Park City Mathematics Institute
PD Development
Module Abstracts
Looking Around With Exponents
Grade Level: 6th grade - 11th grade
Subject: Algebra, Exponents
Authors: Matthew Engle and Morondo Lewis
If you are like us, you often have students in your class with misconceptions of exponents that build into misconceptions of further algebra topics. We will analyze student weaknesses when dealing with exponents and look specifically at the limitations of seeing exponents as repeated multiplication. Teachers will identify and analyze student misconceptions so that they can better monitor their progress and help them to move forward with their learning.
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The Red Pen Has Met its Match: The SMP's
Grade Level: Grade Level: Middle School and High School Math Teachers
Subject: General Math (Standards for Mathematical Practice)
Authors: Jon Sturtevant, Alexandra Chanysheva, Aurora Alamillo
We have all heard of the Standards for Mathematical Practice (SMP's), but how do we use them to assess student learning? In this workshop you will learn valuable techniques to not only assess the SMP's, but more importantly, learn how your students can use the SMP's to gauge their ability to think and reason mathematically. We as teachers often prioritize the end product of student work rather than their thinking, reasoning, communication, and problem-solving skills. Content might be easier to evaluate, but understanding where your students are in their mathematical development is arguably more important than knowing if they can use a specific formula. A student who can self-assess their mathematical thinking and reasoning will have the tools to grow into not only a better math student, but a more cognitive learner. Through this practice, students will develop self-motivation, more confidence, and yes greater mastery of the content! The two goals for this workshop are: (1) Participants will learn ways to communicate the SMP's to students; (2) Participants will learn ways students can self-assess using the SMP's. Participants will leave with many useful handouts and a great framework that they can use in their classroom right away. Come join the revolution and stop using the red pen as your only tool for assessment.
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Differentiate That: How to differentiate your assessments to meet the needs of your students
Grade Level: K-12
Subject: Differentiated Assessments for Mathematics
Authors: Chris Watts and Samantha O'Connor
Alternative assessment is more than a buzzword; it's a means for students to explore mathematics and display their knowledge in novel and enjoyable ways. In this practical workshop, participants will extend their current understanding of Gardner's Multiple Intelligences, including some modifications and misconceptions to his findings and how these impact all classrooms. They will be provided with an arsenal of creative alternative assessments that helps students access content appropriately. All participants will leave with a plan to implement one differentiated task in their next unit, having already received feedback from experts and peers.
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Differentiated Questioning
Grade Level: 7 - 12
Subject: How to differentiate questioning to support all students' learning
Authors: Sheana Powell and Samantha Warrick
Differentiated instruction is an umbrella phrase that is used often by teachers and administrators, but many educators feel overwhelmed by its concept. This is because how to seamlessly integrate differentiation practices into the classroom without it being time consuming and overwhelming is neglected. During this workshop, participants will tackle one of the lesser focused on components of differentiation: differentiated questioning. Participants will develop a working definition of differentiated questioning and will practice using various tools to be able to quickly and effectively create leveled questions. This practice is necessary to reach the needs of the various levels of learners in the classroom.
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Effective Formative Assessment--Introduction to using effective questions to gather formative data.
Grade Level: Any grade level
Subject: Implementing Effective Formative Assessments
Authors: Brian Newmark and Wayne Smith
Participants will get a chance to experience, evaluate, and perform formative tasks. Teachers have heard that formative assessments are crucial to gain insight into students' understanding, but often don't include the components that make these formative assessments effective or why they are necessary. Participants will understand the importance of eliciting information from students, effective questioning, and providing feedback before engaging in a practice formative assessment activity. Participants will also have the opportunity to discuss how grades can be tied in with formative assessments, establish goals around formative assessments, and look at possible future formative assessment topics to study and implement.
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Connect Four with Functions
Grade Level: 8 - 10
Subject: Multiple Representation of Functions
Authors: Dan Lao, Barbara Lynch

This professional development session is designed to provide participants connections between the four representations of functions. (Graph, Table, Equation, Verbal/Visual). We will explore why it is important to show different representations of a function. Participants will be exposed to several problems that demonstrate the connections between four representation of a function. One task depicts speed using four representations, participants will determine the connections between them. Using multiple representations will evolve into a deeper understanding of how a function "works."

Connections will be made through comparing different representations that lead to seeing that functions are used to understand, to develop, and to communicate different mathematical features of the same scenario, as well as connections between different representations.
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Developing a Growth Mindset for Teachers & Students
Grade Level: All levels
Subject: MP1/Growth Mindset
Authors: Andrew Giang, Brittany Cuff & Gail Kusano
Are you interested in the research behind growth mindset and its application to the classroom, but not sure how to implement it? In this workshop, participants will be given an overview of growth mindset, its connections to brain science and the research conducted by Carol Dweck. A self-assessment survey and a sample activity will give participants a small snapshot of how teachers can implement tasks that help promote growth mindset in their own classroom. Participants will leave this workshop with resources and suggested curriculum ready to be adopted and used in their first week of school.
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How to get from "teacher-talk" to positive interdependence by scaffolding students' conversations.
Grade Level: High School & Middle School
Subject: Let's Talk About Math
Authors: Oksana Reznikova & Phiola McFarlane
Teachers need to be able to anticipate the needs of their students, monitor their progress, and take strategic action which assists students in discourse that leads to mathematical understanding. In using deliberate structures to engage students' thinking about mathematics students get an opportunity to engage with their own ideas in various ways. In this session participants will learn several strategies for developing productive math discussions and analyze video. Finally participants will collaboratively generate solutions for "unproductive elements" of discussion to use in their classrooms.
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Social Dynamics and Math Discussions: Practical Strategies to Have Students, "Construct Viable Arguments and Critique the Reasoning of Others"
Grade Level: K-12
Subject: Student Social Dynamics and the Common Core Mathematical Practice Standard 3 (Construct Viable Arguments and Critique the Reasoning of Others)
Authors: Benjamin Walker and Joseph Herbert
Do students actually listen to each other during math discussions, or do they just talk past each other? What structures and routines can you create in your classroom to help students engage in genuine mathematical discourse? This workshop explores these questions and how social dynamics in the classroom can promote or inhibit genuine mathematical discussion and argumentation. Participants will leave with concrete tools to foster mathematical discourse in their classrooms.
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Vertical Alignment with the CCLS in Middle School
Grade Level: Middle School, Grades 6 - 8
Subject: Progressions of Mathematical Understanding through Middle School
Authors: Ben Allen & Jennifer Parker
We identified a lack of vertical alignment between teachers of different grade levels within the middle school. With the transition to the Common Core Learning Standards it is valuable for teachers to be familiar with the curricula they teach, but also the content of the younger grades and the high school standards that middle school work builds towards. By examining the development of systems of equations as one particular progression during middle school, we hope to foster a stronger understanding of the middle school progressions, and empower with appropriate resources to examine any progression of skills that takes place during the middle school years.
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Building Flexible, Connected Knowledge: Look For and Make Use of Structure
Grade Level: 6th - Algebra I
Subject: MP7: Look For and Make Use of Structure
Authors: Dylan Kane and Nicole Hansen
When students are simply following rules and using strategies dictated by the teacher, they are missing out on developing and using deeper understanding of content. When students use Math Practice 7, look for and make use of structure, they build a capacity to work deeply and flexibly with content in order to apply their knowledge in the future. This session will explore a framework for categorizing different types of structural thinking by solving and analyzing tasks that span sixth grade through Algebra I.
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Problem-Based Learning: What Makes a Good Problem?
Grade Level: Pedagogy: K-12 Math Content: Middle School (but adaptable)
Subject: Problem-Based Learning
Authors: Jennifer Osgood and Scott Matthews
Many of us have heard of Problem-Based Learning (PBL) and want to use it in the classroom, but are not quite sure where to start. If you can relate to this description, this workshop is for you. This workshop will give you the tools that you need to both identify good PBL problems and turn traditional problems into PBL appropriate ones that will help your students genuinely engage in the mathematics they are working on. During the workshop, you'll have a chance to look at the important features of a good PBL problem and the opportunity to practice taking traditional problems and "tweaking" them to make them more suitable for PBL. If you have a good summative question that has come up in your curriculum that seems too traditional for PBL, bring it with you, and you'll have time to work on it at this workshop. Don't have a problem? Don't worry, there will be great example problems that you can use for practice. In addition to finding or creating PBL problems, you'll have the chance to examine appropriate levels of scaffolding for a PBL experience and to practice putting scaffolding in place on an open ended problem. Finally, every participant will receive a list of resources that provide good PBL problems or offer guidance in creating your own. Come and learn how to find and make good PBL problems that will motivate your students to investigate, question and make sense of the mathematics that they are learning!
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Practicing Endings: Debriefing Problem Based Learning
Grade Level: Grades 5 - 12
Subject: Problem Based Learning
Authors: Cary Riina, Grant Chen, MaryAnn Moore
In the book 5 Practices for Orchestrating Productive Mathematics Discussions, Stein and Smith identify the practice of Connecting as "the most challenging of all of the five practices because it calls on the teacher to craft questions that will make the mathematics visible and understandable". Though this final practice is the most challenging, it often receives the least amount of time in terms of professional development and teacher preparation. The purpose of this professional development is to direct teachers in practicing writing de-brief questions and protocols that will effectively guide students in uncovering specific mathematical content standards following a Problem Based Learning (PBL) task. Participants in this professional development will expand their toolbox of protocols and questions for extracting and coalescing specific content knowledge from diverse student solutions to a problem based learning experience. Participants will also understand that successful extraction and coalescing of knowledge after PBL experience is an art that relies on detailed planning of protocols and the posing of connecting questions during the debrief stage to reach a specific content standard.
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Dive in, You Won't Drown! Strategies to Help Students Engage in Problem-based Learning
Grade Level: 6-12
Subject: Problem-based learning; SMP 1: Make sense of problems and persevere in solving them.
Authors: Julia Penn and Meghan Riling
Have you ever selected a juicy problem, handed it excitedly to your students, and then watched them give up almost immediately? In this session, we will share strategies to get students started on new problems, introduce habits of mind that students can use as problem-solving tools, and discuss group work norms and structures that empower all students to actively participate. Teachers will analyze which habits they use as they solve a problem, determine how to best introduce problems to a class, watch how social dynamics play out in problem-solving, and brainstorm potential classroom norms. The goal of the presented resources is to help students to become powerful math learners who take risks, contribute productively, and persevere. Embedded within these structures is a shift away from a classroom where precision and speed are the only math abilities that students value; we want students and teachers to know that "no one of us alone is as smart as all of us together." (Smarter Together! NCTM)
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Taking Time to Talk: Using Number Talks to Facilitate Mathematical Understanding Through Discourse
Grade Level: Kindergarten through Grade 2
Subject: Number Talks
Authors: Trish French and Amy TerEick
Facilitating meaningful mathematical discourse is one of the eight Mathematics Teaching Practices outlined in NCTM's Principles to Action. This training module for teachers in grades K - 2 focuses on using number talks as a vehicle to foster mathematical understanding through discourse. Participants will investigate four different examples of number talks, as well as develop their own number talk to implement in their classrooms.
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Mathematics Performance Based Assessment Tasks (PBATs)
Grade Level: High School
Subject: Performance Based Assessments, Project Learning and Assessments, Assessment Rubrics
Authors: Monica Ferraro and Carol Kinney
Many schools in NYC and around the country are relying more on Performance Based Assessment Tasks rather than, or in addition to, standardized testing. Together we will examine what makes a good Mathematics PBAT, the mathematics behind the various PBATs, as well as what makes a Mathematics PBAT worthy of satisfying the graduation requirement. Two additional goals of this PLT are to gather a collection of Math PBAT tasks, evaluate the tasks and implementation process, and work together to improve the PBATs to be the best possible. Pre-PLT Preparation by Participants: Participants will bring, or e-mail ahead of time, PBATs and/or mini-PBATs from their schools including any rubrics. Additionally we will review sample student PBAT work that falls into each of the Consortium Categories: Needs Revision, Competent, Good, and Outstanding. Overall we will be resources to each other about how to best implement, evaluate, and improve PBAT tasks and processes.
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Writing and mathematics: Generating student curiosity and inquiry through writing
Grade Level: Middle School and High School
Subject: Writing exercises supporting MP3 and MP6
Authors: Evelyn Baracaldo and Graham Rosby
Formative math activities and assessments should solidify understanding and communicate gained knowledge. Writing is an ideal medium for these tasks. Participants will explore a novel math problem and reflect on their problem solving using three writing exercises. By experiencing the writing process as both a student and a teacher, participants will learn how to generate better samples of writing from their students. Finally, we allow time to plan and organize the implementation of these exercises in your classroom at all levels of math and writing ability.
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© 2001 - 2018 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

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.