Mathematics Teacher Educator Podcast
The Mathematics Teacher Educator Podcast accompanies the Mathematics Teacher Educator Journal and is co-sponsored by the Association of Mathematics Teacher Educators and the National Council of Teachers of Mathematics. It explores topics relevant to mathematics teacher educators, including research, practice, and policy. Episodes feature discussions with experts and practitioners in the field.
Episodes
Episode 61: Critically Conscious Mathematics Leaders: Fostering Specialists’ Learning and Transformative Leadership
In this episode, we explore a recent article, titled “Critically Conscious Mathematics Leaders: Fostering Specialists’ Learning and Transformative Leadership”, from Volume 14, Issue 3 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 episode includes the article au
Episode 60: Preservice Teachers’ Evolving Knowledge Around Technology for Teaching Mathematics
In this episode, we explore a recent article, titled “Preservice Teachers’ Evolving Knowledge Around Technology for Teaching Mathematics”, 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
Episode 59: Adapting Messages and Materials for Multiple Communities: Using Teacher Recruitment Materials With Integrity
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
Episode 58: Engaging in Equity-Oriented Mathematics Teaching Together: A Tool to Support Mentor and Teacher Candidate Learning
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
Episode 57: Dilemmas and Design Principles in Planning for Justice-Oriented Community-Based Mathematical Modeling Lessons
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
Episode 56: Are We Preparing Agents of Change or Instruments of Inequity? Teaching Toward Antiracist Mathematics Teacher Education
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
Episode 55: When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation
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 PT
Episode 54: “Rahul is a Math Nerd” and “Mia Can Be a Drama Queen”: How Mixed-Reality Simulations Can Perpetuate Racist and Sexist Stereotypes
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
Episode 53: Building Mathematics Professional Development With an Explicit Attention to Concepts and Student Opportunities to Struggle Framework
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.
Episode 48: Design Principles That Support Course Design Innovation for Elementary Mathematics Methods Courses
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 conten
Episode 52: Adaptations to Support the Flint Water Task
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
Episode 49: Filling a “Void”: The Mathematical Quality in Planning Protocol for Mathematics Teacher Educators
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
Episode 51: Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board
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
Episode 47: Taking a Spatial Turn in Mathematics Teacher Education
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 im
Episode 46: Developing Equity Literacy and Critical Statistical Literacy in Secondary Mathematics Preservice Teachers
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’ de
Episode 50: Engaging Teachers in the Combination of Statistical Investigation and Social Justice: Fairness in School Funding
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 statistic
Episode 44: Continuous Improvement Lesson Study: A Model of MTE Professional Development
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. Thi
Episode 45: From Argumentation to Truth-Telling: Critical Race Theory in Mathematics Teacher Education
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,
Episode 43: Developing Preservice Teachers’ Understanding of Area Through a Units Intervention
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 ide
Episode 42: Language Demands Tool: Attuning Prospective Teachers’ Vision to the Role of Language in Mathematics Education
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 designe
Episode 41: Centering Professional Development Around the Instructional Quality Assessment Rubrics
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 instructio
Episode 40: Conversation with MTE editors: Vision, Submission Advice, Etc.
Special Guests: Kate Johnson and Michael Steele .
Episode 39: Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students
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 deve
Episode 37: Supporting Preservice Teachers’ Growth in Eliciting and Using Evidence of Student Thinking: Show-Me Narrative
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
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 promo
Episode 36: Supporting Prospective Teachers in Problem Solving: Incorporating Mindset Messaging to Overcome Math Anxiety
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 prospecti
Episode 34: Mathematics Teachers’ Understanding of Privilege and Oppression
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,
Episode 35: If the World Were a Village: Learning Mathematics While Learning About the World
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
Episode 32: Developing an Asset-Based View of Students’ Mathematical Competencies Through Learning Trajectory-Based Lesson Study
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
Episode 33: Exploring Power and Oppression: An Examination of Mathematics Teacher Educators’ Professional Growth
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
Episode 31: Learning to Launch Cognitively Demanding Tasks: A Practice-Based Unit for Secondary Methods
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, pre
Episode 30: Student Argumentation Work Sample Sorting Task and Teachers’ Evaluations of Arguments
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
Episode 29: Double Demonstration Lessons: Authentically Participating in an Inquiry Stance
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 activ
Episode 28: Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use
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 fou
Episode 27: Editorial February 2021: Considering Connections Across Research Questions, Data, Methods, and Claims
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 researc
Episode 24: Representing Student Voice in an Approximation of Practice: Using Planted Errors in Coached Rehearsals to Support Teacher Candidate Learning
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 coach
Episode 25: Creating a Third Space for Learning to Design Technology-Based Mathematics Tasks
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 knowle
Episode 23: Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers
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 f
Episode 26: Fostering Middle School Teachers’ Mathematical Knowledge for Teaching via Analysis of Tasks and Student Work
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 ha
Episode 22: Interventions, Tools, and Equity-Oriented Resources in the MTE Journal
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 a
Episode 21: Undergraduate Research in Mathematics Education: Using Qualitative Data About Children’s Learning to Make Decisions About Teaching
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 undergra
Episode 20: Learning to Launch Complex Tasks: How Instructional Visions Influence the Exploration of the Practice
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
Episode 19: Do You See What I See? Formative Assessment of Preservice Teachers’ Noticing of Students’ Mathematical Thinking
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 appro
Episode 18: Design Principles for Examining Student Practices in a Technology-Mediated Environment
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 lear
Episode 17: Editorial: Analyzing Eight Years of Mathematics Teacher Educator Articles: Where We Were, Where We Are, and Where We Are Going
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;
Episode 16: Diverge then Converge: A Strategy for Deepening Understanding through Analyzing and Reconciling Contrasting Patterns of Reasoning
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 engageme
Episode 15: Noticing Aloud: Uncovering Mathematics Teacher Noticing in the Moment
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 arti
Episode 14: Supporting Teachers to Use Formative Assessment for Adaptive Decision Making
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 report
Episode 13: Visions of the Possible: Using Drawings to Elicit and Support Visions of Teaching Mathematics
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 dep
Episode 12: Complex and Contradictory Conversations: Prospective Teachers Interrogating Dominant Narratives Within Mathematics Education Discourse
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
Episode 11: Using Coordinated Measurement with Future Teachers to Connect Multiplication, Division, and Proportional Relationships
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’
Episode 10: Engaging Preservice Secondary Mathematics Teachers in Authentic Mathematical Modeling: Deriving Ampere’s Law
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 peda
Episode 9: The Three-Minute-Rehearsal Cycle of Enactment and Investigation
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
Episode 8: Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task
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 w
Episode 7: Noticing and Wondering: A Language Structure to Support Mentoring Conversations
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
Episode 6: The Decision-Making Protocol for Mathematics Coaching
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 (D
Episode 5: The Student Discourse Observation Tool: Supporting Teachers in Noticing Justifying and Generalizing
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 pur
Episode 4: Preservice Teachers’ Mathematical Visual Implementation for Emergent Bilinguals
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 problem
Episode 3: Assessing Prospective Teachers’ Analysis of Teaching: How Well Can They Link Teaching and Learning?
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
Episode 2: Using Narrative Writing to Learn What Beginning Teachers Notice
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 beginnin
Episode 1: Encouraging Teachers to Make Use of Multiplicative Structure
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
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