Mathematics Teacher Educator Podcast

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

February 26th, 2020  |  Season 3  |  21 mins

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).

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.

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

June 12th, 2019  |  Season 2  |  24 mins 46 secs

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.

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

March 7th, 2019  |  Season 1  |  21 mins 1 sec

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.

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

February 2nd, 2019  |  Season 1  |  22 mins 42 secs

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.

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

February 1st, 2019  |  Season 1  |  27 mins 13 secs

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.

Episode 1: Encouraging Teachers to Make Use of Multiplicative Structure

January 29th, 2019  |  Season 1  |  29 mins 12 secs

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.