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Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169–202.) professional noticing of students' thinking framework to guide the design and analysis of prospective secondary mathematics teachers' (PSMTs) noticing of high school students' thinking on two geometry tasks: a paper and pencil task and a technology task. High school students' written work and a video clip were shared as the artifacts from which to notice for each task. PSMTs responded to a set of noticing prompts to capture how they were attending, interpreting, and deciding to respond to students' thinking for each task. Their written responses to these questions were then open coded for each noticing component and codes from each task were compared to reveal any differences in the content of PSMTs' noticing across task types. Results revealed differences between tasks for each component skill of noticing. Implications of these findings for mathematics teacher educators and future research are discussed. [ABSTRACT FROM AUTHOR]

Increasing demand for high‐quality STEM education calls for the formation and retention of effective educators with STEM expertise; yet endeavors to meet this demand require organizational structures and supports that can overcome the lack of collective understanding around STEM education, limited STEM knowledge by leadership, and mounting teacher attrition. STEM teacher leadership is one mechanism for addressing this challenge by empowering excellent classroom teachers with opportunities to institutionally shape STEM learning, without extracting them from their instructional role. This paper offers a STEM teacher leadership framework that targets teachers' identity development toward an equity‐focused, transformational STEM teacher leader. First, we examine the field of teacher leadership (both STEM‐specific and generally) to provide a foundation for the areas of potential impact by STEM teacher leaders, as well as dispositions and stances that support their emergent leadership. Complementing the literature, we explore and elevate aspiring STEM teacher leaders' perspectives, drawn from baseline surveys and interviews of a multi‐year professional development program for middle grade teachers in STEM disciplines. The framework, iteratively informed by these sources, includes our stance on equity in STEM education, eight dispositions, and four domains of knowledge and practices that shape STEM teacher leadership in K‐8 school settings. [ABSTRACT FROM AUTHOR]

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted. [ABSTRACT FROM AUTHOR]

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

Recent research demonstrates that mathematics teachers rely on a variety of curriculum materials and must make meaning and synthesize these materials for use in a particular place with particular students. While there are multiple theories about the nature of this work and the factors which influence this work, the field continues to lack a theoretical basis with which to understand this multifaceted and complex work. This paper seeks to illuminate the process by which teachers come to make meaning from curriculum materials by the daily practices of one team of teachers. Findings supports a transactional view of curriculum in which students, teachers, curriculum materials, and contexts work with and on each other as curriculum emerges. Using this theory as a framework, multiple understandings of teachers' work with curriculum can be synthesized as highlighting particular aspects of a larger curriculum system. [ABSTRACT FROM AUTHOR]

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific mathematical concept. The present study examined third grade teachers' reported use of visual representations for teaching multiplication and division. Findings indicate prevalent use of discrete models and infrequent use of continuous models. Length models and number lines are rarely used across all Common Core standards focusing on multiplication/division, with numeric‐only representations being reported frequently across all standards. Groups‐of and array models were the most prevalent visual model reported by third grade teachers. Although teachers report higher degrees of access to certain materials than previous reports on manipulative use, interview data suggests this may have more to do with purchase agreements between school districts and textbook companies than pedagogical preferences of classroom teachers. Supporting findings in prior decades, teachers in the present study report prevalent use of flashcards, charts and grid paper, and variations of counters. [ABSTRACT FROM AUTHOR]

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic elementary mathematics classrooms. Findings indicated that two of the three components of professional noticing (attending and interpreting) showed statistically significant increases in a treatment group that did not occur in a comparison group. The deciding component remains a challenge that warrants further research. [ABSTRACT FROM AUTHOR]

STEAM, where the 'A' represents arts and humanities, is considered a transdisciplinary learning process that has the potential to increase diverse participation in science, technology, engineering, and math (STEM) fields. However, a well-defined conceptual model that clearly articulates essential components of the STEAM approach is needed to conduct empirical research on STEAM's efficacy-in particular, the teaching content that should be considered when enacting STEAM teaching practices. This paper proposes a conceptual model of STEAM, providing educators with the opportunity to teach effectively using transdisciplinary inquiry. The instructional content domain of the model includes problem-based delivery, discipline integration, and problem-solving skills. [ABSTRACT FROM AUTHOR]

This paper brings together research on slope from mathematics education and research on line of best fit from statistics education by considering what knowledge of slope students transfer to a novel task involving determining the placement of an informal line of best fit. This study focuses on two students who transitioned from placing inaccurate to accurate lines of best fit during a task-based interview. The analysis focuses on describing shifts in slope reasoning that accompanied the change to accurately placed lines, and investigates factors that may have influenced the shift in reasoning. The results have implications for the teaching of both slope and the line of best fit. [ABSTRACT FROM AUTHOR]

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth-grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry-based experiences, fewer student-to-student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district. [ABSTRACT FROM AUTHOR]

This paper summarizes and integrates the lessons learned from the last decade of professional development efforts based on the standards of the National Council of Teachers of Mathematics (1989, 1991, 1995). The fundamental challenges to such reform are identified, then the rest of the paper is dedicated to strategies that have been helpful in overcoming these obstacles. The challenges include both the teachers' views of mathematics and their image of teaching. The Immerse and Instill approach describes strategies that encourage teachers to implement standards-based teaching upon entering the teaching field (Immerse) as well as instilling some of the professional habits necessary to keep teachers and their students actively engaged (Instill). [ABSTRACT FROM AUTHOR]

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous. [ABSTRACT FROM AUTHOR]

Mathematics autobiographies have the potential to help teachers reflect on their identities as mathematics learners and to understand their role in the development of their students' mathematics identities. This paper reports on a professional development project for K-2 teachers ( n = 41), in which participants were asked to write mathematics autobiographies. Using an adaptation of an existing framework for characterizing teachers' mathematics stories, we describe the consistencies among the participants' experiences as mathematics learners and the events that are identified as being the impetus for a transition from a negative to a positive attitude toward mathematics. Implications for both teachers and teacher educators are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States ( N= 89) and Taiwan ( N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple-choice test items. The items were categorized into four different types of fundamental fraction constructs, including part-whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings. [ABSTRACT FROM AUTHOR]

In spite of repealed reform efforts, there is research and data that suggest that teachers lack the needed knowledge to successfully teach elementary mathematics. Some argue that teachers lack the needed content knowledge while other argue that a lack of confidence and practice are impacting teachers `ability to successful leach mathematics. As a result of these issues, this paper looks at the impact of a service-learning experience on pre- service teachers' confidence and preparation in the area of mathematics. The service-learning experience had a number of intended and unintended outcomes. As a result of the service-learning experience. pre-service teachers noted increased understanding, innovation and confidence in the area of mathematics. [ABSTRACT FROM AUTHOR]

When worthwhile mathematical tasks are used in classrooms, they should also become a crucial element of assessment. For teachers, using these tasks in classrooms requires a different way to analyze student thinking than the traditional assessment model. Looking carefully at students' written work on worthwhile mathematical tasks and listening carefully while students explore these worthwhile tasks can contribute to a teacher's professional development. This paper reports on a professional development activity in which teachers analyzed mathematical tasks, predicted students' achievement on tasks, evaluated students written work, listened to students' reasoning, and assessed students' understanding. Teachers' engagement in this way can help them develop flexibility and proficiency in the evaluation of their own students' work. These experiences allow teachers the opportunity to recognize students' potential, strengthen their own mathematical understanding, and engage in conversations with peers' about assessment and instruction. [ABSTRACT FROM AUTHOR]

In this paper a framework is proposed for analyzing the deliberate actions taken by a teacher to participate in or influence the discourse in mathematics classrooms, and such actions are referred to as the teacher's discourse moves. This work synthesizes elements of several other discourse frameworks, including those of Richards, Sfard, Cobb, and Knuth and Peressini. Expanding on the improvisational dance metaphor of Heaton's, the framework views the teacher in the additional multiple roles as a Choreographer/Stage Manager/Director of classroom discourse. Several research applications of the discourse framework to collegiate mathematics education are discussed, including discourse around collaborative problem solving in Treisman Emerging Scholars workshops, a video-based study of a college-level geometry course for teachers, discourse in wireless networked classrooms, and the asynchronous discourse in an online statistics course. [ABSTRACT FROM AUTHOR]

Induction programs play a critical role in the development of professional educators. While induction programs are a necessity for all beginning teachers, science teachers need carefully crafted programs that meet their unique needs. This paper reports the barriers and pathways that were experienced during a 3-year period when an induction program was developed and implemented for secondary science teachers. This information is provided to assist future university, college, or school district induction program developers. [ABSTRACT FROM AUTHOR]

The article offers information on various research papers published within the issue including one on underrepresented students in outreach programs, one on students' and teachers' attitude in learning science and mathematics and one on preservice elementary teachers.