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In this editorial, we provide suggestions for authors who are preparing a manuscript for the Mathematics Teacher Educator journal that is based on a dissertation. We recommend that authors begin by examining their findings and identifying a focus that addresses a shared problem of practice for mathematics teacher educators. Authors should become familiar with the journal by reading editorials and related articles published in the journal. Finally, the Writing Tool can serve as a guide for preparing an outline for the manuscript, which can be shared with the editors and colleagues for feedback.
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.
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.
Headlines reach readers' email in-boxes on a weekly basis. The widespread use of Twitter (#iteachmath) and blogs (#mtbos) brings prospective and in-service teachers unprecedented access to knowledge and guidance that can inform teaching, but the sheer volume of available information comes at a cost: Authors feel they must entice readers with catchier titles and bolder claims, a phenomenon that is referred to in the popular media as clickbait. As readers are learning from the current political climate, U.S. culture may be becoming increasingly entranced with compelling headlines and less engaged with evidence to support those headlines.
In this editorial, we focus on the unsuspecting challenge that many prospective authors encounter when writing manuscripts for this journal–that of clearly situating their manuscript as relevant and connected to a significant and compelling shared problem of the practice of mathematics teacher educators. In our previous editorial (Crespo & Bieda, 2017), we introduced a writing tool that organizes and makes visible all five review criteria for this journal into a writing template (reproduced here in Figure 1). This tool is meant to help prospective authors foreground the criteria as they conceive, outline, draft, review, edit, and revise their manuscripts. As prospective authors have begun to try this tool and share their outlined manuscripts with us, the challenge of articulating a shared problem of practice in MTE manuscripts has become more evident.
When describing MTE, we often hear things like, " It is a practitioner journal, " " It is not like JRME, " and " It is more rigorous than MT, MTMS, or TCM journals. " All these things are true but do not quite capture what it is that makes MTE a journal dedicated to growing the knowledge base of mathematics teacher educators. What this says is that it is easier to state what MTE is not, and much more dif cult to provide a clear-cut description of what the journal publishes. MTE is a journal attempting to do something that no other journal, not even those in other disciplines, has done. Although it may be convenient to try to understand the journal and the kinds of articles it publishes by comparing it with other journals we are familiar with, these comparisons ultimately fall short of providing the support needed to generate a manuscript that is a good "fit" for MTE. In this editorial, we offer a tool that could help prospective authors conceptualize and write manuscripts for this journal.
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.
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.
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.
In our recent editorials (Cai et al., 2019a, 2019b), we discussed the important roles that research questions and theoretical frameworks play in conceptualizing, carrying out, and reporting mathematics education research. In this editorial, we discuss the methodological choices that arise when one has articulated research questions and constructed at least a rudimentary theoretical framework. Just as the researcher must justify the significance of research questions and the appropriateness of the theoretical framework, we argue that the researcher must thoroughly describe and justify the selection of methods. Indeed, the research questions and the theoretical framework should drive the choice of methods (and not the reverse). In other words, a sufficiently well-specified set of research questions and theoretical framework establish the parameters within which the most productive methods will be selected and developed.
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