning: regression and classification. We will learn the basics of the Python programming language along with commands and functions for manipulating, transforming and graphically displaying data. Throughout the course we will use Python modules that are essential to data science: numpy, matplotlib, pandas, scikit-learn. The course will conclude with participants learning how to design activities that can be distributed to students through Jupyter notebooks.

**22 – Trigonometry, Redesigned: Collaboration, Discourse and Modeling **

**Leader: **Greta Mills, The Greene School

Whether you teach trigonometry as a stand-alone course or as part of an Algebra 2/Precalculus sequence, the topics are perfect for reinforcing the modeling process through collaboration, discussion and projects. Participants will learn how to introduce and scaffold trigonometry concepts, and how to use questioning and inquiry in a discussion-based lesson. We will use trigonometry (and other ancillary functions) to model a wide range of phenomena, including the path of a bungee jumper, the sound of a plucked ukulele string, and the timing of a seconds pendulum.

**23 - Mathematical Modeling in Calculus **

**Leader: **Christine Belledin, North Carolina School of Science and Mathematics

Mathematical modeling can bring calculus to life and allow students to see how math can be used to investigate important and interesting real-world problems. We will explore problems that give students an opportunity to think creatively, deepen their understanding of calculus concepts, and develop their mathematical modeling ability. Problems will span a variety of contexts, including the measurement of income inequality, the spread of disease, and the path of a spacecraft around the moon. We will use Desmos and GeoGebra as tools to help students explore and solve modeling problems.

**24 - Creatively Integrate Algebra, Geometry, Precalculus, Trig Activities with Individualized Solutions **

**Co-Leaders:** Jeff McCalla, St. Mary's Episcopal School and Tom Reardon, Austintown Fitch High School and Youngstown State University

Twelve problem-solving activities. For each of the following applied problems you will obtain 60 different student versions and 60 complete solutions with all intermediate answers (using spreadsheets): The Great Applied Problem, Baseball Problem, Nail in the Tire, Plane Wind Vectors, Solve Any Quadrilateral, Circular Garden, Linear Applications. Also learn how to create your own individualized activities. Modeling activities include The Twelve Days of Christmas, the Wolf Population problem, field goal for the win, and deriving summation formulas. Bonus: use parametric equations cleverly to teach inverses.

**25 - Just a Bunch of Good Geometry Labs **

**Leader: **Dan Butler, The Lovett School

By the time students get to precalculus, a lot of their geometry know-how has gone the way of the slide rule. Let's bring excitement back to geometry through great problems and great explorations, and discover how geometry really lies at the heart of all mathematics. In this course we will explore how soap bubbles can solve a max-min distance problem, see why taxicab geometry says pi is equal to four, and find out the mathematical reason that giant humans cannot exist. We will also take some time to discuss what needs to be in a geometry course and how to fit these problems into a full curriculum.

**26 - Using the United Nations' Sustainable Development Goals to Create Applied World Problems**

**Leader:** Thomas Hill, Brewster Academy

In 2015 the United Nations set 17 goals to drive world leaders to a better future. How are we doing eight years later? We will explore how we can use these goals and the information available from the U.N. and other sources to lead students through “real mathematical problems.” We will look at a project that uses linear, quadratic and exponential modeling to extrapolate current trends. You will have time to collaborate with peers to create your own project or lesson plans around world issues.

**27 - Using Excel to Help Students Effectively Organize, Analyze and Represent Data **

**Leader:** Ken Collins, Charlotte Latin School

Understanding how to analyze data is increasingly important in our personal, professional and civic lives. This course focuses on how to use Excel to analyze data in middle and upper school classes. Excel is an excellent program for storing and calculating data. It has all the tools for data analysis. It is easy to create data visualizations with charts and graphs. You can use it to print reports. You can work with it online and with a mobile app. Participants completing this course will be able to use these applications in their classes and help prepare their students for a digital future.

**28 - Proportional Reasoning 101 **

**Co-Leaders:** Laurie Cavey, Boise State University and Tatia Totorica, Boise State University and Boise School District

Proportional reasoning has often been referred to as the cornerstone of advanced science and mathematics. We will explore what it means to be successful with proportional reasoning — yes, it is more than just correctly setting up a proportion and solving! By solving a range of problem types, we will learn that proportional reasoning, at its core, involves reasoning sensibly about multiplication and division. And, by considering samples of student work, we will learn about a range of productive ways students can reason about proportional situations without the use of a formal algorithm.

**29 - Writing a Problem-Based Curriculum**

**Leader:** Diana Davis, Phillips Exeter Academy

Students learn math by doing math – specifically, by solving problems. In this course, you'll work on transforming one of your courses into a problem-based curriculum. You will figure what you want to accomplish, determine the steps along the way, map out when you will do all these things, and write the problems. We will also learn to analyze Exeter's problem-based curriculum so that you can pull problems out of it for your own use. We'll work through each other's problems and give each other feedback. At the end of the week, you will be well on your way to writing your curriculum.

**30 - Linking Mathematics with Real Life Experiences, Cross-curricular Connections and Photographs**

**Co-Leaders:** Ron Lancaster and Gurpreet Sahmbi, University of Toronto

Takeaways from this course will include strategies to develop math questions and tasks linked to daily life, other disciplines, media, and photographs. The culmination of this course will be the development of a math walk on the campus of Phillips Exeter Academy. Participants will gain experience in developing a walk so that they can create one for their students on the campus of their school or in many other locations. The ultimate goal of this course is to help teachers find ways of empowering students to notice math everywhere, to wonder, to ask questions, and to take pleasure from their studies in math.