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.

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 last 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

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 last 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

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.

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.

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.

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.

ROUNDING UP: SEASON 4 | EPISODE 21

If you ask an educator to share some of the most important ideas in elementary mathematics, most would include place value on that list. But what does it mean to understand place value, really? And what types of language, practices, and tools support students as they build understanding?

In this rerelease of an episode from Season 2, we discuss these questions and more with Dr. Eric Sisofo from the University of Delaware.

BIOGRAPHY

Dr. Eric Sisofo is an assistant professor specializing in mathematics education in the School of Education at the University of Delaware. He earned his EdD in educational leadership, curriculum, and instruction; his MEd in curriculum and instruction with a concentration in mathematics education; and his BS in mathematical sciences from the University of Delaware. With a focus on mathematics education, Dr. Sisofo's education leadership portfolio, the capstone project for his doctoral degree, investigated the effects of lesson study on teacher candidates' use of student thinking when planning and reflecting on their teaching.

RESOURCE

National Council of Teachers of Mathematics

TRANSCRIPT

Click here for a full episode transcript.