In this episode of Room to Grow, Joanie and Curtis continue the season 5 series on the Mathematics Teaching Practices from NCTM’s Principles to Actions, celebrating it’s 10th anniversary. This month’s practice is “Use and connect mathematical representations.” Our hosts describe the five representations outlined in Principles to Actions, which include visual, symbolic, verbal, contextual, and physical descriptions of mathematics, but emphasize that the representations are not meant to be a check list to be covered during instruction. Rather, the different representations provide a framework for explore important mathematical concepts through different lenses, allowing students to build and deepen their understanding as they consider these ways of engaging.

In addition to deep understanding, teachers’ attending to different representations will allow different students in the class to be elevated, as their unique strengths and preferences will have the opportunity to come out and be showcased.

Additional referenced content includes:

· NCTM’s Principles to Actions

· NCTM’s Taking Action series for grades K-5, grades 6-8, and grades 9-12

· Making Connections Explicit​ (NCTM requires subscription)

· Supporting Understanding Using Representations​ (NCTM requires subscription)

· Three Ways to Enhance Tasks for Multilingual Learners​ (NCTM requires subscription)

· Interpreting Distance-Time Graphs – lesson referred to in this episode

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.

In this episode of Room to Grow, Joanie and Curtis continue the season 5 series on the Mathematics Teaching Practices from NCTM’s Principles to Actions, celebrating it’s 10th anniversary. This month’s practice is “Implement Tasks that Promote Reasoning and Problem Solving.” Our hosts being by expounding on the difference between selecting a task and implementing it, and that selecting a good task does not guarantee good implementation. They bust the idea that the only way to engage students in reasoning and problem solving is with a rich task, by considering how educators can weave together procedural learning with conceptual understanding.

Next, they connect reasoning and problem solving to the Standards of Mathematical Practice, particularly practices 7: Attend to and make use of structure and 8: Look for and express regularity in repeated reasoning. Capitalizing on students’ natural noticing and shining the light on the underlying mathematics leads to stronger connections and increasing students’ ability to generalize their understanding.

By building a foundation of reasoning and sense-making, and helping students understand that this is a resource for them tap into, that allows for the learning and engagement beyond rote classroom experiences.

Additional referenced content includes:

· NCTM’s Principles to Actions

· NCTM’s Taking Action series for grades K-5, grades 6-8, and grades 9-12

· Selecting and Creating Mathematical Tasks article from Smith and Stein

· A Teacher’s Guide to Reasoning and Sense-Making from NCTM

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.

In this episode of Room to Grow, Joanie and Curtis begin a season 5 series on the Mathematics Teaching Practices from NCTM’s Principles to Actions, celebrating it’s 10th anniversary. This month’s practice is “Facilitating Meaningful Mathematics Discourse.” Our hosts first identify what they mean by discourse and why it is important: that students are able to communicate their mathematical thinking in ways that others can clearly understand for the purpose of furthering their own mathematics learning.

Next, Curtis and Joanie unpack how to get students talking in math class, a necessary condition for meaningful math discourse. Classroom culture is a key element to ensure that students feel safe and comfortable enough to share their mathematical thinking. Implied in this is that the teacher must hold themselves to precision of language as well, and should understand when to require precision from students and when to be more flexible with informal language.

Finally, their conversation suggests that effective math discourse is not improvisational, but rather something teachers can and should plan for, and use as a strategy for an equitable classroom.

Additional referenced content includes:

· NCTM’s Principles to Actions

· NCTM’s Taking Action series for grades K-5, grades 6-8, and grades 9-12

· Strategies for facilitating math discourse in the classroom

· Latrenda Knighten, NCTM President’s message on Let’s Give Students the Gift of Time

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.