Learning Mathematics Through Sense-Making

In this episode of Room to Grown, our hosts revisit some topics from past episodes to revisit conversations about what it means to learn mathematics, and what mathematics is important for students to understand in an age of pervasive technology and AI. They confirm their beliefs that learning should be grounded in curiosity, should connect to previous learning, and the tension that educators might feel when they are among coworkers who have a different belief about what teaching mathematics should look like. Check out these resources to go deeper into these ideas ●      Room to Grow The Math that Matters with Aly Martinez●      Room to Grow Decluttering Mathematics  with the Decluttering Mathematics book author team●      Room to Grow Centering Student Reasoning 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 [email protected] . Be sure to connect with your hosts on LinkedIn and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Curtis and Joanie host Vanessa Vakharia, in person! Their conversation explores the concept of math trauma, which Vanessa defines as “a negative experience with math that sticks with you long after the experience is over.” We learn about how Vanessa overcame her own math trauma after failing grade 11 twice, and explore the ways in which teachers can ensure that students have positive, trauma-free learning experiences in math class.Resources mentioned in this episode and ways to learn more:Math Therapy  book by Vanessa VakhariaThe Math Guru tutoring services in Toronto, CanadaThe Math Therapy podcast, Vanessa’s weekly podcast on all things Math Trauma/Math TherapyFind and follow Vanessa on social media: Instagram @themathguru and TikTok @themathguru 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 [email protected] . Be sure to connect with your hosts on Instagram: @JoanieFun and @cbmathguy.

In this episode of Room to Grow, Joanie and Curtis learn about a new publication: Decluttering Mathematics: 5 Fundamental Understandings That Unleash Meaningful Student Thinking Grades 6-12. Three of the book’s authors join us to share how that when secondary mathematics instruction is cluttered with disconnected procedures and a focus on computation without meaning, students are essential being handed a huge pile of tiny puzzle pieces without ever building or even seeing the picture on the puzzle box. Ted, Scott, and April call out the clutter and describe how educators can connect the disconnected and focus on what’s important to allow students the opportunity to think, reason, and make sense of mathematics. In the conversation, the authors touch of the five fundamental understandings in the book: Measurement, Comparison, Proportional Relationships, Equivalence, and Graphical Representations, and provide examples of how and why attention to student thinking leads to better teaching and better student learning. Curtis and Joanie appreciated the approach of having students “think first; compute only if necessary,” and the idea of retiring some common topics to the “math attic.” The authors share their grounding the book in ways of thinking, ways of approaching, and ways of doing mathematics, all in the service of doing bigger things in math class.  Resources mentioned in this episode and ways to learn more:·       Order the book HERE or HERE or HERE·       Ted’s website https://www.coequalmath.com/home and LinkedIn page https://www.linkedin.com/in/tedcoe/ ·       April’s LinkedIn page https://www.linkedin.com/in/aprildstrom/ , BTC info page https://www.buildingthinkingclassrooms.com/team/april-strom ·       Scott’s website https://www.scottadamsonmath.com/ and LinkedIn page https://www.linkedin.com/in/scott-adamson-465202327/ ·       James’ website https://jamestantonmath.com/ and LinkedIn page https://www.linkedin.com/in/james-tanton-9920bb58/   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 [email protected] . Be sure to connect with your hosts on Instagram: @JoanieFun and @cbmathguy.     

In this back to school episode, Curtis and Joanie discuss key ideas for starting the new school year off right, to ensure effective teaching and learning for teachers and students. How do you spend the first day of school with your students? Do you get them working in groups right away like Curtis, learning about them as students and how they engage with math and each other? Or maybe you focus on learning their names and helping them learn each other’s names like Joanie, ensuring a community is built as early as possible.  Our hosts discuss ways to frame struggle and mistakes, and how to be sure that what you put in place the first week stays aligned through your words and actions all year long, ensuring that students “end the school year with a more positive math identity than when they started.” Resources mentioned in the episode and others to follow up on:·       NCTM President’s Message (Latrenda Knighten) for August 2026 (no login required) ·       Book Productive Math Struggle·       Edutopia blog post Instructional strategies for managing student mistakes in math and Mathnasium blog post for parents·       Youcubed Week of Inspirational Math – Activities and resources for the first week of school (or anytime) to support positive math identity and student engagement ·       Book Impact of Identity in K-12 Mathematics: Rethinking Equity-Based Practices  

What do kindergarten counting concepts have to do with high school algebra? More than most teachers realize. In this episode, Joanie and Curtis sit down with Erin Wahler-Cleveland, founder of Roots and Wings Math, to explore how deep understanding of early and elementary mathematics lays the groundwork for everything that comes later — and what teachers at every grade level can do to better support that understanding.Erin opens with a thought-provoking coordinate-plane framework that distinguishes between easy/hard (subjective) and simple/complex (objective). The key insight? As we gain expertise, complex things start to feel simple — and that's exactly what makes teaching so hard. Early numeracy lives in the easy yet complex quadrant, and its depth is routinely underestimated by the adults who teach it.We discuss important instructional shifts for teachers at every level, and land on an important key takeaway: The central challenge of teaching mathematics is maintaining awareness of a complexity that has become invisible through expertise. The remedy — at both elementary and secondary levels — is giving teachers genuine learner experiences with the content they teach, paired with disciplined questioning practices that reveal student thinking rather than assume it.Resources & Links MentionedRoots and Wings Math – https://www.rootsandwingsmath.com/The Dunning-Kruger Effect - https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effectRoom to Grow Podcast – www.roomtogrowmath.com  

In this episode of Room to Grow, Ali Martinez, Chief Program Officer for Math at Student Achievement Partners (SAP), joins Joanie and Curtis for a conversation about the math that matters. In the current era, math teachers face too much content and too little time to feel or be effective in allowing students the chance to learn math deeply.Aly shared information about SAP’s national initiative to identify essential mathematics content for high school, and to integrate data science competencies. The work builds on COVID-era prioritization efforts and aims to address curriculum overload through systems-level change involving standards revision, instructional materials alignment, and cross-sector collaboration. The conversation acknowledges and elevates the role of durable skills, the rising importance of data literacy, and the need for systemic change to realize these desired outcomes.Be sure to check out these resources, referenced in this month’s episode.Learn more and stay in touch with Math that Matters resource: https://learnwithsap.org/math-that-matters/ Durable skills in math https://learnwithsap.org/durableskills/ High School redesign: https://learnwithsap.org/overlap-to-opportunity/ Research into high school math textbooks https://learnwithsap.org/math/a-rare-look-inside-high-school-math-textbooks-and-what-publishers-say-needs-to-change/        Coherence Map from Student Achievement Partners      Data Science for Everyone website   

In this episode, Curtis and Joanie sit down with Mahmoud Harding from Data Science 4 Everyone (www.ds4e.com)  to explore the growing role of data science in K-12 education.Mahmoud breaks down the key distinction between data science and data literacy — two terms that are often used interchangeably but carry very different meanings for educators and students alike. The conversation dives into why data science matters for all educators right now, regardless of subject area or grade level, and why the time to act is today. And taking action doesn’t mean you need math expertise or to steer away from the standards and curriculum your students need to know!Mahmoud also shares practical, accessible ways teachers can get started with data-centered lessons in their classrooms — regardless of grade level or content area.Whether you're a curious educator or ready to dive in, this episode will leave you inspired to bring data to life for your students.Resources:●      https://www.datascience4everyone.org/about   (DS4E Homepage)●      https://www.datascience4everyone.org/resources  (DS4E Resources)●      https://ds4e-org.github.io/CPN_rubric/   (DS4E Content Partner Network)●      https://ds4e-org.github.io/technologytoolkit/   (DS4E Technology Tools for working with data)●      https://datasciencelearning.org/ (K12 Data Science Learning Progressions) ●      https://datasciencelearning.org/blog/five-basic-concepts-for-teachers-new-to-data-science  (DS4E Blog: Five basic concepts for teachers new to data science)●      https://hkurzweil.github.io/ds4e-teacher-pd/frontmatter.html (DS4E Data Science Starter Kit)

Teaching math in 2026 is demanding in ways that are structural, cultural, and relentless — and yet the conversation about teacher sustainability rarely makes space for what math educators are actually carrying. In this episode, Curtis and Joanie get honest about burnout, purpose, and community in the math teaching profession.Drawing on research from burnout science, teacher identity, and professional resilience, this conversation explores three ideas that don't get discussed enough: why burnout is a systemic signal rather than a personal failure, how math teachers can reconnect with a durable and honest sense of purpose when the hard days start to outnumber the good ones, and why professional community isn't a luxury — it's the infrastructure that makes long, sustainable careers possible.This episode is for math teachers who are tired but not done. It won't tell you to practice more gratitude or look on the bright side. It will tell you the truth — and give you something useful to do with it.Books:●      Burnout: The Secret to Unlocking the Stress Cycle by Emily Nagoski & Amelia Nagoskiwww.burnoutbook.net●      The Courage to Teach: Exploring the Inner Landscape of a Teacher's Life by Parker J. Palmerwww.couragerenewal.org/parker/writings/courage-to-teach●      Onward: Cultivating Emotional Resilience in Educators by Elena Aguilarwww.brightmorningteam.com/onward●      Mathematical Mindsets: Unleashing Students' Potential through Creative Math by Jo Boalerwww.youcubed.org/mathematical-mindsetsOrganizations & Communities:●      Colorado Council of Teachers of Mathematics (CCTM)www.cctmath.org●      National Council of Teachers of Mathematics (NCTM)www.nctm.org

This episode of Room to Grow, Curtis and Joanie reflect on topics about which they have changed their minds. Although their minds have changed about different things, in their conversation, they have captured bigger ideas about what goes into changing one’s mind, and have applied that to what goes into changing a teacher’s practice. Importantly, the recognize that change is a highly personal experience and is an inevitable part of continued growth.As you listen to Joanie’s thoughts about how students develop conceptual understanding, and Curtis’ thoughts about AI in math education, you may wish to consider these additional resources, referenced in this episode:·       NCSM guidance on AI in Math Education·       Adding It Up report from the National Research Council·       Principles to Actions from NCTM and NCTM’s “Teacher’s Guide to Reasoning and Sense Making”·       Pam Harris’ Math is FigureoutableDid 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 [email protected] . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.  

This episode of Room to Grow, Curtis and Joanie welcome Zandra de Araujo to the podcast. Zandra and her colleagues, Sam Otten and Amber Candella created math classroom “Instructional Nudges,” small tweaks to classroom practice that can make a significant impact on student engagement, learning, and sense making of mathematics.  The conversation reveals the origin of the Instructional Nudges project, some specific example nudges and how they work, and the coming soon Instructional Nudges aligned to the Mathematics Language Routines. Everyone will walk away with an idea or two to implement right away in the classroom! Additional referenced content includes:·       Zandra’s personal webpage·       Practice-Driven PD webpage which houses all of the Instructional Nudges·       NCTM article – Rate and Review nudge·       Incremental PD guide·       Two-minute teacher guide videos 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 [email protected] . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.