Park City Mathematics Institute
Professional Learning Development
Project Abstract
Making Math Meaningful with Anchor Tasks
Grade Level: Middle/High School
Subject: Middle/High School Mathematics
Topic:Worthwhile Tasks
Authors: Sean Corey, Cindy Ruhsam, & Brooke Sossin
Teachers are frequently encouraged to use open-ended tasks to improve student engagement, understanding, and cognitive demand. However, because teachers emphasize the final mathematical takeaway, students often overlook the original context of the problem and the meaningful discoveries they made. Teachers can support students' retention and sense-making by intentionally revisiting certain tasks, called "anchor tasks," at several points throughout the year. Each time we revisit a task in this way, by exploring extensions and considering alternative methods, we enable students to make connections between key course concepts and deepen their understanding of each one.
In this session, we will investigate anchor tasks by working through two open-ended tasks and discussing opportunities for revisiting with references and extensions. Together, we will generate a sample progression for each anchor task, specifically for Algebra I and Algebra II courses. In closing, participants will brainstorm possible anchor tasks for their own class and how they can effectively implement these tasks. Participants will receive handout guidelines for identifying and finding open-ended tasks, and session notes will provide strategies for maximizing the takeaways of a single anchor.
By selecting several such anchor tasks for a given course, teachers can help students develop overarching coherence of key concepts.
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Getting Started: Strategies to Tackle Problems
Subject: Secondary math
Topic: Problem-solving strategies
Authors: Ariel Kramer, Naira Harutyunyan, and Johnson Nguyen
This Professional Development session is focused on helping students start problems. You know how sometimes your students will sit and stare at a problem and claim they don't know how to start? The goal is to have participants build a list of strategies that will help their students get started.
During this PD session, participants will have the opportunity to try out math tasks and organize their strategies into categories that they can bring back to their classroom and school. The beauty of these strategies is that they can be used for all types of problems and all types of content, not only math tasks.
Participants will also be able to take the processes and ideas from this session back to their classroom to replicate with their students. Through these activities, students will be able to build their own list of strategies and take ownership of their learning.
When students have a toolbox of resources, they have multiple strategies to approach a question so they can be successful no matter what they are working on.
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Playful Math Appetizers: Not participating is only wrong answer
Grade Level: 4-12, especially Middle School through Algebra
Topic/Subject: Warm-ups, Promoting daily student discourse
Authors: Diana McClean, Natalie Miroshnichenko, Marissa Walczak
Let's be honest - we all have students that are typically not engaged in the mathematics of our lessons, no matter how much effort we put into the planning. How do we get these students to participate and engage in mathematics every day along with the rest of the class? In our presentation, we will demonstrate short playful math activities (appetizers) for engaging all math students. The presentation includes discussion and examples on how math teachers may incorporate these appetizers in their own classroom. The appetizers include: Estimation 180, Find a mistake, Notice and Wonder®, Which One Doesn't Belong?, and Set.
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Low-Floor High-Ceiling Tasks
Grade Level: 9-12
Subject: Algebra & Geometry
Authors: Tino Elicegui, Sam Kaplan, Mark Dittmer, and Anna Blinstein
In our PD, we let participants grapple with a rich low-floor, high-ceiling task, letting them experience how it allows for better learning opportunities for students in the math classroom. Having established that rich tasks foster students constructing multiple representations, engaging in mathematical discourse and sense-making, and owning the mathematics in a way that many math textbook tasks do not, we challenge participants to brainstorm characteristics of rich tasks, discuss ways to modify tasks to make them more open, and then give them a chance to make their own modifications to textbook tasks presented to them, based on content they teach.
The goal of our workshop is to show that rich tasks result in an increase in cognitive demand on all students, and then to give participants suggestions to help them modify traditional problems on their own. Teachers can start to see modifications on a spectrum, find their current comfort level with open tasks, and start to push themselves towards greater levels of openness. The practice and feedback in the workshop will help teachers leave the workshop empowered to enact these principles with their students, along with specific examples of tasks they can implement right away.
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Choose Your Own Mathematical Discourse Adventure
Grade Level: K - 12
Subject: Pedagogy
Authors: Jennifer Parker, Alison Mall, Genevieve Esmende
Do you have structures in place that support mathematical discourse? Have you ever wanted a toolbox to support you in creating these structures? This workshop will give you an exposure to a variety of tools that can support the flow of discourse throughout a task. When students engage in mathematical discourse, they are given the opportunity to deepen their understanding of the mathematical ideas. The tools are used to support launching the problem, exploring the problems and summarizing the problem. During the workshop, some of the tools will be modeled and rehearsed. You will be provided with a document which includes information about all of the other tools that are not discussed.
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Increasing Cognitive Demand through Problem Solving Tasks
Grade Level: Middle School and High School Educators
Topic/Subject: Problem Solving Tasks
Authors: Linda Nguyen, David Martin, and Melanie Brintnall
Problem solving tasks spark student engagement with math concepts on a variety of levels and enable students to make connections between topics. These tasks encourage mathematical discussion and provide students the opportunity to support and defend their reasoning. However, developing cognitively demanding tasks can be a challenging process. In this series of sessions, teachers will experience high cognitively demanding tasks first-hand, identify the features of such tasks, discover strategies for developing tasks, and practice creating tasks for use in their classrooms.
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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.