Mathematics Teacher Educator Podcast

Episode Archive

Episode Archive

21 episodes of Mathematics Teacher Educator Podcast since the first episode, which aired on January 29th, 2019.

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

    September 18th, 2020  |  Season 5  |  30 mins 45 secs
    undergraduate research; design-based research; clinical interviews; formative assessment; classroom data analysis

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

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

    September 11th, 2020  |  Season 5  |  25 mins 53 secs
    instructional vision; practice-based teacher education; teacher learning cycle; launch; complex tasks

    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

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

    September 4th, 2020  |  Season 5  |  37 mins 27 secs
    formative assessment; professional noticing; approximations of practice

    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.

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

    August 28th, 2020  |  Season 5  |  36 mins 53 secs
    technology; function; preservice secondary mathematics teachers

    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.

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

    June 29th, 2020  |  Season 5  |  34 mins 57 secs

    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.

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

    June 18th, 2020  |  Season 4  |  31 mins
    classroom discourse; enacting mathematical practices; pre-service content courses

    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.

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

    May 28th, 2020  |  Season 4  |  23 mins 46 secs

    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.

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

    May 18th, 2020  |  Season 4  |  32 mins 11 secs
    professional development; research on professional development; formative assessment

    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.

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

    April 21st, 2020  |  Season 4  |  26 mins 34 secs

    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.

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

    March 26th, 2020  |  Season 3  |  29 mins 43 secs

    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.

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

    March 21st, 2020  |  Season 3  |  19 mins 56 secs

    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.

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

    February 26th, 2020  |  Season 3  |  21 mins
  • Episode 8: Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task

    September 11th, 2019  |  Season 2  |  26 mins 4 secs
    mathematical modeling; mathematics; social justice; teacher education

    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.

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

    August 12th, 2019  |  Season 2  |  25 mins 29 secs
    field experiences; mentoring; prospective teachers; student teaching; teacher noticing

    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.

  • Episode 6: The Decision-Making Protocol for Mathematics Coaching

    August 1st, 2019  |  Season 2  |  32 mins 49 secs
    coaching framework, coaching practices, mathematics coaching, teaching practices

    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.