Identifying Critical Moments for Mathematical Sensemaking with Lynsey Gibbons, Jamila Riser & Corey Drake ROUNDING UP: SEASON 5 | EPISODE 6 Planning and teaching with a curriculum is a challenging process. It requires teachers to understand the relationship between the design of a lesson and the stated learning goal, and to recognize the role individual lessons play in a unit of study. What types of practices and protocols can help teachers navigate this important work?  Joining us to discuss this question are MLC Director of Professional Learning Corey Drake as well as Jamila Riser and Lynsey Gibbons, two of the architects of the Transforming and Understanding Professional Learning (TUPL) project at the University of Delaware. BIOGRAPHIES Dr. Lynsey Gibbons is an associate professor specializing in mathematics education at the University of Delaware. Her research focuses on designing for, facilitating, and examining teacher learning; and identifying tools and resources to support instructional leaders and teacher educators. Dr. Jamila Riser is a mathematics educator, professional learning leader, and researcher with more than 40 years of experience supporting teachers, instructional coaches, administrators, and state leaders in strengthening mathematics teaching and learning. RESOURCES The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom book by James W. Stigler & James Hiebert Discretionary spaces research by Deborah Loewenberg Ball "Theories of Action Needed to Guide Emerging Models for Professional Learning" journal article by Lynsey K. Gibbons, James Hiebert, and Kelly McKie The NTCM article Lynsey Gibbons mentioned is in press; the link will be added here once it is available. To be informed when the article is published, email [email protected]. CHAPTERS 00:00 - Introduction • The TUPL Project 02:37 - High-Quality Instructional Materials & Preservice Teachers 07:12 - Critical Moments & Learning Goals 16:06 - What Planning for Critical Moments Looks & Sounds Like 20:49 - Collaboratively Determining Learning Goals & Next Steps 27:47 - Pacing & Discretionary Spaces 33:31 - Resources, Protocols & Questions to Consider 42:14 - Wrapping Up: Engage with Rounding Up TRANSCRIPT Click here for a full episode transcript.

Instructional Routines That Support Mathematics Identity Development with Dr. Fawnda Norman ROUNDING UP: SEASON 5 | EPISODE 5 Supporting students' math identity has become a priority for many elementary mathematics teachers. But recognizing the importance of helping students build a positive math identity is not the same as knowing how to make that happen on a day-to-day basis. During this episode, we'll talk with Fawnda Norman from the University of Wisconsin-Oshkosh about the ways educators can integrate identity-supporting practices into daily math routines.  Bio: Dr. Fawnda Norman is an assistant professor of mathematics education at the University of Wisconsin-Oshkosh. She teaches elementary and secondary mathematics methods and action research courses. Her teaching emphasizes culturally responsive mathematics instruction, integrating practices that provide students with multiple ways to access, represent, and engage with mathematical concepts. She prepares future teachers to create safe, inclusive, and equitable learning environments for all students. Her central focus with preservice teachers is mathematics identity development. She designs opportunities for teachers to critically reflect on their own experiences as mathematics learners and examine how those experiences shape their emerging teacher identities. To support positive mathematics identity development in K–12 classrooms, Dr. Norman has developed five classroom routines that help students see themselves as capable and valued mathematics learners. Resources: WISE Learn website Full episode transcript Chapters: 00:00 - Introduction • Building Math Identity in Students 07:23 - Notice and Wonder & Worked Examples 14:48 - Exploring Worked Examples 18:04 - Understanding Worked Examples23:21 - Wrapping Up • Engage with Rounding Up

The How, When & Why of Physical & Digital Manipulatives with Natalie Crist & Patrick Vennebush ROUNDING UP: SEASON 5 | EPISODE 4 Recently, there's been a great deal of debate around the role digital manipulatives should play in an elementary math classroom. In this episode, we'll talk with Patrick Vennebush and Natalie Crist about the role physical and digital manipulatives can play in a classroom. We'll try to clarify the opportunities, the limitations, and the questions teachers should ask themselves when they consider using these powerful tools.  BIOGRAPHIES Patrick Vennebush is the chief learning officer at The Math Learning Center, where he manages the development curriculum products and professional learning services, including the newly released Math MultiApp by MLC. Natalie Crist is the director of content development at The Math Learning Center, where she leads the development of curriculum products, including Bridges in Mathematics. In addition to her work for MLC, Natalie is an adjunct faculty member at Towson University and McDaniel College.  RESOURCES Math MultiApp by MLC app "Meet the Math MultiApp by MLC: All Your Math Tools in One Place" webinar "The Benefits of Virtual Manipulatives" article CHAPTERS 00:00 - The Role of Manipulatives in Math Education 02:27 - Physical vs. Digital Manipulatives 05:40 - Benefits of Physical Manipulatives 10:05 - Exploring Digital Materials 14:13 - Limitations of Manipulatives 21:36 - Choosing the Right Manipulative 24:46 - Planning for Effective Instruction 27:58 - Introducing the Math MultiApp 32:19 - Accessing the Math MultiApp TRANSCRIPT Click here for a full episode transcript.

See It! Say It! Symbolize It! with Dr. Patrick Sullivan ROUNDING UP: SEASON 5 | EPISODE 3 Representations, language, and symbols are all important ingredients in building students' conceptual understanding and fluency. But how can we understand the relationship between those three ingredients? And what happens if we leave any one of them out of the recipe?  In this episode, we explore these questions with Dr. Patrick Sullivan, professor of mathematics at Missouri State University. BIOGRAPHY Dr. Patrick Sullivan teaches mathematics content and methods courses for future K–12 teachers at Missouri State University. His work focuses on helping teachers unleash children's mathematical brilliance, particularly in the areas of number, fractions, multiplication, and mathematical reasoning. He has published in the areas of elementary mathematics education, mathematical authority, technology-supported learning, and statistics education.  Dr. Sullivan is the author of See It, Say It, Symbolize It (Solution Tree), which challenges educators to rethink how mathematics is taught and learned. He is also the past president of the Missouri Council of Teachers of Mathematics and the founder and director of the Young Mathematics Teacher Academy, a program designed to encourage and mentor high school students interested in becoming mathematics teachers. Formerly, he served as a school leader and high school mathematics department chair. He has received the Presidential Award for Excellence in Mathematics and Science Teaching and the Missouri Teacher Educator of the Year Award. RESOURCES See It, Say It, Symbolize It book Unleashing Mathematical Brilliance website CHAPTERS 00:00 - Introduction • Building Mathematical Understanding 00:32 - Grandma Edna's Math Lesson 05:44 - See It, Say It, Symbolize It 09:21 - Concept Images & Fractions 14:07 - Language as the Connector 21:46 - Equal Exchange 26:02 - Making Sense of Symbols 32:51 - Connecting Math Across Grades 37:43 - Wrapping Up TRANSCRIPT Click here for a full episode transcript.

Organizing Board Space to Support Reasoning & Connection, Part 2, with Dr. Tutita Casa & Katherine Mack ROUNDING UP: SEASON 5 | EPISODE 2 Repositioning the classroom board as a shared space for teachers and students can create opportunities for deeper student learning and have a subtle but significant impact on students' math identities. In part 2 of this two-part series, Mike talks with Tutita Casa and Katherine Mack from the University of Connecticut about ways teachers can use the board to reflect student reasoning, draw attention to key ideas, and close a lesson without funneling students to a correct answer.   BIOGRAPHIES Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut. Her work is aimed at supporting teachers to empower students to grapple with the mathematics and engage with the discipline in ways similar to how mathematicians go about their work. Katherine Mack is a doctoral student in curriculum and instruction at the University of Connecticut. She examines how elementary teachers can facilitate mathematical discourse by repositioning the instructional board as a space that centers student reasoning and makes it visible.  RESOURCES Listen to part 1 of the conversation with Tutita and Katherine. Listen to Tutita's first appearance on the podcast. TRANSCRIPT Click here for a full episode transcript. CHAPTERS 00:00 - Introduction • Exploring Classroom Communication & Board Dynamics 02:35 - The Importance of Anchoring Tasks in Mathematics 04:52 - Understanding Shared Attention & Student Engagement 08:35 - The Role of Bookending in Classroom Discussions 11:31 - Validating Student Ideas & Understanding 13:39 - Creating a Safe Space for Incorrect Ideas 18:26 - Practical Steps for Teachers to Enhance Board Use 22:17 - Wrapping Up • Share Your Thoughts

Organizing Board Space to Support Reasoning & Connection, Part 1, with Dr. Tutita Casa & Katherine Mack ROUNDING UP: SEASON 5 | EPISODE 1 Classroom boards have traditionally been a space that belongs to the teacher, even as technology changes. What would it look like to rethink our relationship with the board, repositioning it as a shared space for teachers and students alike? In part 1 of this two-part series, Mike sits down with Dr. Tutita Casa and Katherine Mack from the University of Connecticut to talk about ways teachers can establish norms and develop practices that make the board a shared space that reflects students' reasoning.    BIOGRAPHIES Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut. Her work is aimed at supporting teachers to empower students to grapple with the mathematics and engage with the discipline in ways similar to how mathematicians go about their work. Katherine Mack is a doctoral student in curriculum and instruction at the University of Connecticut. She examines how elementary teachers can facilitate mathematical discourse by repositioning the instructional board as a space that centers student reasoning and makes it visible.  RESOURCES  Listen to Tutita's first appearance on the podcast. TRANSCRIPT Click here for a full episode transcript. CHAPTERS 00:00 - Introduction • Rethinking the Classroom Board 00:43 - Making the Board Student-Centered 03:40 - Shifting Classroom Norms 08:31 - Capturing Student Reasoning 11:35 - Helping Students Follow the Math Story 14:19 - Using Color & Space for Clarity 18:57 - Adapting Board Work in the Moment 22:14 - Connecting Spoken Language to Written Math 24:51 - Wrapping Up • Part 2 Coming Soon

Looking Ahead to Season 5 Rounding Up returns next week for its fifth season, examining even more ideas, concepts, and practices that shape teaching and learning in elementary mathematics classrooms. This season, we invite our listeners to engage with us by leaving a comment on our website, mathlearningcenter.org/podcast. We look forward to hearing from you! TRANSCRIPT Mike Wallus: Rounding Up returns for Season 5 next Thursday, September 3rd, with brand-new episodes. We'll examine ideas, concepts, and practices that shape teaching and learning in elementary mathematics classrooms. I'm your host, Mike Wallus, the vice president of educator support at The Math Learning Center, the organization behind the Bridges in Mathematics curriculum for early childhood learners all the way through fifth grade. This season, we'll chat with experts in classroom infrastructure— Tutita Casa: We're trying to take those unspoken norms that the board is a space that traditionally is led by the teacher, commanded by the teacher, too often didactically, and how can we open up that space to reflect what our students are thinking? Mike: Content— Patrick Sullivan: I felt like my teaching improved exponentially when I just started listening to my students. And I'm like, "Oh, they don't really understand that the way I thought they would." And OK, so now I can modify and I can latch on to what they're telling me as opposed to just me thinking, "Oh, this is what's going to be best." Mike: Math identity and classroom culture— Fawnda Norman: Math is about making connections and communicating with each other. It's not just about solving the problem and getting the right answer. And so, if we can get students to communicate with each other, they're gonna learn that they are all mathematicians and we can all do this. Mike: Identifying critical moments in the classroom— Jamila Riser: Where's this moment in the lesson where the students have potentially the greatest, most visible opportunities to make the key connections that they had identified in the lesson to reach that goal? Mike: And a whole lot more.  Make sure to subscribe on your preferred podcast app so you don't miss an episode, or head over to mathlearningcenter.org/podcast, where you can share your thoughts and experiences relating to each episode with us.  Rounding Up is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover their mathematical confidence and ability.

Recording Student Thinking During a Mathematics Discussion with Nicole Garcia ROUNDING UP: SEASON 4 | EPISODE 24 Learning to record students' mathematical thinking might best be described as "on-the-job training" with a great deal of trial and error and a lot of practice.  In this rereleased episode from Season 1, Nicole Garcia from the University of Michigan talks about the practice of recording student thinking and offers insight on this challenging but crucial practice. BIOGRAPHY Nicole Garcia is an experienced mathematics teacher, professional developer, and teacher educator focused on practice-based approaches to teacher learning. In her work as the associate director of TeachingWorks at the University of Michigan, she supports teachers, coaches, administrators, and teacher educators to ensure that all students have access to strong instruction. RESOURCES "Recording Student Thinking in a Mathematics Discussion" journal article Inside Mathematics website TRANSCRIPT Click here for a full episode transcript.

Making Sense of Fractions with Susan Empson, PhD ROUNDING UP: SEASON 4 | EPISODE 23 For quite a few adults, fractions were a stumbling block in their education, causing them to lose their footing and begin to doubt their ability to make sense of math. But this doesn't have to be the case for our students! In this rerelease of an episode from Season 2, we're talking with Susan Empson, PhD, about big ideas in fractions and how we can make them more meaningful for our students. BIOGRAPHY Susan B. Empson is an emerita professor in the department of Learning, Teaching, and Curriculum at the University of Missouri. She and Vicki Jacobs are currently collaborating on a National Science Foundation research grant to study elementary teachers' learning and development centered on teaching in ways that are responsive to children's mathematical thinking in the domain of rational numbers. Her research on children's thinking about fractions is the topic of her 2011 book, Extending Children's Mathematics: Fractions and Decimals (with co-author Linda Levi), and she has published widely in refereed journals, including Cognition and Instruction, Journal for Research in Mathematics Education, Educational Studies in Mathematics, Teaching Children Mathematics, and Journal of Mathematics Teacher Education. She has been a researcher of Cognitively Guided Instruction since 1989 and is a co-author of Children's Mathematics: Cognitively Guided Instruction (1st and 2nd editions).  RESOURCES Extending Children's Mathematics: Fractions and Decimals book by Susan B. Empson and Linda Levi Mathematics Teacher: Learning and Teaching PK-12 journal articles authored and co-authored by Susan Empson TRANSCRIPT Click here for a full episode transcript.

Breaking the Cycle of Math Trauma with Kasi Allen, PhD ROUNDING UP: SEASON 4 | EPISODE 22 If you are an educator, you've likely heard people say things like "I'm not a math person." While this may make you cringe, if you dig a bit deeper, many people can identify specific experiences that convinced them that this was true. In fact, some of you might secretly wonder if you are a math person as well.  In this rerelease of an episode from Season 3, we're talking with Kasi Allen, PhD, about math trauma: what it is and how educators can take steps to address it. BIOGRAPHY Kasi Allen serves as the vice president of learning and impact at The Ford Family Foundation. She holds a PhD degree in educational policy and a bachelor's degree in mathematics and its history, both from Stanford University. RESOURCES "Jo Boaler Wants Everyone to Love Math" article in Stanford Magazine R-RIGHTS Learning to Love Math by Judy Willis, MD TRANSCRIPT Click here for a full episode transcript.