In this episode of Room to Grow, Joanie and Curtis host special guest Dr. Katey Arrington to discuss the importance of teacher content knowledge. Dr. Arrington is the Associate Director of the UTeach Institute at the University of Texas at Austin. She is also serving in the Presidential line for NCSM: Leadership in Mathematics Education from 2022-2026. Previously, she led the K-12 system services work at the Charles A. Dana Center, served as a mathematics coordinator for a growing, diverse district in Texas, instructional coach, and taught in both K-12 and community college systems. Katey earned a Ph.D. in Educational Policy and Planning, Master of Arts in Mathematics Education, and Bachelor of Science in Mathematics. She has extensive experience in leading networks for growing impact and designing and implementing system-level change for increasing equitable outcomes. Early on in the conversation, it is agreed that caring about students in a non-negotiable and important component of effective teaching, but caring without math content knowledge is not likely to result in student learning. Our hosts and their guest explore the ideas of pedagogical content knowledge, math content for teaching, and approaching mathematics as ways of thinking, not just ways of getting answers. Expanding learning is presented as a group endeavor, but also something a teacher can pursue on one’s own. We encourage you to explore the resources below, referenced in this episode:The Developing Mathematical Ideas (DMI) professional learning programNumberphile on You Tube is one of Curtis’ favorite sources to explore mathematical curiosityThe Coherence Map from Student Achievement Partners on the Achieve the Core website provides a clickable visual map of how content standards connect and build on one anotherDid 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis talk about an important role of math education: preparing students for the life they want to pursue after high school. Whether it’s college, trade school, the military, or directly into the work force, a student’s goals and desires should drive their learning experiences throughout their PK-12 years, and the course offerings, counseling and advising, and school system overall should, ideally, prepare all students for the outcomes they desire.They recognize early in the conversation that this isn’t just about high school, isn’t just about courses, and isn’t just about math. They dive into ideas around career choices, advocating for students’ best interests, and the challenges in creating a system with the depth, breadth, and flexibility required to truly prepare all students. There aren’t easy answers to these questions, but we hope the conversation sparks thinking, discussion, and actions in your setting that support more students to be better prepared for their chosen futures.We encourage you to explore the resources below, referenced in this episode:American Progress Math Pathways: The Way Forward report: https://www.americanprogress.org/article/math-pathways/ NCTM’s former President Robert Berry’s blog post on Mathematics Pathways from December, 2019:  https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Robert-Q_-Berry-III/Lets-Talk-About-Mathematics-Pathways/ EdWeek article challenging calculus as the “peak of high school math” https://www.edweek.org/teaching-learning/calculus-is-the-peak-of-high-school-math-maybe-its-time-to-change-that/2018/05 Just Equations report on calculus and college admissions: https://justequations.org/resource/a-new-calculus-for-college-admissions-how-policy-practice-and-perceptions-of-high-school-math-education-limit-equitable-access-to-college 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis explore ideas around the emotional side of learning and how it impacts students in their academic growth. Because we and our students are humans - and humans have emotions - it is impossible to learn without a connection to our emotions, whether those emotions are positive or negative. As educators reflect over the summer and begin to plan for the upcoming school year, we hope you’ll consider the emotional side of your students’ experiences in math class.Joanie and Curtis suggest planning for the emotional experiences alongside planning for content. As a teacher, how might you consider the ways students will feel in sharing their early thinking, perceiving their responses or others as “incorrect,” or being influenced by previous traumatic experiences with math? With some thoughtful planning and attention, these emotional experiences can be managed and leveraged to support learning for all student in the classroom, including those who are traditionally successful and may have positive feelings about math. We hope the content in this episode will help you consider ideas you may not have thought about before, and spark discussion with your educator friends.We encourage you to explore the resources below, referenced in this episode:Special issue of Mathematics Teacher: Learning and Teaching PK-12 on Social and Emotional Learning and Mathematics Learning from November, 2022 (membership required).Access, Power, Identity, and Healing in Mathematics by Sara Gartland, Shellee Wong, and Laurie Silverstein (membership required).Our previous conversation on Room to Grow with Juliana Tapper in August, 2022. Rough Draft Math by Amanda JansenJo Boaler article on connection between timed tests and math anxietyDid 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis talk about teaching strategies for remembering in mathematics, such as mnemonic devices, tricks, and gimmicks. They challenge the notion that teaching with tricks is inherently bad, and discuss how to determine when a strategy intended to help students learn might actually work against their understanding of the underlying mathematics. For instance, “FOIL” and “SOH-CAH-TOA” are both frequently taught in high school math classes, yet one is a way to remember mathematical definitions (not a trick!) and the other is a random association for a limited procedure (a trick!). So what about if a student creates their own strategy or trick while learning math?  Join our hosts in trying to make sense of how and when remembering strategies are helpful and when they might be more harmful.We encourage you to explore the resources below, referenced in this episode:Nix the Tricks – available to download for freeThirteen Rules that Expire is an article from Teaching Children Mathematics (NCTM membership required) about commonly taught ideas in elementary school that don’t support long-term learning. This blog about the article does not require NCTM membership.Twelve Math Rules that Expire in the Middle Grades is a similar publication from Mathematics Teaching in the Middle School (NCTM membership required) with middle school-specific ideas.This EdWeek article includes a commentary from Dr. Hilary Kreisberg about “nixing tricks.”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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis share a friendly debate about which math topic is the most important for students to learn. There are many math topics that could be argued as the most important, and we’d love to hear your hot take, too! Take a listen to Curtis explaining why the meaning of the equals sign is crucial and Joanie arguing that proportional relationships are especially important. Then reach out to agree with one of them, or share a different topic that you find most important.We encourage you to explore the resources below, referenced in this episode:Resources related to the meaning of the equals sign:Texas Instruments Building Concepts activities around the equals sign and the meaning of equationsMarilyn Burns’ take on The Equals Sign: What it Really MeansIf you are a research-y type, you might enjoy this research article Understanding the Equals Sign as a Gateway to Algebraic Thinking or this thesis paper Making Sense of the Equal Sign in Middle School MathematicsGeorge Strait song All My Exes Live in Texas 😊Resources related to proportional relationships:The progressions document on Ratios and Proportional Relationships from the University of Arizona supporting how proportional relationships develop in middle school standardsThe Coherence Map from Achieve the Core showing how the concept of proportional relationships is connected to many other important math conceptsA blog post titled  Proportionality Confusion which explains how common  methods for teaching about proportion often loses the big idea of proportional relationships 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis talk with Rachel Lambert, known for her research on teaching mathematics to students with disabilities. Rachel’s passion and enthusiasm is matched by her knowledge, and the combination makes for a powerful conversation full of great resources, ideas, and suggestions for classroom teachers. If you haven’t heard Rachel speak before, you are in for a treat!We encourage you to explore the resources below, referenced in this episode:Rachel’s website where she provides free access to her research: https://mathematizing4all.com/ Jay T. Domage’s book on Universal Design for Learning (UDL), Academic Ableism. Choose the “Open Access” or “Audio Download” versions which are free.General information about Universal Design for Learning HERE and HEREEdmund Harriss’ website and a really cool mathematical adult coloring book he co-created Learn more about neurodiversity and what it means for teachers and schools HERE and HEREDid 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis discuss and asset-based approach to teaching and learning mathematics. They emphasize that all students bring strengths to learning mathematics, whether it be from a cultural, language, or ways of thinking lens, and that by assuming that all students have and bring strengths, math educators invite even more learners to be successful. As usual, our hosts share their personal experiences, anecdotes and ideas that they hope you’ll relate to.We encourage you to explore the resources below, referenced in this episode:Classroom practices that compliment and asset-based approach to teaching and learning math https://www.ifl-news.pitt.edu/2021/09/three-practices-that-compliment-an-asset-based-approach-to-teaching-and-learning-in-math-classrooms/ Edutopia article on setting a high bar for all students https://www.edutopia.org/article/using-asset-based-approach-instruction-and-assessment/Research from the Journal for Research in Mathematics Education about asset-based mathematics instruction https://www.jstor.org/stable/10.5951/jresematheduc.49.4.0373 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis share a powerful conversation with Dr. Julia Aguirre, co-author of the book The Impact of Identity on K-8 Mathematics: Rethinking Equity-Based Practices. This publication, and additional work led by Julia at the University of Washington, Tacoma, has influenced countless math educators across the country who want to ensure that all students have the opportunities, support, and classroom experiences that lead to deep learning of meaningful mathematics. She challenges us all to not only bring our personal experiences and passions as teachers to our students, but to also tap into their experiences, passions, cultures, and communities as opportunities to make sense of and engage with mathematics. We think this episode will get you thinking and will give you some ideas about supporting your students’ math identities.We encourage you to explore the resources below, referenced in this episode:You can learn more about Julia and her work here: https://sites.google.com/a/uw.edu/dr-julia-aguirre/home?pli=1You can purchase Julia’s book here: https://www.nctm.org/store/Products/The-Impact-of-Identity-in-K-8-Mathematics--Rethinking--Equity-Based-Practices/You can find the TODOS paper Julia mentions here: https://www.todos-math.org/assets/images/The%20Movement%20to%20Prioritize%20Antiracist%20Mathematics%20final%203.0_v6.pdfDid 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis take some time to have fun with math. We share some of the puns, memes, and GIFs about math that make us laugh, make us think, and have been or would be great to share with students.We all appreciate the chance to laugh, and although puns and memes are often silly and sometimes groan-worthy, sharing the lighter side of ourselves and of math with students is a great way to build relationships and classroom culture. No doubt, your students will appreciate knowing what makes you laugh or groan when it comes to math. Bear with us as we describe our favorites, and click below to find the visual images we discuss in this episode. Share YOUR favorites with us using our email address, roomtogrowmath@gmail.com. We encourage you to explore the resources below, referenced in this episode:A snow “angle” Tweet by STEM SparkJoanie’s Algebra 1 textbook with punny word problems (it does still exist!) “Dad jokes” for mathGraph of past relationshipsWhat does Bob have now?Seven-digit numberFactored quadratic expression Tweet by David GlasbergVisualizing the quadratic formula by Lane Walker on myNCTM (NCTM membership required)Schoolhouse Rock! The PreambleQuadratic formula songClock with math expressionsWilly Wonka memeDid 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 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=enDid 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Curtis and Joanie dig into a conversation about data science. They start by trying to define what data science is, describing it as the intersection of content, statistics, computer science, problem solving. It is complex, and allows people to interact with information that content, statistics, or computer science couldn’t do alone. In our current technology and data rich world, this topic is timely, relevant, and growing in importance.Curtis and Joanie describe data science as a process by which we start with a question we want to know the answer to, then gather, interpret, analyze, and model data that can help answer the question. Although we acknowledge that data science in school looks different than data science in the world, we recognize it as a valuable way to foster students’ natural curiosity and to build their modeling, problem solving, and communication skills.Our hosts recognize and discuss that not everyone believes that data science is relevant content for K-12 students and educators, and offer the complicating factors that come alongside bringing new ideas such as these to the curriculum. We encourage you to explore the resources to decide for yourself! Blog series in support of data science https://justequations.org/blogArticle expressing critique against using data science in place of calculus-centered courses Jo Boaler and youcubed data sicence big ideas for K-8 https://www.youcubed.org/data-big-ideas/UCLA data science course https://www.introdatascience.org/ Berkeley data science course: http://data8.org/Cal State free Course for teachers Course Kata: https://coursekata.org/Jo Boaler and youcubed data sicence big ideas for K-8 https://www.youcubed.org/data-big-ideas/Data talks for students in younger grades https://www.youcubed.org/resource/data-talks/ New York Times’ What’s going on with this graph? https://www.nytimes.com/column/whats-going-on-in-this-graph Data Science 4 Everyone: https://www.datascience4everyone.org/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 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 resourcesProductive Math Struggle, Kevin’s book co-authored with available for purchaseThe 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 roomtogrowmath@gmail.com. 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 Juliana Tapper, Math Intervention Specialist and Founder of CollaboratEd Consulting. We start by apologizing for mispronouncing Juliana’s last name when she is introduced at the start of the podcast! Please note that her last name is Tapper, rather than Trapper. We are so sorry, Juliana! Juliana brings her experience teaching and supporting middle and high school math teachers and math interventionists to help us consider ways to break what she calls the “struggle stigma” in math class. She grounds our conversation with powerful results from research around math anxiety, which suggest that math anxiety activates the same fear centers in the brain as seeing a snake! When teachers use this understanding, we can create more effective responses to students who are experiencing math anxiety in our classes.Along with Juliana, your hosts discuss the importance of establishing a classroom culture that makes space all the “mathematical baggage” that students might bring with them. Providing the opportunity to talk about past experiences, positive and negative, allows students to understand that our classroom is a safe and welcoming place, where struggle becomes a normal and expected part of the learning process. Juliana has some practical tips for using instructional protocols with no math to build that classroom culture. She also shares how she established participation as an expectation rather than an option, and how those expectations along with appropriate scaffolds create small successes for students to build on.We know you’ll walk away with some great ideas that will help you better reach more students in your classroom.We encourage you to explore these resources, mentioned and referenced in this episode:Juliana’s website with resources and much more information about supporting students in math www.Collaboratedconsulting.org, or email Juliana directly at juliana@collaboratedconsulting.org.The youcubed® article Valuing Difference and Growth Juliana refers to the findings in this paper about how math anxiety lights up the same centers of the brain as physical fear such as seeing a snake.Juliana mentioned this The Dismantling Racism in Mathematics Instruction Course from Student Achievement Partners; the third course of the series will be available in the fall and you can take it without having taken the first two.Juliana suggested this Good Groupwork activity for helping to build a classroom culture that supports all students’ learning from youcubed.®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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Curtis and Joanie tackle ideas around rigor in mathematics. We start by defining what we mean by rigor, acknowledging that it’s a frequently used term that invokes different ideas and meanings! We believe that it means something different than just “difficult,” but frames a way of describing deep, robust, and applicable understanding of mathematical ideas, and we share a couple of visual images that help make sense of this complexity. Through our exploration of rigor as an integral part of learning math, we connect it to previous conversations about productive struggle, making connections in math, and student agency and identity. Rigor isn’t just for high level math courses and high-achieving students, rigor is for everyone and may even be an unexpected approach to overcoming struggle in learning mathematics!We believe that the best way to address rigor in the classroom is by intentional, collaborative planning, where teachers decide which obstacles they want to steer students around and which obstacles they want to steer students straight into! We hope you enjoy the episode and hear a new idea or two to consider for your own setting.We encourage you to explore these resources, mentioned and referenced in this episode:Definition of “rigor” from Achieve the Core: College- and Career-Ready Shifts in MathematicsThis report from the Dana Center at the University of Texas, Austin: What is Rigor in Mathematics Really?This archived (free) blog post from former NCTM President Linda Gojak: What’s All This Talk About Rigor? myNCTM discussion about rigor (membership required): Archived HERE 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 Twitter and Instagram: @JoanieFun and @cbmathguy. 

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 ActElementary and Middle School Mathematics: Teaching Developmentally by John van de WallePresentation of From Student-Invented Strategies to Standard Algorithms: What’s the Rush by Fran HuntoonDiscussion 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 roomtogrowmath@gmail.com. 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=jprEdutopia 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 roomtogrowmath@gmail.com. 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-stengerArticle 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-feedbackArticle/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.pdfShare your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode, we discuss grades in mathematics courses. Although we don’t claim to have a recommendation or even an opinion about what might be the right way to handle grades, we hope to bring up considerations for our listeners to talk about and think through as they reflect on their own grading practices.We wonder if many grading practices are in place are just legacy practices, handed down and sustained by teacher teams and departments, or schools with prescribed grading requirements, and we recognize the challenges of balancing grades with academic performance as well as other classroom contributions that we value.We wrestle with what grades communicate to different audiences. What does a grade tell a student? The student’s family? Other school personnel? The student’s next school? How does a student’s participation in the academic work of math class shift based on the value they put on their grade in math class? And we consider the guiding question of “what is the impact of…?” as educators consider the structure and components of their grading practice.We wrap up by reflecting on the impact of COVID-19 on our educator friends. We believe that the last two years have brought incredible challenges to educators already giving everything they have to their students and communities. We are in awe of you, we admire you, and we thank you for all that you do each and every day. Additional resources to explore:Blog Post: “Grading Is Due for an Overhaul” https://www.nais.org/magazine/independent-school/winter-2022/grading-is-due-for-an-overhaul/ Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy

In this episode, we build on our previous conversation about fostering curiosity in our students by focusing on the role of math teachers in encouraging students to be curious and creative in math class. With full awareness that we are teaching and influencing students who will leave our classrooms and schools to go contribute to the world, and that we are preparing our students for jobs that don't exist now, we acknowledge how important it is to attend to a culture of curiosity and creativity in math classrooms. We talk about the importance of fostering intrinsic motivation so that a passion for learning follows them into their lives beyond school.We wrestle with the challenge of wanting to provide structure and efficiencies in ways that can sometimes unknowingly stifle students' creative freedoms. We acknowledge that in our desire to make learning meaningful and impactful, we can inadvertently provide too much structure or control, stealing students' "lightbulb" moments in their learning journey. We know that no teacher creates classroom practices that detract from learning, and that there are appropriate times and situations where more structure and more directed learning is the best way for students to learn. But we also challenge that a teacher should always be the sole source of knowledge and learning in the classroom. We also recognize that teachers' tendency to control the classroom is based in a feeling of responsibility for students' learning. We suggest that fostering creativity and curiosity allows students to take more responsibility for their own learning, which can be freeing for us as educators.We wrap up by sharing some practical ideas for fostering curiosity and creativity. We know that this will look different in every classroom and would love for you, our listener, to share how you do this in your setting! Additional resources to explore:·       Ken Robinson’s Ted Talk Do Schools Kills Creativity? https://www.ted.com/talks/sir_ken_robinson_do_schools_kill_creativity?language=en·       Daniel Pink’s Drive – Book: https://www.amazon.com/Drive-Surprising-Truth-About-Motivates/dp/1594484805; RSA Animation summary: https://www.youtube.com/watch?v=u6XAPnuFjJc·       Peter Liljedahl’s Building a Thinking Classroom in Mathematics – https://us.corwin.com/en-us/nam/building-thinking-classrooms-in-mathematics-grades-k-12/book268862 ·       Creativity by asking questions: https://www.creativityatwork.com/teaching-for-creativity-asking-questions/ (100 questions activity)·       Ways to develop creativity in our students: https://www.edutopia.org/article/4-ways-develop-creativity-students·       NCTM article - Graphing Portfolios in Calculus: Reinforcing Concepts and Inviting Creativity: https://pubs.nctm.org/view/journals/mt/98/6/article-p404.xml?tab_body=pdf (Members only access)Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In the first episode of Season 2, Curtis and Joanie discuss one of Curtis' favorite ideas - fostering curiosity and exploration in the math classroom. It's a common idea that math teachers can support students in "exploring the world through math," but in this episode we think about turning that phrase on its head and wondering how we can "explore mathematics through the world?" With this goal in mind, educators could provide experiences where they are asking the questions that drive their learning. Creating these experiences for students requires intentional teacher planning, and doesn't mean that we allow the learning to be a free-for-all! Teachers will need to find balance between providing the structure required to keep the learning focused, while allowing students the freedom to explore, question, and engage in the learning. And since math classrooms are already packed with content, we discuss how to find the time to include curiosity as part of the learning experience.  We hope these ideas help you to pass along a legacy of curiosity to your students!Resources to explore:To help identify the big mathematical ideas for your course or grade level, check out the Focus By Grade Level documents from Achieve the Core: https://achievethecore.org/category/774/mathematics-focus-by-grade-levelFor more practical steps on developing student curiosity in your math classroom, check out this blog post from David Wees: https://davidwees.com/content/how-do-you-help-develop-mathematical-curiosity/Read about the brain research that supports the importance of curiosity in education: https://www.edutopia.org/blog/why-curiosity-enhances-learning-marianne-stengerShare your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode, Joanie and Curtis consider the balance between conceptual understanding and procedural fluency in mathematics teaching and learning. Acknowledging that this idea is like a pendulum that has swung back and forth over several decades, they unpack the meanings of these terms and discuss the impact and implications on student learning.They use the 2001 publication Adding It Up to describe how conceptual understanding and procedural fluency come together with three other ideas to form an understanding of mathematics proficiency, and share examples of what happens when students have one type of learning without the other. You’ll hear our hosts wrestling with differing perspectives to better understand how educators can support students’ conceptual understanding and their procedural fluency together in ways that support deep learning and readiness for future math experiences. Listeners are encouraged to consider these additional resources mentioned in the episode:The book Adding It Up can be found here: https://www.amazon.com/Adding-Up-Helping-Children-Mathematics/dp/0309069955/ref=asc_df_0309069955/?tag=hyprod-20&linkCode=df0&hvadid=312695266310&hvpos=&hvnetw=g&hvrand=6263244698394065341&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9026941&hvtargid=pla-384970287053&psc=1 A PDF overview of Adding It Up  that includes the five strands of mathematics proficiency: https://www.nctm.org/Handlers/AttachmentHandler.ashx?attachmentID=GcfUPPya8lw%3DGrant Wiggins’ blog post on conceptual understanding: https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-in-mathematics/ Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode, Joanie and Curtis continue their conversation with Robert Ahdoot, founder of Yay! Math. We continue the conversation from Episode 9, digging into how teachers can address students’ math anxiety. We discuss the idea that teaching could be considered a service profession, and how that perspective can support teachers in building trust with their students. Robert shares a powerful story of a discipline issue in his classroom, and how approaching the situation with the humanness we share with students supported a positive outcome. Although Robert’s creative, outgoing, and exuberant personality are part of who he is as a teacher, he reminds us that any personality type can be a profoundly impactful educator by working to connect with and understand students. After all, Robert suggests, students just want to know that we have their backs.Listeners are encouraged to consider these additional resources mentioned in the episode:Robert Ahdoot’s website, https://www.yaymath.org/  where you can find videos, courses, Robert’s blog and more to help inspire the students in your care;Robert’s Algebra 1 lesson on ratios and proportions for Texas Instruments’ “Smart Space” video series: https://www.youtube.com/watch?v=5itAHkH0YH4&list=PLQa_6aWmaC6AebhOVkKXC8Vags6D1TVaz ;Jo Boaler’s research article on timed tests: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/03/nctm-timed-tests.pdf More about our guest, Robert Ahdoot: Robert Ahdoot is a math teacher and founder of YayMath.org, a free online collection of math video lessons filmed live in his classroom, in the studio, and even as street performance art, using iconic costumes and characters. Robert has given TEDx talks and travels to schools and conferences promoting his message of achieving positive learning through meaningful human connections. He is the author of One-on-One 101: The Art of Inspired and Effective Individualized Instruction, and the creator of online Algebra and Geometry math courses.Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

Joanie and Curtis host their first guest on this episode of Room to Grow. Robert Ahdoot taught high school math and found his strength in connecting with and engaging students, leveraging his enthusiasm and creativity to build strong relationships with students. He found that his humor, compassion, and excitement for mathematics content helped students overcome their anxiety about and struggles with learning math. Robert brings a contemplative and self-reflective spirit to our conversation, bringing in knowledge about the physiology of stress and the workings of our brains alongside his passion for human connection and relationships, making this a conversation unlike any other. We tackle issues that almost every math teacher has dealt with: supporting students who struggle, who are unengaged, and who experience math anxiety, causing them to underperform. Robert gives practical and actionable tips, and reminds us to not take ourselves too seriously along the way. You’ll leave wanting more, and you’ll get it! This episode is the first of two conversations with Robert. You won’t want to miss a minute of this conversation!Listeners are encouraged to consider these additional resources mentioned in the episode:Robert Ahdoot’s website, https://www.yaymath.org/  where you can find videos, courses, Robert’s blog and more to help inspire the students in your care;Robert’s Algebra 1 lesson on ratios and proportions for Texas Instruments’ “Smart Space” video series: https://www.youtube.com/watch?v=5itAHkH0YH4&list=PLQa_6aWmaC6AebhOVkKXC8Vags6D1TVaz ;YouCubed video on the importance of struggle: https://www.youcubed.org/resources/the-importance-of-struggle/ One of Robert’s favorite riddles: You have 9 marbles. One is slightly heavier than each of the other 8. Using a balance scale only twice, how can you determine which is the heavier marble? The answer is elegant and without "out of the box" thinking, which is generally welcomed of course, but no need here. No weighing marbles with your hands, dropping them, using water somehow, etc. You can determine which is the heavier marble using the balance scale twice.More about our guest, Robert Ahdoot: Robert Ahdoot is a math teacher and founder of YayMath.org, a free online collection of math video lessons filmed live in his classroom, in the studio, and even as street performance art, using iconic costumes and characters. Robert has given TEDx talks and travels to schools and conferences promoting his message of achieving positive learning through meaningful human connections. He is the author of One-on-One 101: The Art of Inspired and Effective Individualized Instruction, and the creator of online Algebra and Geometry math courses.Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

In this episode of Room to Grow, Joanie and Curtis discuss the challenge of pandemic “learning loss” and provide ideas for math teachers to reframe this concept. They speak about the potential negative impacts of deficit language as students return to classrooms across the country, and emphasize the importance of creating a positive classroom culture for learning, grounded in beliefs that all students can and will be successful. Acknowledging that educators are facing significant pandemic-related challenges, our hosts also talk about the power of collaboration and how it is even more important for the success of teachers and students in the 2021-22 school year.Listeners are encouraged to consider these additional resources for managing learning in the new school year:Continuing the Journey: Mathematics Learning 2021 and Beyond – joint publication from the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM) and the Association for State Supervisors of Mathematics (ASSM).Learning Acceleration for All: Planning for the Next Three to Five Years – TNTP’s resource for educators responding to Covid-19’s impact on learningThese blog posts on The False Construct of Readiness in Mathematics and A Process to Address Unfinished Learning in Middle School Math (which has ideas applicable to all grade levels). Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

The article referred to in the podcast for building back better can be found here: https://www.forbes.com/sites/lindadarlinghammond/2021/04/05/accelerating-learning-as-we-build-back-better/?sh=33b314156722&fbclid=IwAR2QaW5oCyel5PxBECCziT9c6bKr3osAUSTj81ZP5gdi09cyvIJQN8JmT7U Restart and Reinvent report: https://restart-reinvent.learningpolicyinstitute.org/Effortful Thinking: https://www.edsurge.com/news/2021-06-28-better-questions-in-the-classroom-lead-students-to-think-harder-and-learn-deeperShare your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

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/1951600800Joanie 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 roomtogrowmath@gmail.com. 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 roomtogrowmath@gmail.com. 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=1631Learn 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 roomtogrowmath@gmail.com. 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-geometryShare your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. 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 roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.