2022 TCM Presentations

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. 

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.

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. 

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. 

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

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. 

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.  

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.

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. 

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).