Room to Grow - a Math Podcast

How does what we believe as teachers impact our students and their learning? What about their beliefs about themselves as learners and doers of mathematics? In this episode of Room to Grow, Curtis and Joanie explore these ideas and more from the perspective of continuous improvement and growing awareness as educators. They share stories from their own experiences where naming a fundamental belief about teaching and learning mathematics provides a powerful reminder of habits, actions, or decisions that work against our fundamental beliefs. 

As former classroom teachers, Joanie and Curtis know how challenging it is to meet the needs of a full class of students, and working to be a better teacher from day to day and year to year. They talk about shifting the thinking from doing something more to doing something different when a teacher wants to make a change in their classroom to better align their practice with their beliefs.

And of course, students’ beliefs are part of the mathematics achievement equation, too, so our hosts share some ideas about how teachers can help bolster students’ beliefs in themselves and in their abilities to learn mathematics.

• Learn more about students' mathematical identities in this book: https://www.nctm.org/Store/Products/The-Impact-of-Identity-in-K-8-Mathematics--Rethinking--Equity-Based-Practices/
• Learn about supporting equitable outcomes in your math classroom in this book: https://www.amazon.com/Choosing-See-Framework-Equity-Classroom/dp/1951600800
• Joanie mentions this book where she explored ideas of developing students’ social and academic capital: https://www.amazon.com/Heterogenius-Classrooms-Detracking-Science-Groupwork/dp/0807752460 

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

Productive Struggle is a key component of students’ mathematical learning. But struggle can shift from “productive” to “unproductive” at different rates and for different reasons for different students (and teachers!). Ensuring that students engage in productive struggle is complex, nuanced, and dependent on a healthy classroom culture and strong teacher-student relationships. 

In this episode, Curtis and Joanie explore what productive struggle looks like and how to recognize when a student’s struggle is heading for an unproductive state. They consider the characteristics of tasks and activities that lend themselves to supporting productive struggle, including the “just right” level of difficulty, and that students have enough familiarity with the topic that they believe they can be successful with the task.

Next, our hosts unpack the idea of the “Learning Pit” from James Nottingham, and how effective and well-timed questions from the teacher can help students who are stuck in the pit to find the proverbial rope they can use to pull themselves out and find success. 

Finally, Joanie shares a challenging geometric puzzle and the conversation she had with Curtis where he supported her productive struggle in finding the solution, tying together the ideas from this episode into an authentic situation from the hosts’ own lives.

Explore more about the Learning Pit and other ideas from the Challenging Learning Group here: https://www.challenginglearning.com/learning-pit/  

Consider extending your learning about productive struggle with these resources from NCTM (membership required for access):

• Productive Struggle in Action (access at www.nctm.org/mtlt11305g3).
• By way of introduction: Productive Struggle (Mathematics Teaching in the Middle School, Vol. 23, No. 4, January/February 2018).

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, our hosts discuss the importance of mathematical representations for students' deep learning of mathematics. The five representations described in NCTM's Principles to Actions include Physical, Visual, Symbolic, Verbal, and Contextual. Research shows that attending to and making connections between these multiple representations. National Research Council (2001), "Because of the abstract nature of mathematics, people have access to mathematical ideas only through the representations of those ideas" (p. 94). Joanie and Curtis remind listeners that the purpose of attending to multiple mathematical representations is not simply to check a box, but rather to make connections between the representations, allowing students to recognize the underlying structures and generalities. This deeper level of connection is at the heart of understanding mathematics.

Finally, they consider how mathematical representations support students' development of mathematical discourse and language; after all, student need to understand their representations pretty well in order to explain them to someone else! By incorporating discourse and mathematical language in the classroom, students thinking is validated and they create ownership of the mathematics, both their approaches and those of their classmates.

Be sure to check out these resources, referenced in this episode:

• Math Assessment Project - Shell Center: Comparing strategies lesson (includes the pancake problem discussed in this episode) https://www.map.mathshell.org/download.php?fileid=1631
• Learn more about Using and Connecting Mathematical Representations in NCTM's Principles to Actions https://www.nctm.org/Store/Products/Principles-to-Actions--Ensuring-Mathematical-Success-for-All/
• Learn more about the Five Practices for Orchestrating Productive Mathematics Discussions https://www.nctm.org/Store/Products/5-Practices-for-Orchestrating-Productive-Mathematics-Discussions,-2nd-Edition/

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Curtis and Joanie dive into ideas around exploration and play in mathematics. Although this may seem frivolous and not a priority for time-constrained math educators, our hosts discuss the positive implications on student learning, mindsets, and engagement in the mathematics. By framing an activity as “exploration,” the stress many students carry around learning math can dissipate, opening their minds to better understanding and enjoyment, and allowing them to tap into the power of their common sense and creativity. 

Curtis and Joanie consider how math educators can be strategic in their use of exploration and play so that the time taken is well spent and pays off for learning of important mathematical ideas.

Be sure to check out these resources, referenced in the episode and supportive of including mathematical exploration in your classroom:

• Problems worth solving at https://www.openmiddle.com/. Curtis referenced an exploration of quadratics in standard form, available here: https://www.openmiddle.com/maximum-value-of-a-quadratic-in-standard-form/
• Texas Instruments transformational geometry activities and lesson bundles are great for geometry exploration and can be found here: https://education.ti.com/en/timathnspired/us/geometry/transformational-geometry

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

One of the biggest challenges math teachers face is the variety of mathematical backgrounds students bring with them to math class.  Although state standards describe what students should know and be able to do at the end of the grade, more often than not, students move to the next grade or course with an incomplete mastery of pre-requisite content. In this episode of Room to Grow, Curtis and Joanie suggest that we reframe this reality: instead of thinking this is a problem to be solved, educators can embrace the diversity and leverage it to ensure that all students are progressing in their mathematical learning.

Our hosts start with an acknowledgement that all teachers are doing their best, and that all teachers want their students to be successful. From there, they discuss the importance of establishing strong relationships with student. Although it is cliché, it’s true that “students don’t care how much you know until they know how much you care.” When students know their teacher believes in them and is willing to do what it takes to help them understand math, they are often more willing to put forth the effort and work past obstacles to learning.

Curtis and Joanie complete this episode by sharing planning strategies that keep learning for all students front of mind, and suggest ways that math educators can make adjustments to their planning and instructional practice that help more learners engage. 

Be sure to check out these resources:

• Achieve the Core’s Coherence Map for tracing back pre-requisite math knowledge: https://achievethecore.org/coherence-map/  and this blog post that describes how the Coherence Map helps with unfinished learning: https://achievethecore.org/aligned/unfinished-learning-in-math-how-do-you-address-it/
• Research-backed strategies for supporting students: https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/rti_math_pg_042109.pdf 
• Article discussing Just-in-time vs. just-in-case intervention: https://pubs.nctm.org/view/journals/mtlt/113/10/article-p774.xml (*note: NCTM membership required)

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

Mathematical modeling is a cornerstone of students’ K-12 mathematics learning experiences. In their debut episode, your Room to Grow hosts discuss ideas for including more mathematical modeling in your classroom.

Joanie and Curtis start by acknowledging that the term “modeling” conjures up many ideas for educators and for students, and define their non-negotiable characteristics of mathematical modeling. They suggest the differentiators include that students must have the opportunity to apply the math they know to modeling tasks, and that these tasks are grounded in authentic contexts where the mathematics has real meaning and a real outcome, rather than being a typical math word problem.

Math educators are constantly managing the constraints of time and an excess of content to be taught, so our hosts share their ideas for finding the time to do modeling tasks and ensuring the time is spent well. They remind the listener that mathematical modeling isn’t an experience to tackle frequently, but to invest in these activities when they align with high-leverage math content and ensure deeper levels of engagement and understanding for students. The investment can pay off down the road for educators and students who take the time when it is most beneficial.

Finally, listeners are encouraged to consider when during instruction to bring modeling tasks in and the affordances of using these for formative assessment. Joanie and Curtis suggest that managing cognitive complexity alongside the mathematical demands of a modeling tasks can support effective implementation and the most positive experiences for students. Start small and set yourself up for success!

Be sure to check out these resources to support your mathematical modeling efforts:

• Texas Instruments’ mathematical modeling activities: https://education.ti.com/en/timathnspired/us/mathematical-modeling
• Cognitive complexity in mathematics: https://achievethecore.org/aligned/reaching-new-heights/ 

Share your feedback, comments, and suggestions for future episode topics by emailing [email protected] . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.