Room to Grow - a Math Podcast

In this episode of Room to Grow, Curtis and Joanie consider assumptions that we make during math instruction and how these have the potential to interfere with students’ understanding of the mathematics. Teachers know more math than their students, and as a teacher, it can sometimes be a challenge to remember what it was like before we knew and understood a math concept. This can lead us to inadvertently assuming that students are following our thinking or considering external knowledge that they actually might not yet have access to!

Our hosts get into some math content, specifically talking about the equals sign, solving systems of equations, and the standard algorithm for multiplication. In each of these examples, the common structures of instruction can lead students to an incorrect or incomplete understanding, or can force a focus on procedures without the concepts that back up these ways to doing. Curtis and Joanie had some personal “ah ha” moments during the episode as we discussed these math topics.

Frequent listeners know that Joanie and Curtis don’t claim to have silver bullet solutions, but they suggest that slowing down when planning and teaching, regularly collaborating with other teachers, and stopping to identify assumptions can all contribute to better teaching and learning. Listen to hear more about why Joanie recommends teaching “for big circles, and not pinpricks.”

We encourage you to explore these resources, mentioned and referenced in this episode:

• Teaching Children Mathematics article (subscription required) The Equals Sign: A Balancing Act
• Elementary and Middle School Mathematics: Teaching Developmentally by John van de Walle
• Presentation of From Student-Invented Strategies to Standard Algorithms: What’s the Rush by Fran Huntoon
• Discussion about teaching algorithms on myNCTM (membership required)

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 Twitter and Instagram: @JoanieFun and @cbmathguy.

As we approach the end of the school year, this episode of Room to Grow addresses using self-reflection to celebrate the learning of the year. Our hosts use this definition: “Self-Reflection is the evaluation or judgement of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes (Damore, 2017),” and start with unpacking this quote from John Dewey: “We don’t learn from experiences, we learn from reflecting on our experiences.”
In the conversation, Curtis and Joanie suggest that reflecting at the end of a lesson, unit, month or school year provides the opportunity to be energized by and to benefit from what we’ve experienced and how we use that learning to continue to improve.

After making the case for self-reflection, the discussion shifts to specific ideas for student and teacher self-reflection. Ensuring that students understand the purpose of self-reflection is integral to making the process meaningful for students, and increases the likelihood that their reflective practices will contribute positively to owning their own learning, and to building positive mathematical identities. Some specific reflection questions and protocols are discussed, giving you ideas you can apply in your own setting as we all wrap up the 2021-22 school year.

We encourage you to explore these resources, mentioned and referenced in this episode:

• Dewey quote and Damore’s definition of Self-Reflection came from this post: Routines for Self-Reflection: https://thinkingpathwayz.weebly.com/routinesselfreflection.html
• Journal of Practitioner Research article on reflection as a tool for continuous improvement: https://digitalcommons.usf.edu/cgi/viewcontent.cgi?article=1044&context=jpr
• Edutopia article with specific ideas for engaging students in self-reflection: www.edutopia.org/article/frameworks-reflection
• Tuning protocol as a way for groups of teachers to reflect specifically on student work: http://essentialschools.org/horace-issues/the-tuning-protocol-a-process-for-reflection-on-teacher-and-student-work/
• Teachers and Change: The Role of Reflective Practice: https://www.sciencedirect.com/science/article/pii/S1877042812039870

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 welcome Kevin Dykema, new President of the National Council of Teachers of Mathematics (NCTM). As a practicing classroom teacher, Kevin brings practical knowledge to his NCTM leadership. He reflects on they ways that most school systems have historically addressed students who are struggling in math class, to give them more-of-the-same, or a slower-and-louder approach, and how these typically don’t result in resolving students’ struggles.

Kevin suggests how to decide which mathematics topics are worth intervening on, recognizing that if we worry about student mastery of every single standard or topic of the grade level or course, we overwhelm the students and ourselves. Instead, if we focus on fewer, more important topics, we can support students’ future learning. He suggests that we use timely and relevant data to determine which students need support on which topics, and anticipating and planning for supports that come just-in-time to support new learning.

Acknowledging that intervention structure looks different at the middle and high school level than for elementary school, Kevin shares his thoughts about intentionally targeting math interventions that will support students for the long term, and finding time to intervene that doesn’t take away from their regular math instruction time. He shares the problems behind teaching “tricks” or gimmicks for helping students get answers quickly, but not understand the meaning of the mathematics behind those tricks.

Ultimately, building relationships with our students and attending to building their mathematical identities and agencies is what matters most. We know that every student brings “math brilliance” to the classroom, and finding and tapping into that creates wins for all of us.

This episode is packed full of important ideas and resources – we think you are going to love it!

We encourage you to explore these resources, mentioned and referenced in this episode:

• Rules that Expire blog and link to full article from NCTM journal (membership required)
• Nix the Tricks by Tina Cardone, free online book and resources
• Productive Math Struggle, Kevin’s book co-authored with available for purchase
• The Math Pact series of books by Barbara J. Dougherty, Sarah B. Bush, and Karen S. Karp, available for purchase

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 Twitter and Instagram: @JoanieFun and @cbmathguy.

In this episode, we discuss considerations for providing meaningful feedback to our students. We think this is a great follow-up to our last episode on grading! In preparing for our discussion, we learned about the research supporting effective feedback for learning, which includes suggestions around the type of feedback to give, when to give it, and how meaningful feedback is separate from grading.

Our research articles suggest that feedback is not advice or criticism, but information that helps the receive to understand their next actions. Although it makes sense that students must engage with feedback in order for it to be meaningful, we were intrigued by the suggestion that the receiver of feedback should work harder as a result of the feedback than the giver of the feedback! In other words, our students should work harder than us, their teachers!

We explore some concrete ideas for making your feedback more meaningful, reflect on our own mistakes around providing feedback, and emphasize the fact that in all aspects of a teachers work, relationships matter most.

We encourage you to explore these resources, mentioned and referenced in this episode:

• Blog post from Edutopia. The five suggestions here are backed by research. https://www.edutopia.org/blog/tips-providing-students-meaningful-feedback-marianne-stenger
• Article from the South Carolina Center for Teaching Excellence. This resource is general for all content areas, is a quick read, and includes a list of specific ideas for effective and efficient feedback. https://sc.edu/about/offices_and_divisions/cte/teaching_resources/grading_assessment_toolbox/providing_meaningful_student_feedback/index.php
• Article from ASCD (free if you haven’t already accessed your limit of free articles). Grant Wiggins authors this article that Curtis and Joanie refer to multiple times during this episode. https://www.ascd.org/el/articles/seven-keys-to-effective-feedback
• Article/research summary from the Tang Institute. Although this resource appears longer than the others, the summaries and graphics make it very readable. This would be a great resource for a PLC or professional learning setting. https://tanginstitute.andover.edu/files/Feedback-in-Practice.pdf

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, Joanie and Curtis build the conversation from NCTM's description of access, described as "ensuring that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful."

Our hosts tackle this challenging topic by considering some important high-leverage components, particularly those that are within a classroom teachers’ locus of control. Ensuring that all students have high-quality instruction from an excellent teacher supports the learning of challenging mathematics content. Joanie and Curtis consider that “support for success” extends beyond academic support, and spills over into the importance of classroom culture in access for all students. Teachers can, with intention, ensure that all students know they are viewed as doers of mathematics with ideas that are valuable for the learning of the entire class.

The conversation then shifts to discussing how the Standards for Mathematical Practice can help teachers not only understand what access looks like, but also helps students realize the relevance of the mathematics they are learning. Unsurprisingly, our hosts circle back to the importance of relationships with our students for their successful learning.

We encourage you to explore the resources below, referenced in this episode:

• NCTM’s Statement on Access and Equity in Mathematics Education https://www.nctm.org/Standards-and-Positions/Position-Statements/Access-and-Equity-in-Mathematics-Education/
• Supporting students’ identity and agency in mathematics https://www.nctm.org/Store/Products/The-Impact-of-Identity-in-K-8-Mathematics--Rethinking--Equity-Based-Practices/
• Blog about Minimizing the “Matthew Effect” https://buildingmathematicians.wordpress.com/2018/01/15/minimizing-the-matthew-effect/
• Skew the Script AP Statistics resources for relevant mathematics https://skewthescript.org/
• Implementing the Standards for Mathematical Practice https://achievethecore.org/peersandpedagogy/wp-content/uploads/2016/06/Implementing-Standards-for-Mathematical-Practices-Updated-2016.pdf
• Instagrammer with Bachelor and Bachelorette data: https://www.instagram.com/bachelordata/?hl=en

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 Twitter and Instagram: @JoanieFun and @cbmathguy.