Mathematics Teacher Educator Podcast

Episode 57: Dilemmas and Design Principles in Planning for Justice-Oriented Community-Based Mathematical Modeling Lessons Oct 24, 2023

This article details the development of design principles to support teachers in planning for a Community-Based Mathematical Modeling task with a focus on social justice in the elementary grades. By reflecting on the dilemmas we encountered in the design and enactment of the tasks, we developed five design principles that allowed us to address issues of social justice as well as attend to powerful mathematical ideas to bring awareness and take action around a local problem. Through our article, we hope to share with mathematics teacher educators
design principles to help plan for tasks with pre- and in-service teachers that prioritize connecting mathematics to social issues and empower both teachers and students to take action to make a positive impact in the community.

Special Guests: Holly Nicole Tate and Jennifer Suh.

Episode 56: Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education Oct 11, 2023

The authors began this work with the understandings that (a) there is no “neutral” when it comes to the teaching of mathematics, and (b) mathematics teacher educators need to do something to help produce teachers of mathematics that develop students’ relationships with mathematics and push against the inequities that exist both within and outside of the classrooms in which they will teach. In response, the authors created, deployed, and studied a learning module in an attempt to enact antiracist mathematics teacher education. The learning module activities, the findings about the learning from the prospective teachers who engaged in the module, and messages for mathematics teacher educators who want to engage in this work are shared.

Special Guests: Anne Marie Marshall, Joel Amidon, and Rebecca E. Smith.

Episode 54: “Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes Sep 12, 2023

This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates mixed-reality simulations of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated
overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.

Special Guests: Daniel Reinholz and Liza Bondurant.

Episode 55: When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation Sep 12, 2023

We introduce a teacher learning practice called EQUIP-ing, which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.

Special Guest: Sunghwan Byun.

Episode 53: Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework Aug 31, 2023

Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students’ opportunities to struggle, have been consistently linked to improving students’ mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of professional development (PD) offerings. We describe three examples of how the framework is used to support teacher learning and classroom instructional practice: a state-mandated course, lesson studies, and a large-scale teacher–researcher alliance. Initial findings suggest that consistently emphasizing this framework provides both content and structural guidance during PD development and gives coherence and focus to teachers’ PD experiences.

Special Guests: Gwyneth Hughes, Joe Champion, Lindsey Yundt, and Michele B. Carney.

Episode 48: Design Principles That Support Course Design Innovation for Elementary Mathematics Methods Courses Jun 01, 2023

Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist mathematics teacher educators in designing their courses to maximize their instructional time.

Special Guests: Brette Garner, Claudia Bertolone-Smith, Evthokia Stephanie Saclarides, Gladys Krause, and Jen Munson.

Episode 49: Filling a “Void”: The Mathematical Quality in Planning Protocol for Mathematics Teacher Educators Jun 01, 2023

This article explores one novice mathematics teacher educator’s initial use of the Mathematical Quality in Planning Protocol, an innovative tool that was developed to assist in providing feedback on the mathematical quality of novice mathematics teachers’ lesson plans. The protocol was devised to help mathematics teacher educators bridge the gap between prospective teachers’ mathematical content knowledge and their mathematical content knowledge for teaching. Results of our analysis on an initial use of the protocol point to its potential as a tool to help mathematics teacher educators direct their feedback from being overly focused on the pedagogical aspects of the lesson (e.g., timing, planned activities) to the mathematical content prospective teachers are attempting to teach (e.g., anticipated student solutions, problem-solving strategies).

Special Guest: Kevin Voogt.

Episode 51: Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board Jun 01, 2023

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/ revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

Special Guests: Margaret Rathouz and Nesrin Cengiz-Phillips.

Episode 52: Adaptations to Support the Flint Water Task Jun 01, 2023

This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 of MTE. The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical modeling while building awareness of social justice issues. This Perspectives on Practice article focuses on two adaptations of the task—gallery walks and What I Know, What I Wonder, What I Learned (KWL) charts—that we have found to enhance these learning opportunities. We found that the inclusion of a gallery walk supported our students in the development of their mathematical modeling skills by enhancing both the mathematical analyses of the models and the unpacking of assumptions. The KWL chart helps students document their increase in knowledge of the social justice issues surrounding the water crisis. Using the mathematical modeling cycle to explore social justice issues allows instructors to bring humanity into the mathematics classroom.

Special Guests: Dana L. Grosser-Clarkson and Joel Amidon.

Episode 47: Taking a Spatial Turn in Mathematics Teacher Education Jun 01, 2023

The spaces we inhabit and the physical communities in which we learn all affect how we come to experience the world, construct what mathematics is to us, and develop how we teach mathematics. In this theory-to-practice article, we discuss why explicitly considering spatial ways of knowing is important in mathematics teacher education. We begin by providing theoretical arguments for the importance of considering space in mathematics education. We then present a rationale for why considering space is so important in mathematics teacher education, specifically discussing links to the practice of teaching mathematics. Examples of how to consider tasks related to spatial justice are provided to help reimagine what an mathematics teacher education task can look like.

Special Guests: Lisa Poling and Travis Weiland.

Episode 46: Developing Equity Literacy and Critical Statistical Literacy in Secondary Mathematics Preservice Teachers May 22, 2023

There is a lack of teacher education materials that develop equity literacy in content courses for preservice secondary mathematics teachers. In response, we created teacher education curriculum materials for introductory statistics that include an integrated focus on developing equity literacy and critical statistical literacy. In this article, we provide an overview of our materials’ design along with a detailed look at one activity regarding racial demographics and tracking in high school STEM courses. We present evidence regarding the positive impact of these materials on the teacher candidates’ competency, value, and likelihood of applying their equity literacy and critical statistical literacy. Implications for mathematics teacher educators working to develop equity literacy together with content knowledge are discussed.

https://modules2dotcom.wordpress.com

Special Guests: Andrew Ross and Stephanie Casey.

Episode 50: Engaging Teachers in the Combination of Statistical Investigation and Social Justice: Fairness in School Funding May 15, 2023

This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 of MTE. We built on Aguirre et al.’s (2019) integration of mathematical modeling and social justice issues in mathematics teacher education to similarly integrate statistical investigations with social justice issues.

Link to resources: www.modules2.com

Special Guests: Liza Bondurant and Stephanie Casey.

Episode 44: Continuous Improvement Lesson Study: A Model of MTE Professional Development Oct 19, 2022

A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.

Special Guests: Dittika Gupta, Lara K. Dick, and Mollie Applegate.

Episode 45: From Argumentation to Truth-Telling: Critical Race Theory in Mathematics Teacher Education Oct 19, 2022

Critical Race Theory (CRT) has entered into public discourse at an accelerated rate. Instead of using CRT as a basis to produce a more racially conscious populace, the latest hysteria, unfortunately, has centered on ban- ning CRT. Governmental actions have been instituted to establish executive orders to forbid CRT training. Administrators and educators have been written up, sus- pended, and even terminated for teaching about race. The current landscape around CRT is about censoring race-related discussions and obstructing any advance- ments in service to racial equity and justice. In the edu- cational arena, more than 20 states have banned CRT from being taught in our nation’s public school class- rooms. A new report from the Institute for Democracy, Education, and Access found that 35% of all students in U.S. K–12 schools have been affected somehow by local anti-CRT efforts (Pollock & Rogers, 2022). CRT proper is not taught in K–12 schools, so these efforts clearly demonstrate that those who are championing them are ill-informed about where CRT is taught in the first place.

Special Guests: Cathery Yeh, Christopher Charlie Jett , and Maria Zavala.

Episode 43: Developing Preservice Teachers’ Understanding of Area Through a Units Intervention Oct 19, 2022

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

Special Guest: Megan Wickstrom.

Episode 41: Centering Professional Development Around the Instructional Quality Assessment Rubrics Oct 03, 2022

In this article we detail a research study using the Instructional Quality Assessment (IQA) Rubrics (Boston, 2012) as the frame for a professional development with mathematics teachers in grades 3-8. We wanted to create a professional development around a tool that was typically used in research as a way to observe teachers,
as a tool to use with teachers on their reflection of instruction. In this study we share both the researchers’ and teachers’ perspectives of affordances and constraints of the professional development and observational rubrics.

Special Guests: Amber Candella and Melissa Boston.

Episode 42: Language Demands Tool: Attuning Prospective Teachers’ Vision to the Role of Language in Mathematics Education Oct 03, 2022

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception
that mathematics is somehow language- free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics methods courses. The intervention was designed to attune prospective teachers’ noticing to the language modalities and supports in mathematics teaching and learning. The intervention began with an observation tool that prospective teachers completed in their field placement classrooms. This article classifies prospective teachers’ noticings and explicates how these noticing became a pedagogical catalyst for further learning and discussion in subsequent mathematics methods classes.

Special Guest: Amanda Sugimotto.

Episode 40: Conversation with MTE editors: Vision, Submission Advice, Etc. Mar 11, 2022

Special Guests: Kate Johnson and Michael Steele .

Episode 39: Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students Feb 08, 2022

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy”) on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

Special Guests: Corey Webel and Sheunghyun Yeo.

Episode 37: Supporting Preservice Teachers’ Growth in Eliciting and Using Evidence of Student Thinking: Show-Me Narrative Feb 08, 2022

Special Guests: Esther M. H. Billings and Swartz, Barbara.

Episode 38: Support and Enrichment Experiences in Mathematics (SEE Math): Using Case Studies to Improve Mathematics Teacher Education Feb 08, 2022

This article describes an innovation in an elementary mathematics education course called SEE Math (Support and Enrichment Experiences in Mathematics), which aims to support teacher candidates (TCs) as they learn to teach mathematics through problem solving while promoting equity during multiple experiences with a child. During this 8-week program, TCs craft and implement tasks that promote problem solving in the context of a case study of a child’s thinking while collecting and analyzing student data to support future instructional decisions. The program culminates in a mock parent– teacher conference. Data samples show how SEE Math offers TCs an opportunity to focus
on the nuances of children’s strengths rather than traditional measures of achievement
and skill.

Special Guests: Crystal Kalinec-Craig, Emily Bonner, and Traci Kelley.

Episode 36: Supporting Prospective Teachers in Problem Solving: Incorporating Mindset Messaging to Overcome Math Anxiety Feb 08, 2022

Prospective and practicing elementary teachers have historically demonstrated anxiety about mathematics, which can affect their mathematics teaching and their students’ math anxiety. Yet, developing productive dispositions prior to teacher preparation programs is rarely addressed in the research. We propose mindset messaging in mathematics courses as an intervention to influence prospective teachers’ (PSTs’) self-reported mathematical mindsets and math anxiety.

Survey results indicated shifts toward growth mindsets and decreases in math anxiety. Further analysis of PSTs’ written responses suggests that mindset messaging may support
PSTs in overcoming math anxiety, and that perseverance during problem solving is critical for PSTs’ mathematical improvement. Additionally, some PSTs connected course experiences to future mathematics teaching practices. Results propose MTEs might consider explicitly offering mindset messaging in mathematics courses.

Special Guests: Erica Slate Young and Sarah Roller Dyess.

Episode 35: If the World Were a Village: Learning Mathematics While Learning About the World Dec 15, 2021

Long-standing and ongoing calls exist for making mathematics meaningful, relevant,
and applicable outside the classroom. Major mathematics education organizations (National Council of Teachers of Mathematics [NCTM], National Council of Supervisors of Mathematics [NCSM], Association of Mathematics Teacher Educators [AMTE], TODOS: Mathematics for ALL) have called for mathematics to be seen as a tool for understanding and critiquing the world. To prepare students and teachers to do this, we must go beyond “everyday” contexts and include analysis of social justice issues into our courses. We share an activity designed to address these calls while also addressing the mathematics goals of the course. We share data showing that prospective teachers learned mathematics while also learning about their world and reframing their view of mathematics as a tool to make sense of the world.

Special Guest: Courtney Koestler.

Episode 34: Mathematics Teachers’ Understanding of Privilege and Oppression Dec 15, 2021

The Access, Allies, and Agency in Mathematical Systems project team designed
a professional development for mathematics teachers positioning equity at the systemic level and activities aimed at supporting mathematics teachers in considering the influence of privilege and oppression on mathematics teaching and learning (Scroggins, 2017). Here, we examine the levels of oppression activity, aimed at supporting mathematics teachers in understanding that oppression operates at multiple levels (i.e., as a system) and that these levels exist and operate in/on mathematics education. Such understanding can support mathematics teachers in disrupting inequities, and how mathematics teachers engage in this activity can support mathematics teacher educators in preparing teachers to do such work. Specifically, we explore the question: How does this activity support mathematics teachers’ understanding of levels of oppression?

Special Guests: Bartell, Tonya, Courtney Koestler, and Mary Q Foote.

Episode 32: Developing an Asset-Based View of Students’ Mathematical Competencies Through Learning Trajectory-Based Lesson Study Dec 15, 2021

This article details the design and implementation of a professional development model called Learning Trajectory-Based Lesson Study focused on issues of equity, identity, and agency. We developed the Vertical Articulation to Unpack the Learning Trajectory (VAULT) tool to orient teachers’ instructional planning toward an asset-based view of students’ mathematics competencies. We examined teachers’ use of the VAULT to plan, implement, and debrief on student strategies for one spatial reasoning task in elementary, middle, and high school classrooms. The VAULT facilitated intentional planning for a progression of anticipated strategies and equitable access to instruction. Teachers demonstrated an asset-based view of all student thinking independent of grade-level expectations.

Special Guests: Jennifer M. Suh and Sara Birkhead.

Episode 33: Exploring Power and Oppression: An Examination of Mathematics Teacher Educators’ Professional Growth Dec 15, 2021

The preparation of mathematics teacher educators (MTEs) varies widely, with little
guidance regarding the essential skills and knowledge necessary to tackle the field’s
looming challenges. Equitable access to, and engagement with, mathematics has
surfaced as an elusive goal of mathematics education organizations. MTEs, therefore, ought to identify and engage with resources that help them comprehend and confront systemic oppression and inequities. We present the process and reflections from an examination of MTEs’ professional growth through engagement in a collaborative interrogation of critical texts outside of mathematics education. Participation in this series of structured readings and dialogue led MTEs to develop a deeper understanding of the historical movements and events that created today’s local and global status quos. Furthermore, MTEs could more readily make connections between macrocontexts of colonialism, violence, and oppression, and the micromanifestations of power and marginalization within mathematics education. Implications for future development of MTEs are discussed.

Special Guests: Jill Newton, Michael R Lolkus, Troy Bell, and Willey, Craig Joseph.

Episode 31: Learning to Launch Cognitively Demanding Tasks: A Practice-Based Unit for Secondary Methods Jun 01, 2021

Cognitively demanding tasks provide important opportunities for students to develop an understanding of mathematics; however, they are challenging to launch and implement. The authors designed a secondary methods unit on launching tasks. Participants in the study were enrolled in five different methods courses. Using a noticing framework, findings suggest that by engaging in the unit, preservice teachers developed a greater understanding of the four aspects of an effective task launch. When viewing video examples, preservice teachers were able to talk about the four aspects of a task launch with increased specificity. Additionally, they began to identify ways of developing common language without reducing cognitive demand. We discuss implications of this work and offer suggestions for future teacher education research.

Special Guests: Christopher W. Parrish, Mark A. Creager, and Rachel B. Snider.

Episode 30: Student Argumentation Work Sample Sorting Task and Teachers’ Evaluations of Arguments May 25, 2021

To support teachers in implementing ambitious reform efforts, professional developers and teacher educators need to know more about teachers’ thinking about argumentation. Specifically, there is a need to understand more about teachers’ views and evaluations of students’ mathematical arguments as they play out in practice. In this article, we share a tool developed to elicit teachers’ pre- and post evaluations of students’ mathematical arguments on a problem-solving task. We discuss the design of the tool and provide evidence of its utility. Our findings indicate that the tool can be used to (a) identify changes in teachers’ evaluations of student mathematical arguments over time and (b) inform the design of professional learning experiences

Special Guests: Jillian Cavanna, and Megan Staples.

Episode 29: Double Demonstration Lessons: Authentically Participating in an Inquiry Stance May 18, 2021

Research has shown that the ways in which teachers engage in professional development activities vary widely. Farmer et al. (2003) identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that teachers took an active role in changing an observed lesson and then viewing the impact of those changes as a second lesson was taught. We share evidence that this modified structure provided opportunities for teachers to engage in an inquiry stance on teaching and discuss implications for professional development providers in structuring activities to foster an inquiry stance.

Special Guests: Angela T. Barlow and Natasha Gerstenschlager.

Episode 28: Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use May 11, 2021

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses
requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

Special Guests: Charmaine Mangram and Kathy Liu Sun.

Episode 27: Editorial February 2021: Considering Connections Across Research Questions, Data, Methods, and Claims May 04, 2021

A key component of a Mathematics Teacher Educator (MTE) journal article is a description of the innovation or tool that was used with teachers and a report of the details of the research on that innovation/tool. In our September editorial we highlighted the innovation. In this editorial, we will focus on the importance of aligning research questions, data, and claims with existing research and theories to present a strong and coherent argument about the contribution the innovation/tool makes to mathematics teacher education.

Special Guests: Heather West and Karen Hollebrands,.

Episode 24: Representing Student Voice in an Approximation of Practice: Using Planted Errors in Coached Rehearsals to Support Teacher Candidate Learning Jan 04, 2021

Approximations of practice provide opportunities for teacher candidates (TCs) to engage in the work of teaching in situations of reduced complexity. A problem of practice for teacher educators relates to how to represent student voice in approximations to engage TCs with interactive practices in meaningful ways. In this article, we share an analysis of our use of “planted errors” in coached rehearsals with secondary mathematics TCs focused on the practice of responding to errors in whole-class discussion. We highlight how different iterations of the planted errors affect the authenticity of how student voice was represented in the rehearsals and the resulting opportunities for TC learning. We offer design considerations for coached rehearsals and other approximations of practice.

Special Guests: Erin E. Baldinger, Foster Graif, and Matthew P. Campbell.

Episode 26: Fostering Middle School Teachers’ Mathematical Knowledge for Teaching via Analysis of Tasks and Student Work Jan 04, 2021

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers’ mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and student work. Although multiple studies have shown that professional development can contribute to teachers’ MKT globally, little is known about how this knowledge grows and how specific domains of MKT can be targeted through professional development. Findings in this study show how professional development positively influenced participants’ knowledge of content and teaching and knowledge of content and students, two domains of MKT, through teachers’ twinned analyses of tasks and student work in proportional reasoning.

Special Guests: Jennifer M. Lewis,, S. Asli Özgün-Koca,, and Thomas Edwards.

Episode 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers Jan 04, 2021

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

Special Guests: Gülseren Karagöz Akar and Mervenur Belin.

Episode 25: Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks Jan 04, 2021

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and use both academic and practitioner knowledge while creating technologybased tasks for high school students to use. Our results revealed increased focus on pedagogical decisions in areas such as technology-task design and questioning techniques. The data also indicate that the success of this collaboration was connected to fair distribution of work, feeling valued, and personal benefit and challenges centered on maintaining rejection of hierarchy.

Special Guest: Allison W. McCulloch,.

Episode 22: Interventions, Tools, and Equity-Oriented Resources in the MTE Journal Dec 13, 2020

The Mathematics Teacher Educator journal is co-sponsored by the National Council of Teachers of Mathematics and the Association of Mathematics Teacher Educators. In June, both organizations released statements that call for mathematics teachers and mathematics teacher educators (MTEs) to “engage in anti-racist and trauma-informed education in our daily practices as processes of learning and adjustments” (NCTM, 2020) and to “actively work to be anti-racist in our acts of teaching, research, and service” (AMTE, 2020). This editorial highlights equity-related interventions and tools that can be implemented by MTEs. We reiterate statements made by NCTM and AMTE, describe key features of interventions and tools, and share equity-related resources published in the journal for MTEs to use with teachers.