Park City Mathematics Institute
Professional Learning Development
Project Abstract
Calculus by Inquiry
Grade Level: High School, Calculus Teachers
Subject: Calculus Instruction
Title: Establishing a Conceptual Foundation for the Study of Calculus
Authors: Shannon Hammond, Michael Powell, Nataša Sirotić
The typical high school calculus course progresses through a study of topics beginning with limits, continuing with the derivative and its applications, and finishing with integral calculus and its applications. The connection between differential and integral calculus is not apparent to most students of calculus until late in the course. In this workshop, participants will have the opportunity to experience and engage with a less typical approach to calculus instruction - one that begins with the uncovering of the fundamental theorem of calculus as a first experience for students. Participants will take away a practical instructional approach that can be directly implemented in the classroom and revisited throughout the course to illuminate the big ideas of calculus and to support the learning of concepts and procedures related to the study of calculus. When students experience an activity that engages the big ideas and makes connections with prior knowledge, it motivates the learning of new concepts and procedures. This is consistent with a learning model perspective by which educators harness emotions, train behavior, and educate the mind.
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Promoting Growth Mindset and SMP1 through Strategies
Grade Level: Middle/High School Maths
Subject: Growth Mindset & Perseverance
Authors: Leah Lorton, Sahar Khatri, Heather Stone
Many students believe they are unable to succeed in mathematics. Participants will learn how to transform students' thinking to encourage perseverance during problem solving and teach students to have a new appreciation for a mathematical struggle. The participants will leave with a better understanding of how students view mathematics, appropriate language frames in order to give productive feedback, and six strategies that can be utilized to encourage a change in students' thinking.
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Assessing with the End in Mind: Responsive Teaching through Formative Assessment and Re-teaching/Extension
Grade Level: 8th grade standards and materials, but the strategies can be extended to any grade level from K - 12.
Subject: Expressions and Equations 8 CCSS
Authors: Ann Nguyen, Katherine Wittig, Jeffrey Zivkovic
So we all know how to give formative assessments, right? But what do you (and your students) do with the results? How do you engage students in thinking about their understanding and performance both during AND after completing activities or assessments? In this PD, we'll engage with various strategies for responding to formative assessment results, with focus on two strategies in particular. 1) "Formative Self-Check" is a checklist of criteria that invites individual students to evaluate their own progress and understanding during a group task. 2) "Desk Consultants" is a strategic grouping structure for peer re-teaching that ensures that struggling learners make progress on objectives which they haven't yet mastered. (Emphasis on the word "yet"!) This strategy also ensures that your "on-track" and "advanced" learners continue to deepen and extend their own comprehension. As a participant, you'll get the chance to reflect on your current practices and share your strategies. You'll also discuss important criteria of responsive teaching with formative assessment, and analyze student work on a sample assessment to practice categorizing errors and misconceptions. You'll even have the opportunity to revise one of your own assessments to take an improved version back to your classroom.
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Cultivating Growth Mindset
Grade Level: Secondary Mathematics
Subject: Growth Mindset
Authors: Samantha Mazzeo, Gabrielle Mathiesen Ayesha Saletore
The focus of this workshop is to expose teachers to math, protocols, and ways of communication and learning which value mistakes as an opportunity for growth and promote perseverance. During this 90 minute professional development teachers will engage in challenging problem solving, share and learn ideas on classroom protocols, and build a toolbox of research based classroom procedures. This will be accomplished through a combination of critical analyses of important educational text, experiential learning, and collaboration.
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Narrative Through Numbers: The Olympic Games
Grade Level: All educators, especially high school
Subject: Quantitative Literacy
Authors: Mandy Lenham, Danny Persia
Numbers strengthen arguments. But how do get our students to want to use numbers? How do we build quantitative literacy across the curriculum...and how do we have fun and stay relevant in the process? Since the first modern games in 1896, the Olympics have been a marker of national and international community. The vision: fame, glory and cooperation across difference. But what about the $43 billion it cost to run the Olympics in Beijing, or the hundreds of residents displaced from their homes in East London? Whose stories aren't being told, and what numbers might help us tell those stories? This session will engage participants in an ongoing debate on the Olympic legacy, paying careful attention to numbers in constructing historically accurate narratives. Participants will be grouped into host cities-Athens 2004, Beijing 2008, London 2012, to name a few-and asked to apply their reasoning skills to a comprehensive set of evidence related to the Games. The entire session will be a simulation of a classroom activity designed to engage students in the processes of inquiry, discovery, and interpretation through a quantitative lens.
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Selecting and Sequencing Student Work for Facilitating Productive Mathematical Discourse
Grade Level: Middle School
Subject: Pedagogy
Authors: Becky Bob-Waksberg, Genevieve Esmende
Many teachers have started using low-floor high-ceiling tasks in their classroom, but to facilitate productive mathematical classroom conversation consistently can be difficult. Based on 5 Practices for Orchestrating Productive Mathematical Discussions by Stein and Smith, this session will focus on the practices of selecting and sequencing student work, which help students learn from each other and move forward in their thinking. Participants will experience a low-floor high-ceiling task and see how we model the process of selecting and sequencing. Participants will also analyze student work and experience the process of selecting and sequencing the work that will be presented to the class.
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Launch Pad: Introductory Tasks for CC Algebra 2
Grade Level: High school Algebra 2 teachers or those interested in CC Algebra 2
Subject: CC teaching methods for Algebra 2
Authors: Hannah McDowell, Stephen Ishii, Mary Vélez
Tired of never making it to the fun application problems at the end of the unit? Looking for a new way to start teaching a unit? Wondering how to implement more mathematical practices? We can help! You will participate in a model lesson to introduce trigonometry in a CC Algebra 2 classroom that helps you get to the heart of accessing prior knowledge and using it as the basis for new learning. At the same time you will experience the mathematical practices of perseverance, abstract reasoning, constructing and critiquing arguments, and modeling, just like your students will. Prepare to work your math muscles and take away tasks on polynomials, quadratics, probability, trigonometry, and exponentials for your classroom.
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Rubric to Assess Standards for Mathematical Practice
Grade Level: Elementary school and High School Educators
Subject: Standards for Mathematical Practice
Authors: Danilsa Fernandez, Elizabeth Houwen, Elissa Kaufman
The Standards for Mathematical Practice are outlined in the Common Core State Standards as a list of eight areas of expertise that teachers should develop in their students in conjunction with mathematics content standards. Although a variety of resources have been made available to educators to help them implement these practices, there are limited assessment tools with a precise focus on such practices.
The purpose of this project was to develop a rubric that will assist educators to measure student skill levels in each of the eight categories. The rubric is intended to be used by teachers, administrators, and maybe students, as a tool to assess student work and discourse and illuminate how students can improve their use of the practices. Included in the rubric is a selection of "student work" examples of various grade levels ranging from elementary school to high school. The "student work" examples help highlight various proficiency levels listed in the rubric. The rubric also has built in flexibility allowing educators to choose any of the practices they are assessing. Furthermore, the language in the rubric is not specific to any grade level and is adaptable for use in elementary school through high school.
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Differentiating Instruction Using Low Floor/High Ceiling Tasks
Grade Level: K-12
Subject: Mathematics
Authors: Kiaundra Smith, Alex Sczesnak
Imagine a classroom culture where all students are engaged and the problems lead to the appropriate mathematics. A middle school administrator and high school math teacher have outlined how low floor/high ceiling tasks promote and provide opportunities to differentiate instruction. They describe three ways to differentiate instruction, through content, process, and product. Participants experience completing low floor/high ceiling tasks and then conduct a strategic cross walk of other high quality tasks to find opportunities for differentiation in their classroom. The marriage of these two practices promotes making connections, focuses on conceptual understanding, and emphasizes the NCTM Mathematics Teaching Practices.
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Building a Community of Social Learners and Problem Solvers
Grade Level: Elementary and Middle School teachers
Subject: Group work and social learning
Authors: Irene Espiritu and Lisa Soltani
Many teachers use group work to structure the learning in their math classrooms. However, in order for students to work effectively in groups, particularly mixed groups where students may access tasks at different levels, teachers need to set expectations and help students to develop social learning skills.
To this end, teachers will consider the importance of explicitly creating opportunities for students to practice social learning skills in the context of group problem solving. Teachers will analyze a video of a classroom where students are engaged in effective group problem solving. Through an activity known as "Mission Control," participants will reflect on social learning skills through an activity that requires consensus building, communication and listening skills. In groups participants will engage in a mathematical task known as "Cube Building." In this activity, participants will build three-dimensional structures with connectors and straws and notice the mathematical relationships embedded in their structures. Finally, participants will reflect on their effectiveness as a group and discuss how these tasks might unfold in their own classrooms.
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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

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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.