Park City Mathematics Institute
Professional Learning Development
Project Abstract
Blue Group
Reflections of PCMI
View their project Wisdom of Practice in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Subject: Blog
Authors: Deb Barnum, Robin Lam, Roxanne Terry
We hope that readers of our blog, Wisdom of Practice, will be able to learn from our own personal experiences at PCMI 2018. We want readers who are participants and non participants alike to feel as if they were at each morning’s Reflection of Practice session and learn at least one tangible strategy to try in their classroom next school year. Further, we also are encouraging participant discussion via the comments in order to have PCMI participants share their own experiences (either from within or across different rooms). We also hope that teachers from across the MTBoS will comment on both PCMI and researched based posts, sharing their own best practices and creating a reflective database we can refer back to for years to come. By the end of the three weeks, we hope to have over 15 blog posts written describing the Reflection of Practice sessions and further diving into tools to increase motivation in our own classrooms.
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Brown Group
SMPs through journals
View their project Yes We Can!(notate) in the Repository of Wisdom of Practice.
Grade level: Middle/High School
Authors: Stephanie Hironaka, Daniel Moscoe, Hector Nieves
We seek to fill a critical gap between the findings of academic research on education and the practical wisdom of the country’s most skilled teachers. As a first step, we offer a guide to identifying and strengthening the Standards for Mathematical Practice (SMPs) using problem-solving journals. Our guide will present a rationale for problem-solving journals, related research, and specific classroom strategies for eliciting structured student reflection on mathematical problem-solving. Our work is motivated by the finding that engaging students in verbal explanations of their reasoning can reveal deeper evidence of SMPs than their written math work alone (Burns 2013). Therefore young writers need support in converting verbalized ideas into text. We propose an annotation structure for students to reflect on their use of the SMPs in their progressing mathematical work.
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Fuchsia Group
View their project Math Amnesia Blog: Rx for Math Amnesia in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Subject: Blog
Authors: Josie Del Duca, Jane Juten
We aim to provide teachers with strategies to help ease the process of moving learning into students' long-term memory. There has been much research into this process, which is very useful for educators, and we would like to bring this to the forefront within the mathematics education community. Some strategies that we will explore include frequent low stakes quizzing, spiraling and interleaving, study strategies, questioning strategies, spaced practice, engagement, collaboration, and more. For each strategy we will discuss the research behind it, how we have implemented it in a middle school and secondary school classroom and some ideas to get you started in your own classroom. We will be using resources from a variety of math people who have found tools that work. Teaching is a collaborative effort and we hope to pull together the research and resources in an informative and easy to use blog.
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Green Group
View their project Metacognition in the Repository of Wisdom of Practice.
Grade Level: High School
Authors: Dan Henderson, Kai Sam Ng, Elli Simonen
We believe that students will become better problems solvers if they are aware of their mathematical thinking. As mathematicians, we know the process of getting through a problem is just as important as the "answer" itself, but as teachers of mathematics, we often find it difficult to spark this same attitude within our students. In this PD, three experienced teachers share strategies we each use to improve metacognition, ultimately fostering a student-centered problem-solving culture in our classrooms. Teachers will complete a sample task as students, and then as teachers reflect on how the task was facilitated as a model. We will discuss the specifics of how to select a good task, build a safe space for thinking, create time and space for processing, model how students should engage, and evaluate student products. Secondary math teachers will leave this PD knowing how to deliberately foster an “aha” moment, rather than rely on luck and student talent to do so.
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Grey Group
Mathematical Modeling
View their project Modeling2: Examples and Practice in the Repository of Wisdom of Practice.
Grade Level: Middle School, High School
Subject: Modeling2 : Examples and Practice
Authors: Robert Calungsod, Aziz Jumash, Peter Petto
Mathematical modeling is a process that uses math to represent, analyze, make predictions or otherwise provide insight into real-world phenomena. (GAIMME, p.8) Participants are expected to understand, experience the practice of, and acquire resource materials related to mathematics modeling. This workshop will provide examples and best practices of the modeling process as described in the GAIMME & NCTM frameworks. Ample time is allotted for participants to read and reflect on some research on the benefits of modeling to the students. Participants will also conduct a basic hands-on simulation and also be shown a way to automate simulation using computer code that they can access, modify and extend. (Random number production and code execution will require a web browser.) Introduction and opening activities take 25 minutes; math modeling exemplar 40 minutes with 5-minute break & 10 minutes of extension activities leading to the conclusion and Q&A. Takeaway: Binder of MODELING materials.
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Orange Group
Area Model
View their project Area Model in the Repository of Wisdom of Practice.
Grade Level: High School
Subject: Algebra I, Algebra II
Authors: Matthew Cheng, Rachel Griffin, Bryant Lucas
Join us for an interactive session on incorporating area models into your Algebra 1 and Algebra 2 curriculums. Participants will dive deeper into how area models can be used to multiply, divide, and factor polynomials, as well as complete the square. We will discuss benefits of using these models and how they help students develop understanding of otherwise abstract mathematical algorithms. This 60 minute session will provide time to explore the models on paper and with algebra tiles. We will also discuss student errors and misconceptions and brainstorm the best teacher responses and interventions to address them. Participants will leave with a solid understanding of area models, editable examples of student tasks, and pedagogical methods for addressing misunderstanding.
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Pink Group
Blended Learning
View their project Blended Learning in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Authors: Fredric Borne-Dumont, Evie Jones, Carol Wu
Are you looking to change things up in your math class? Do you want to incorporate more student centered learning in your classroom, but don’t know how to do so most effectively? Find out how blending your classroom can increase student agency and allow for a more individualized learning experience for your students. Learn the basics of blended learning including the elements and models of blended learning, the benefits for both you and your students, and find a list of resources and ideas on how to blend your math classroom. Check out our website at! Explore the website at your own pace, and feel free to share any ideas that you have used in your own classroom that have worked for you and your students. Created by math teachers from across the country just like you!
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Purple Group
Teacher Collaboration Protocol
View their project Teacher Collaboration Protocol in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Authors: Joey Kelly, Christopher Norris-LeBlanc, Samantha O'Connor
High cognitive demand tasks which spark student engagement through inquiry and relevant problem solving have been shown to have positive effects on critical thinking skills and academic achievement. Research shows that collaborative planning and co-teaching lead teachers to enact more high cognitive demand tasks in the classroom. The more attention that teachers pay to task design, especially during collaborative planning, the more likely the task will increase student interest and understanding.
Inevitably, common planning time is insufficient and teams must divide some of the work to be completed separately. This protocol aims to help teaching teams reach their potential by prioritizing the time they spend together around understanding a high cognitive demand task’s mathematical goals and revising the task so that it is relevant, engaging, and meets the particular needs of their students.
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Red Group
Reframing Tasks through Social Justice
View their project Reframing Tasks through Social Justice in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Authors: Ana Castillo, Linda Nguyen, Michelle Sims
Participants will be introduced to the concept of social justice through a relevant mathematical problem involving a current societal issue. This workshop will outline how social justice can play a part in our math curricula and the importance of exposing our students to these concepts. Participants will examine a generic textbook problem that has been modified to include a social justice issue and discuss strategies of how to modify problems in their current application based problem set. Participants will then practice integrating social justice issues with mathematical content using a provided list of data resources. Time will be provided for participants to share their work and discuss the strengths and challenges of merging social justice with mathematics into the curriculum. Laptops or tablets are required for the problem development portion of this workshop.
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Tan Group
Proportional Reasoning
View their project Proportional Reasoning in the Formative Years in the Repository of Wisdom of Practice.
Grade Level: Middle School
Authors: Tun Bhothinard, Sharon Goodman, Shana Henry
Proportional reasoning is heavily highlighted in the beginning years of middle school. This session aims to help teachers distinguish between the different types of proportional thinking that fifth through eighth graders frequently encounter.
After creating a working definition of proportional reasoning, teachers will spend 15 minutes independently examining a set of 8 problems that require different types of proportional reasoning. Teachers will then work with a partner for 15 minutes to describe the similarities and differences in the types of thinking that are required, and categorize the problems in a way that makes sense to them. After a group share lasting 10-15 minutes, teachers will read a short article that defines 4 different types of proportional reasoning problems (mixtures, rates, part:part:whole, similarity), and compare their ideas with the research. Last, teachers explore how these middle school standards lay the foundation for students’ success in high school courses.
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Yellow Group
View their project Assessment in the Repository of Wisdom of Practice.
Grade Level: Middle/High School
Authors: Peter Horsh, Angel Kuo, Betty Hwang
"When the focus and form of assessment are different from that of instruction, assessment subverts students' learning by sending them conflicting messages about what mathematics is valued."(NCTM, 1995, p. 13) Thinking about this quote from the Assessment Standards, we will help fellow teachers to reflect on the difference between the core values in their classroom and the habits, procedural fluency, and conceptual understanding their assessments measure. Teachers will identify their personal goals for assessments and think about how to frame their questions in ways that reflect their teaching philosophy going forward. Additionally, we'll look at examples of rich mathematical tasks that allow students to demonstrate the "hard-to-measure" habits (perseverance, curiosity, resolve, grit) where content ability is embedded within the task.
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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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