Park City Mathematics Institute
High School
Module Abstracts

[Algebra 2 for All]  [Writing and Thinking]  [Differentiation]  [Functions]  [Perseverance]  [Modeling]  [Reasoning]  [Inference]  [Reflection

Algebra 2 for All
Grade Level: Algebra 2
Subject: Algebra 2, Polynomial functions
Title: Targeted Differentiation in an Algebra 2 Task for All Learners
Authors: Kayleigh Rose, Michelle Katz
All students can access a single task if it is written with multiple entry points and teachers are able to actively support them during the learning process. Teachers need to be able to anticipate the needs of their students, monitor their progress, and take strategic action which enable students to move forward. Participants will have the opportunity to engage in an Algebra 2 task and identify the necessary content-based skills for students to be able to access the content. Participants will develop questioning and scaffolding targeted to the individual needs of students.
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Writing and Thinking
Grade Level: Middle School and High School
Subject: Writing exercises supporting MP1 and MP3
Title: Writing and Thinking Practices in the Math Classroom
Authors: Bond Caldaro, Matt Carlberg, David Price, Gabriel Rosenberg
Writing and Thinking protocols are designed for students to formulate ideas, to carefully consider arguments, to reflect on their own thought processes, and to share their ideas with others. Participants will engage in a series of Writing and Thinking exercises and will learn about protocols that can be used to support students in attacking difficult problems, critiquing mathematical claims, and looking back at their own mathematical work. Participants will also explore how these exercises can be applied to a wide variety of problems and content standards; they will engage with writing exercises developed at Bard College's Institute of Writing and Thinking modified for the math classroom.
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Grade Level: HS primarily, though applicable to all levels
Subject: Pedagogy
Title: Differentiating Mathematics Instruction through Questioning
Authors: Kyle Eller, Stephanie Erickson, Craig Russell
The typical high school math classroom has students with a range of abilities, a range of interests, and a variety of learning styles. Due to this, differentiation is an important tool for teachers, and there are many ways to differentiate instruction to meet the needs of all students in a classroom. Here, we model two methods and focus on teacher actions both in lesson design/preparation and in executing the lesson in the classroom. Participants will experience differentiated instruction from the students' perspective, and will begin to develop some strategies for addressing needs of learners at different levels of preparation. They will leave with some resources for further reading and sources for problems.
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Grade Level: 9 - 12
Subject: F.IF.B.4
Title: Connecting the Dots: Contextualizing Functions through Stories
Authors: Meghan McGovern, Benjamin Nockles, Donna Lee Stewart and Paul Otis Winston
In this workshop, participants will have the opportunity to create graphs with few constraints, sort functions by agreed-upon criteria, share their sorting methods with others, and will then determine a context for the graph using a collection of possible Title:s. The crux of this activity is using a low-floor activity to both unlock the creativity of the participants, and to elicit appropriate terminology from them. The creativity and terminology, in turn, can be used to classify graphs of functions, and assign titles to graphs (and vice versa.) Thus, not only are participants connecting dots (in the beginning of this activity), they are also making connections between stories and graphs. They are also anticipating students' potential "stumbling blocks" in this process.
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Grade Level: High School
Standards: Math Practice 1
Subject: Geometry course
Title: Tasks that Promote Perseverance
Authors: Anais Artega, Joan Caraway, Max Oliver, Will Stafford
Building tenacity in your mathematics classroom: Attendees will leave this session able to define the key characteristics of tasks that make use of CCSSM Mathematical Practice One, and identify lesson structures that promote this practice in the classroom. Focus is placed on how the high school teacher enables students to work through conceptually rich mathematics problems without giving up. Activities include evaluating various tasks that will build students' problem solving stamina. Participants will receive a list of resources for continued exploration of MP1.
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Grade Level: 7-11 (Algebra 1, Geometry, Algebra 2 teachers)
Subject: Modeling
Title: Modeling: What, How and Why!
Authors: Mike Calderbank, Clint Chan, Tracey Guida, Eric Henry, Nathan Prescott
This participant-driven workshop gives teachers the tools to rate modeling problems on a 0-3 PISA spectrum and to elevate a low level modeling problem to a higher level. They will examine what the CCSSM has to say about modeling and consider what characteristics make a modeling problem. Then, participants will use a 0-3 rubric to categorize sample modeling questions taken from a real-world example through a guided small group discussion. After, participants will work in grade-level teams to elevate a problem in their current curriculum, ideally Titles they will teach soon. Finally, participants finish with a discussion that anticipates how/when/why questions when it comes to incorporating modeling. At the end of the session, participants will leave with resources that will incorporate modeling into their own classroom.
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Grade Level: 7-11
Subject: Quadratic Functions
Title: Seeing Dots - Supporting Students in Reasoning with Quadratic Equationsk
Authors: Michael Ruppel, Reynaldo Garibay, & Raymond James
The Common Core State Standards ask students in Algebra I to be able to reason with quadratic functions, relate the structure of a quadratic expression to a quantitative relationship, and use quadratic functions to model effectively. In this session, participants engage in a task where a quadratic function arises and relate an algebraic expression to a quantitative relationship. After completing and discussing the task, participants will prepare to implement reasoning tasks in their own classroom. They will discuss what makes a task effective for improving reasoning skills and describe teacher actions that support students in reasoning with and about functions. We will spend time discussing scaffolds and supports that teachers can put in place in order to ensure that all students can improve reasoning skills through rich tasks.
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Grade Level: High School
Subject: Integrated Math 3, Algebra 2 or higher
Title: Inference and Margin of Error
Authors: Fred Dillon, Marianthi Karavitis, Vicki Lyons, Donna Young
Margin of error and inference
The CCSSM Statistics and Probability standards state that students will develop a margin of error from simulations. Meeting this goal means that educators need to have appropriate content knowledge about the underlying statistics, and also a solid conceptual understanding of margin of error. After a framing question that highlights common misunderstandings about making inferences and margin of error, the participants will create sets of simulations for two problem situations in order to understand the process and possible results of sampling. The data collected from the simulations will be used to create estimates about populations and to create margins of error for the estimates. By the close of the session, participants will have a better understanding of what a margin of error is and how to create an estimate and margin of error for a statistical question.
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Grade Level: K-12
Subject: Though designed with a high school math teacher in mind, this PD is open to educators at all levels for all curricula.
Title: The Reflective Teacher
Authors: Paul Kim and Jason Libberton
Reflection is necessary for improvement. It is the teacher's tool for exploring and retaining powerful pedagogical techniques and purging habits that frustrate student learning. Reflection is the critical piece in the cycle of teacher development. By the end of this workshop, teachers will see the need to reflect, be inspired to reflect, and know it is possible to reflect consistently reflect on and improve their [mathematics] teaching. After a guided discussion on reflection, in order to personalize the experience in their classroom, each participant will design a reflection tool that they will be able to use in the immediate future.
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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.