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This study aims to analyze possible connections among the noticing skills of pre-service mathematics teachers, and specifically the skills of attending to students' thinking, interpreting students' mathematical understanding, and proposing teaching alternatives. We characterized these connections in terms of coherency, i.e., the extent to which pre-service teachers take into account (a) an identified critical event—including its mathematics and context—when interpreting students' statements, (b) their own interpretation of students' statements when interpreting the teacher's response, and (c) their own interpretation of students' statements when proposing alternative teaching strategies. The construct of coherency evolved during our attempts to analyze pre-service teachers' interpretations of the critical events they identified while observing mathematics lessons as part of their preparation program. In this paper, we elucidate the construct of coherency and its different levels and demonstrate how this construct relies upon and expands existing ideas from the literature on noticing. We propose a framework for identifying different coherency levels and the different patterns identified when using the framework to noticing among the pre-service teachers. Some of these patterns are supported by previous research, while others were unanticipated. We explore possible explanations for the emergence of these unanticipated patterns. [ABSTRACT FROM AUTHOR]

Learning to name and notice students' mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students' mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students' mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students' mathematical strengths. The paper concludes with implications for future research in teacher education. [ABSTRACT FROM AUTHOR]

Research in mathematics education has placed significant emphasis on teacher identity, particularly during teacher education, since it plays a critical role in shaping the identity of preservice teachers with regard to teaching mathematics. However, as teacher identity is context dependent, it is essential to study preservice teachers' identities in various contexts to develop expertise in mathematics teacher education. This study explored the transformation of preservice mathematics teachers' (PMTs) teacher identity orientations after participating in a video club. Concentrating on task perceptions as the indicator of teacher identity, the change in the teacher roles that PMTs would like to adopt in the future and the student outcomes they associated with these roles were investigated. The analysis of teacher identity orientations before and after participating in the video club revealed that PMTs' teacher identity orientations were transformed by their participation because the video club increased their self-awareness and understanding of the complexity of teaching mathematics. The most noticeable transformation was observed in the didactical roles and their associated outcomes. These roles were transformed from being a didactical expert aiming to develop students' affective outcomes to being a didactical expert who prioritizes students' cognitions. Although PMTs' expertise in teaching mathematics and the content of the video cases limited their orientations, the video club can simulate alternative experiences for teacher education programs aiming to support PMTs' teacher identity orientations. [ABSTRACT FROM AUTHOR]

Background: Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another. Aims: Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics. Sample(s): We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects. Methods: Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied. Results: In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains. Conclusions: Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain. [ABSTRACT FROM AUTHOR]

The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication and division with justification, assisting fictional students to work through their difficulties and helping them to justify their reasoning. Such tasks allow for the examination of the prospective teacher moves to support student reasoning through their imagined action and choice of words. Scripts from forty-one prospective primary teachers were examined for the study, and five clusters based on the type of teacher move for supporting student reasoning were found. Overall, the prospective teachers emphasized the elicitation and facilitation of students' ideas. The cluster analysis, however, provided a nuanced examination of the cohort's teacher moves. While cluster one saw the highest incident of eliciting teacher moves, albeit only in the low potential category, clusters two and three mostly used facilitating teacher moves, but varied in their use of high and low potential moves. Cluster four concentrated moves on facilitating, eliciting, and responding to student reasoning. Cluster five employed teacher moves from all main categories, with some instances of high potential moves in all categories except extending student reasoning, which can better support reasoning. The prospective mathematics teachers' scripts and the five clusters that were found during analysis are discussed with implications for future teacher education and the support of building mathematical reasoning. [ABSTRACT FROM AUTHOR]

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Definitions are an integral aspect of mathematics. In particular, they form the backbone of deductive reasoning and facilitate precision in mathematical communication. However, when multiple non-equivalent definitions for the same term exist, their ability to serve these purposes can be called into question. While ambiguity can be productive, the lack of an agreed upon definition can make the truth value of certain mathematical statements unclear. In this study, we presented pre-service and in-service mathematics teachers with three mathematical claims in which definitional ambiguity was a consideration; then, we asked them to determine the correctness of each claim, justify their positions, and anticipate what reasoning might lead to a possible counterargument. Based on their responses, we identified several factors that influenced the participants' approaches in each situation as well as cross-cutting themes that describe their considerations. Finally, we consider the pedagogical implications of employing such a task in teacher preparation programs and in-service teacher education. [ABSTRACT FROM AUTHOR]

The paper is a reflection on the author's work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author's students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. [ABSTRACT FROM AUTHOR]

Well-written curriculum materials are known to support teacher learning. Less discussion has focused on whether teachers' guides, curriculum materials written specifically for teachers by textbook publishers, provide sufficient support. In this study, I analyse four US-based mathematics teachers' guides to understand the opportunities within them for teacher learning. Drawing on positioning theory, I conceptualised teacher learning opportunities as teacher positionings observable from teachers' guides. With this conceptualisation, I explored teacher positionings that were regularly or idiosyncratically observable from the selected teachers' guides. The results revealed only a small number of regularly observable positionings existed, indicating limited opportunities for teacher learning from the guides. Irregularly, or idiosyncratically observed positionings provided limited opportunities, as well. Based on the findings, I suggest the necessity of presenting diverse positionings to best utilise the potential from teachers' guides as materials for teacher learning. [ABSTRACT FROM AUTHOR]