Mathematics Teacher Educator Podcast

Episode 59: Adapting Messages and Materials for Multiple Communities: Using Teacher Recruitment Materials With Integrity

joel@amidonplanet.com (Joel Amidon) — Tue, 12 May 2026 00:15:00 -0700

In this episode, we explore a recent article, titled “Adapting Messages and Materials for Multiple Communities: Using Teacher Recruitment Materials With Integrity”, from Volume 14, Issue 2 of the Mathematics Teacher Educator journal. In this discussion we will focus on the problem addressed in the article, the work behind it, and what it means for practice. This discussion is led by Joel Amidon and article authors, Jean Lee, Gary Martin, and Glenn Waddell. The article was also authored by Amy Roth McDuffie.

Lee, J. S., Martin, W. G., Waddell, Jr., G., & McDuffie, A. R. (2026). Adapting Messages and Materials for Multiple Communities: Using Teacher Recruitment Materials With Integrity. Mathematics Teacher Educator, 14(2), 72-85. Retrieved Apr 28, 2026, from https://doi-org.umiss.idm.oclc.org/10.5951/MTE.2023-0056

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Mathematics Teacher Education Partnership

Mathematics Teacher Educator Writing Tool

The Mathematics Teacher Educator podcast is supported by Amidon Planet.

Special Guests: Glenn Waddell, Jean Lee, and W. Gary Martin.

Episode 58: Engaging in Equity-Oriented Mathematics Teaching Together: A Tool to Support Mentor and Teacher Candidate Learning

joel@amidonplanet.com (Joel Amidon) — Tue, 21 Apr 2026 00:15:00 -0700

In this episode, we explore a recent article, titled “Engaging in Equity-Oriented Mathematics Teaching Together: A Tool to Support Mentor and Teacher Candidate Learning”, from Volume 14, Issue 2 of the Mathematics Teacher Educator journal. In this discussion we will focus on the problem addressed in the article, the work behind it, and what it means for practice. This discussion includeds article authors, Taylor Stafford, Heather Fink, and Melinda Knapp . The article was also authored by Ruth Heaton and Torrey Kulow.

Stafford, T. E., Fink, H., Knapp, M., Heaton, R., & Kulow, T. (2026). Engaging in Equity-Oriented Mathematics Teaching Together: A Tool to Support Mentor and Teacher Candidate Learning. Mathematics Teacher Educator, 14(2), 121-134. Retrieved Apr 6, 2026, from https://doi-org.umiss.idm.oclc.org/10.5951/MTE.2025-0024

Project website: https://colearnemt.org

Mathematics Teacher Educator Writing Tool

The Mathematics Teacher Educator podcast is supported by Amidon Planet.

Special Guests: Heather Fink, Melinda Knapp, and Taylor Stafford.

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

joel@amidonplanet.com (Joel Amidon) — Tue, 24 Oct 2023 12:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Wed, 11 Oct 2023 16:00:00 -0700

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 55: When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation

joel@amidonplanet.com (Joel Amidon) — Tue, 12 Sep 2023 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Tue, 12 Sep 2023 20:00:00 -0700

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 53: Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework

joel@amidonplanet.com (Joel Amidon) — Thu, 31 Aug 2023 11:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Jun 2023 20:15:00 -0700

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 51: Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Jun 2023 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Jun 2023 20:00:00 -0700

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 49: Filling a “Void”: The Mathematical Quality in Planning Protocol for Mathematics Teacher Educators

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Jun 2023 20:00:00 -0700

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 47: Taking a Spatial Turn in Mathematics Teacher Education

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Jun 2023 19:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Mon, 22 May 2023 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Mon, 15 May 2023 12:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Wed, 19 Oct 2022 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Wed, 19 Oct 2022 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Wed, 19 Oct 2022 19:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Mon, 03 Oct 2022 11:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Mon, 03 Oct 2022 11:00:00 -0700

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.

joel@amidonplanet.com (Joel Amidon) — Fri, 11 Mar 2022 10:00:00 -0800

Special Guests: Kate Johnson and Michael Steele .

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

joel@amidonplanet.com (Joel Amidon) — Tue, 08 Feb 2022 12:30:00 -0800

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

joel@amidonplanet.com (Joel Amidon) — Tue, 08 Feb 2022 12:15:00 -0800

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

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

joel@amidonplanet.com (Joel Amidon) — Tue, 08 Feb 2022 12:00:00 -0800

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

joel@amidonplanet.com (Joel Amidon) — Tue, 08 Feb 2022 12:00:00 -0800

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

joel@amidonplanet.com (Joel Amidon) — Wed, 15 Dec 2021 17:00:00 -0800

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

joel@amidonplanet.com (Joel Amidon) — Wed, 15 Dec 2021 17:00:00 -0800

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

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

joel@amidonplanet.com (Joel Amidon) — Wed, 15 Dec 2021 16:00:00 -0800

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 Suh and Sara Birkhead.

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

joel@amidonplanet.com (Joel Amidon) — Wed, 15 Dec 2021 16:00:00 -0800

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

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

joel@amidonplanet.com (Joel Amidon) — Tue, 01 Jun 2021 05:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Tue, 25 May 2021 05:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Tue, 18 May 2021 05:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Tue, 11 May 2021 05:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Tue, 04 May 2021 20:00:00 -0700

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

joel@amidonplanet.com (Joel Amidon) — Mon, 04 Jan 2021 15:00:00 -0800

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 25: Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks

joel@amidonplanet.com (Joel Amidon) — Mon, 04 Jan 2021 15:00:00 -0800

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 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

joel@amidonplanet.com (Joel Amidon) — Mon, 04 Jan 2021 15:00:00 -0800

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 26: Fostering Middle School Teachers’ Mathematical Knowledge for Teaching via Analysis of Tasks and Student Work

joel@amidonplanet.com (Joel Amidon) — Mon, 04 Jan 2021 15:00:00 -0800

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 22: Interventions, Tools, and Equity-Oriented Resources in the MTE Journal

joel@amidonplanet.com (Joel Amidon) — Sun, 13 Dec 2020 19:00:00 -0800

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.

If you have enjoyed listening to this podcast and are interested in ohter episodes you can see all episodes listed on this website or search by categries at https://evathanheiser.wordpress.com/podcasts/

Special Guests: Emily Elrod and Valerie Faulkner.

Episode 21: Undergraduate Research in Mathematics Education: Using Qualitative Data About Children’s Learning to Make Decisions About Teaching

joel@amidonplanet.com (Joel Amidon) — Fri, 18 Sep 2020 08:00:00 -0700

Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.

Special Guests: Jennifer Bergner and Randall E. Groth.

Episode 20: Learning to Launch Complex Tasks: How Instructional Visions Influence the Exploration of the Practice

joel@amidonplanet.com (Joel Amidon) — Fri, 11 Sep 2020 09:00:00 -0700

This study investigates how the exploration phase of the teacher learning cycle provides 11 novice mathematics teachers with the opportunity to learn about the high-leverage practice of launching a complex task. Findings suggest that the exploration phase of the teacher learning cycle provides novice teachers with opportunities to reflect on how
to launch a complex task within the context of their own instructional practice. Because of this opportunity to deeply consider the pedagogical resource and reflect on it, novice teachers’ instructional visions were a filter through which they interpreted key instructional strategies offered up during the exploration phase of the teacher learning cycle. Further, the authors discuss three key takeaways for teacher educators who are attempting to implement the teacher learning cycle into their teacher education coursework

Special Guests: Anne Garrison Wilhelm and Dawn M. Woods.

Episode 19: Do You See What I See? Formative Assessment of Preservice Teachers’ Noticing of Students’ Mathematical Thinking

joel@amidonplanet.com (Joel Amidon) — Fri, 04 Sep 2020 09:00:00 -0700

Developing expertise in professional noticing of students’ mathematical thinking takes time
and meaningful learning experiences. We used the LessonSketch platform to create a learning
experience for secondary preservice teachers (PSTs) involving an approximation of teaching
practice to formatively assess PSTs’ noticing skills of students’ mathematical thinking.
Our study showed that approximations of teaching practice embedded within platforms
like LessonSketch can enable mathematics teacher educators (MTEs) to carry out effective
formative assessment of PSTs’ professional noticing of students’ mathematical thinking
that is meaningful for both PSTs and MTEs. The experience itself as well as its design features
and framework used with the assessment can be applied in the work of MTEs who develop teachers’ professional noticing skills of students’ mathematical thinking.

Special Guests: Joel Amidon and Stephanie Casey.

Episode 18: Design Principles for Examining Student Practices in a Technology-Mediated Environment

joel@amidonplanet.com (Joel Amidon) — Fri, 28 Aug 2020 13:00:00 -0700

In this article, we present a set of design principles to guide the development of
instructional materials aimed to support preservice secondary mathematics teachers
(PSMTs) examining student practices in technology-mediated environments. To
develop design principles, we drew on the literature related to technological
pedagogical content knowledge (TPACK; Niess, 2005), video cases as learning objects
(Sherin & van Es, 2005), and professional noticing (Jacobs, et al., 2010). After presenting
the design principles, we share a task created using these design principles. Finally, we
share PSMTs’ reflections about changes in their own understanding after examining
students’ practices. Their responses provide insights into the usefulness of the
design principles for deepening PSMTs’ mathematical knowledge and knowledge
of students’ understanding, thinking, and learning with technology.

Special Guests: Allison W. McCulloch, Charity Cayton, Jennifer N. Lovett, and Lara K. Dick.

Episode 17: Editorial: Analyzing Eight Years of Mathematics Teacher Educator Articles: Where We Were, Where We Are, and Where We Are Going

joel@amidonplanet.com (Joel Amidon) — Mon, 29 Jun 2020 08:00:00 -0700

In this editorial, an analysis of articles published in the Mathematics Teacher Educator journal (MTE) from 2012 to 2020, which describes the knowledge base for mathematics teacher educators addressed by MTE authors, is presented. This analysis builds on similar work conducted four years ago (Bieda, 2016). These more recent findings demonstrate that articles focusing on teacher knowledge; mathematical content; student thinking and reasoning;
and models of teacher preparation or in-service professional development (PD) have been the most frequently published in MTE. In contrast, a limited number of articles have focused on discourse; diversity, equity, and language; technology; and methods of research. This examination allows us to assess as a community where we were, where we are, and where we might go in the future.

Special Guests: Karen Hollebrands, and Valerie Faulkner.

Episode 16: Diverge then Converge: A Strategy for Deepening Understanding through Analyzing and Reconciling Contrasting Patterns of Reasoning

joel@amidonplanet.com (Joel Amidon) — Thu, 18 Jun 2020 11:15:00 -0700

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.

Special Guests: Mariana Levin and Theresa J. Grant.

Episode 15: Noticing Aloud: Uncovering Mathematics Teacher Noticing in the Moment

joel@amidonplanet.com (Joel Amidon) — Thu, 28 May 2020 10:00:00 -0700

Understanding mathematics teacher noticing has been the focus of a growing body of research, in which student work and classroom videos are often used as artifacts for surfacing teachers’ cognitive processes. However, what teachers notice through reflecting on artifacts of teaching may not be parallel to what they notice in the complex and demanding environment of the classroom. This article used a new technique, side-by-side coaching, to uncover teacher noticing in the moment of instruction. There were 21 instances of noticing aloud during side by side coaching which were analyzed and classified, yielding 6 types of teacher noticing aloud, including instances in which teachers expressed confidence, struggle, and wonder. Implications for coaching and future research on teacher noticing are discussed.

Special Guest: Jen Munson.

Episode 14: Supporting Teachers to Use Formative Assessment for Adaptive Decision Making

joel@amidonplanet.com (Joel Amidon) — Mon, 18 May 2020 08:00:00 -0700

Formative assessment helps teachers make effective instructional decisions to support students to learn mathematics. Yet, many teachers struggle to effectively use formative assessment to support student learning. Therefore, teacher educators must find ways to support teachers to use formative assessment to inform instruction. This case study documents shifts in teachers’ views and reported use of formative assessment that took place as they engaged in professional development (PD). The PD design considered the formative assessment cycle (Otero, 2006; Popham, 2008) and embedded it within a pedagogical framework (Lamberg, 2013, in press) that took into account the process of mathematics planning and teaching while supporting teachers to learn math content. Teachers restructured their definition of student understanding, which influenced how they interpreted student work and made instructional decisions. Teachers’ pre-PD instructional decisions focused on looking for right and wrong answers to determine mastery and focused on pacing decisions. Their post-PD decisions focused on student thinking and adapting teaching to support student thinking and learning. Implications for PD to support teachers to use formative assessment and research are discussed.

Special Guests: Linda Gillette-Koyen and Teruni Lamberg.

Episode 13: Visions of the Possible: Using Drawings to Elicit and Support Visions of Teaching Mathematics

joel@amidonplanet.com (Joel Amidon) — Tue, 21 Apr 2020 19:00:00 -0700

Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program—snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.

Special Guest: Jennifer Ruef.

Episode 12: Complex and Contradictory Conversations: Prospective Teachers Interrogating Dominant Narratives Within Mathematics Education Discourse

joel@amidonplanet.com (Joel Amidon) — Sat, 04 Apr 2020 06:00:00 -0700

In this conceptual piece, I explore complex and contradictory conversations during an idea mapping task in which prospective elementary teachers interrogated dominant discourses within mathematics education, such as “mathematics is everywhere” and “being a math person.” I argue that this exercise of engaging with contradictions provided prospective teachers with opportunities to tease out nuances for reconstructing ideas that generate new perspectives for teaching and learning mathematics. Sharing my experience with the idea mapping task as a case study, I offer an alternative role for mathematics teacher educators to consider—as facilitators who create spaces for prospective teachers to interrogate complex and contradictory conversations within mathematics education.

Special Guest: Lynette DeAun Guzmán.

Episode 11: Using Coordinated Measurement with Future Teachers to Connect Multiplication, Division, and Proportional Relationships

joel@amidonplanet.com (Joel Amidon) — Thu, 26 Mar 2020 06:00:00 -0700

We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as an equation, to support future teachers’ understanding of these topics. We also used 2 types of length- based math drawings—double number lines and strip diagrams—as media with which to represent relationships among quantities and solve problems. To illustrate the promise of this approach, we share data in which future secondary mathematics teachers generated and explained without direct instruction sound methods for dividing by fractions and solving proportional relationships. The results are noteworthy, because these and other topics related to multiplication pose perennial challenges for many teachers.

Special Guest: Andrew Izsák.

Episode 10: Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere’s Law

joel@amidonplanet.com (Joel Amidon) — Sat, 21 Mar 2020 14:00:00 -0700

Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students’ thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers’ (PSMTs) proficiency with mathematical modeling is by incorporating modeling tasks into mathematics pedagogy courses, allowing PSMTs to engage with mathematical modeling as students and as future teachers. Eight PSMTs participated in a model-eliciting activity (MEA) in which they were asked to develop a model that describes the strength of the magnetic field generated by a solenoid. By engaging in mathematical modeling as students, these PSMTs became aware of their own proficiency with and understanding of mathematical modeling. By engaging in mathematical modeling as future teachers, these PSMTs were able to articulate the importance of incorporating MEAs into their own instruction.

Special Guest: Kimberly Corum.

Episode 9: The Three-Minute-Rehearsal Cycle of Enactment and Investigation

joel@amidonplanet.com (Joel Amidon) — Wed, 26 Feb 2020 14:00:00 -0800

In the last decade, mathematics teacher educators have begun to design learning opportunities for preservice mathematics teachers using a pedagogies-of-practice perspective. In particular, learning cycles provide a structure for engaging PSTs in learning to teach through the use of representations, approximations, and decompositions of practice (Grossman et al., 2009). In this article, we provide details of one learning cycle designed to support secondary mathematics preservice teachers’ learning to elicit and use evidence of student thinking and pose purposeful questions (National Council of Teachers of Mathematics, 2014). Through qualitative analyses conducted on learning reflections, we provide evidence of the impact on engagement of this cycle through the lens of the Framework for Learning to Teach (Hammerness et al., 2005).

Special Guest: Fran Arbaugh.

Episode 8: Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task

joel@amidonplanet.com (Joel Amidon) — Wed, 11 Sep 2019 20:00:00 -0700

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teacher- generated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci—by using mathematical modeling to investigate and analyze important social justice issues—can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed.

Special Guest: Julia Aguirre.

Episode 7: Noticing and Wondering: A Language Structure to Support Mentoring Conversations

joel@amidonplanet.com (Joel Amidon) — Mon, 12 Aug 2019 05:15:00 -0700

Teachers and mathematics teacher education scholars have identified field experiences and quality mentoring as influential components of math teacher preparation and development. Yet, quality mentoring is a complex and demanding practice. Providing educative feedback to novices, particularly that which encourages reflection versus evaluation, can be challenging work for mentors. To study the potential of an intervention for providing professional development for mentors, I worked with pairs of mentors and prospective teachers (PSTs) offering Smith’s (2009) noticing and wondering language as a way of structuring mentoring conversations that maintain both descriptive and interpretive analytic stances. Analysis of before and after conversations provided evidence of how mentor-PST pairs adopted noticing and wondering language, and in particular illuminated the ways in which the language structure might support interpretive mentoring conversations for studying teaching. The results suggest that mathematics teacher educators may want to consider what makes wondering challenging work and how to best support wondering in educative mentoring conversations.

Special Guest: Sarah Roller Dyess.

Episode 6: The Decision-Making Protocol for Mathematics Coaching

joel@amidonplanet.com (Joel Amidon) — Thu, 01 Aug 2019 20:00:00 -0700

More than ever, mathematics coaches are being called on to support teachers in developing effective classroom practices. Coaching that influences professional growth of teachers is best accomplished when mathematics coaches are supported to develop knowledge related to the work of coaching. This article details the implementation of the Decision-Making Protocol for Mathematics Coaching (DMPMC) across 3 cases. The DMPMC is a framework that brings together potentially productive coaching activities (Gibbons & Cobb, 2017) and the research-based Mathematics Teaching Practices (MTPs) in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014) and aims to support mathematics coaches to purposefully plan coaching interactions. The findings suggest the DMPMC supported mathematics coaches as they worked with classroom teachers while also providing much needed professional development that enhanced their coaching practice.

Special Guests: Courtney Baker and Melinda Knapp.

Episode 5: The Student Discourse Observation Tool: Supporting Teachers in Noticing Justifying and Generalizing

joel@amidonplanet.com (Joel Amidon) — Wed, 12 Jun 2019 10:00:00 -0700

In classrooms, students engage in argumentation through justifying and generalizing. However, these activities can be difficult for teachers to conceptualize and therefore promote in their classrooms. In this article, we present the Student Discourse Observation Tool (SDOT) developed to support teachers in noticing and promoting student justifying and generalizing. The SDOT serves the purpose of (a) focusing teacher noticing on student argumentation during classroom observations, and (b) promoting focused discussion of student discourse in teacher professional learning communities. We provide survey data illustrating that elementary-level teachers who participated in professional development leveraging the SDOT had richer conceptions of justifying and generalizing and greater ability to characterize students’ justifying and generalizing when compared with a set of control teachers. We argue that the SDOT provides both an important focusing lens for teachers and a means to concretize the abstract mathematical activities of justifying and generalizing.

Special Guest: Kathleen Melhuish.

Episode 4: Preservice Teachers’ Mathematical Visual Implementation for Emergent Bilinguals

joel@amidonplanet.com (Joel Amidon) — Thu, 07 Mar 2019 10:00:00 -0800

Using visuals is a well-known strategy to teach emergent bilinguals (EBs). This study examined how preservice teachers (PSTs) implemented visuals to help EBs understand mathematical problems and how an innovative intervention cultivated PSTs’ capability of using visuals for EBs. Four middle school mathematics PSTs were engaged in a field experience with EBs to work on mathematical problems; during the field experience, the PSTs received interventions. In one intervention session, the PSTs were asked to make sense of a word problem written in an unknown language with different visuals. After this intervention, they changed their use of visuals when modifying tasks for EBs. The results suggest that immersive experiences where PSTs can experience learning from the perspective of EBs helps PSTs implement mathematically meaningful visuals in a way that makes mathematical problems accessible to EBs.

Special Guest: Ji-Yeong I.

Episode 3: Assessing Prospective Teachers’ Analysis of Teaching: How Well Can They Link Teaching and Learning?

joel@amidonplanet.com (Joel Amidon) — Sat, 02 Feb 2019 12:00:00 -0800

One goal in teacher education is to prepare prospective teachers (PTs) for a career of systematic reflection and learning from their own teaching. One important skill involved in systematic reflection, which has received little research attention, is linking teaching actions with their outcomes on student learning; such links have been termed hypotheses. We developed an assessment task to investigate PTs’ ability to create such hypotheses, prior to instruction. PTs (N = 16) each read a mathematics lesson transcript and then responded to four question prompts. The four prompts were designed to vary along research-based criteria to examine whether different contexts influenced PTs’ enactment of their hypothesizing skills. Results suggest that the assessment did capture PTs’ hypothesizing ability and that there is room for teacher educators to help PTs develop better hypothesis skills. Additional analysis of the assessment task showed that the type of question prompt used had only minimal effect on PTs’ responses.

Special Guests: Christine Phelps-Gregory and Sandy M. Spitzer.

Episode 2: Using Narrative Writing to Learn What Beginning Teachers Notice

joel@amidonplanet.com (Joel Amidon) — Fri, 01 Feb 2019 17:00:00 -0800

This article shares the authors’ use of written teaching replays as part of a professional development experience for beginning secondary mathematics teachers. This form of narrative writing is inspired by Horn’s (2010) descriptions of teachers sharing their practice in professional learning communities. In this study, written teaching replays are used to gain insights about what beginning teachers noticed about their teaching practice and whether these noticings highlighted dilemmas or successes in their teaching practice. The analysis of teaching replays indicated that, despite being in their first years of teaching, these beginning teachers’ narrative writings focused least on management issues. Instead, the writings had a strong focus on mathematics or teaching mathematics as well as on social issues within their classrooms. These findings counter the research literature that suggests beginning teachers are overwhelmingly concerned with classroom management. The authors conclude with their reflections on the potential of this form of narrative writing for beginning teachers and how it could be used by other mathematics educators.

Special Guests: Kimberly Masloski and Rachael Brown.

Episode 1: Encouraging Teachers to Make Use of Multiplicative Structure

joel@amidonplanet.com (Joel Amidon) — Tue, 29 Jan 2019 18:00:00 -0800

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number’s multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers’ procedural knowledge with respect to using a number’s prime factorization to identify its factors, and presents evidence of the impact of the intervention. Results point toward improved abilities to use a number’s prime factorization to sort factors and nonfactors across four factor subtypes, to create factor lists, and to construct numbers with particular divisibility properties. Implications for mathematics teacher education include providing specific materials and strategies for strengthening preservice and in-service teachers’ procedural knowledge.

Special Guest: Ziv Feldman.