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Four case studies of preservice teachers enrolled in a STEM-focused elementary teacher preparation program are used to document changes in mathematics and science teaching efficacy over the course of one academic year. Qualitative analysis revealed that all four case studies experienced changes in their mathematics and science teaching efficacy beliefs over the course of the year. Participants described unique ways of understanding their growth (or lack thereof) in teaching efficacy, the trajectory of teaching efficacy over the course of the year, and the role of teacher training in changing their efficacy beliefs.

This study investigated developmental trajectories of novice elementary "teachers' efficacy beliefs" (i.e., personal teaching efficacy and outcome expectancy) and their "mathematical knowledge for teaching" (MKT). Overall, study findings indicated growth in participants' personal efficacy beliefs and in various assessments for dimensions of MKT. Additional relationships between participants' MKT trajectories and their mathematics efficacy beliefs trajectories were found. Findings from our study can help teacher educators, researchers, and school leaders in better understanding how novice teachers develop their MKT and their teaching efficacy beliefs during the teacher education program and in their first years of teaching.

This research explores the frequency and nature of mathematics-specific feedback given to elementary student teachers by university supervisors across a collection of post-lesson observation forms. Approximately one-third of the forms (n = 250) analysed from five large universities had no comments related to mathematics. Forms that did have mathematics-specific feedback varied in terms of the number of summary, strength, and suggestion (i.e., type) comments and in the pedagogical focus (e.g., tasks, discourse) of those comments. Chi-square tests of independence indicated the frequency of forms with mathematics-specific feedback differed significantly by university. Results of additional Chi-square tests showed significant interactions between the type of comments and university and between the pedagogical foci of the comments and comment type. Contributing factors and implications, including connectedness of the university supervisors to the programs, professional development provided to university supervisors, and the organisation of the forms, are discussed.

The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which "standards-based mathematics teaching practices" were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the affordances and limitations of the M-Scan in capturing standards-based mathematics teaching. We organize the affordances and limitations into three categories: the operationalization of the M-Scan, the organization of the M-Scan, and the M-Scan within the larger ecology of instruction. Our analysis indicates the M-Scan differentiates among lessons in their use of "standards-based mathematics teaching practices" by operationalizing the M-Scan dimensions at the lesson level, sometimes at the expense of capturing the peaks and valleys within a single lesson. Simultaneously, the analysis revealed how the application of the rubrics may be impacted by lesson transcripts. We discuss the theoretical organization of the M-Scan and its implications for researchers and practitioners applying the rubrics. Finally, we point to the affordances and limitations of the M-Scan within the larger ecology of instruction by considering curricular issues and two dimensions of instruction not highlighted by the M-Scan.

The purpose of this study was to investigate the relationship between prospective teachers' (PTs) instructional practises and their efficacy beliefs in classroom management and mathematics teaching. A sequential, explanatory mixed-methods design was employed. Results from efficacy surveys, implemented with 54 PTs were linked to a sample of teachers' instructional practises during the qualitative phase. In this phase, video-recorded lessons were analysed based on tasks, representations, discourse, and classroom management. Findings indicate that PTs with higher levels of mathematics teaching efficacy taught lessons characterised by tasks of higher cognitive demand, extended student explanations, student-to-student discourse, and explicit connections between representations. Classroom management efficacy seems to bear influence on the utilised grouping structures. These findings support explicit attention to PTs' mathematics teaching and classroom management efficacy throughout teacher preparation and a need for formative feedback to inform development of beliefs about teaching practises.

The Instructional Practices Log in Science (IPL-S) is a daily teacher log developed for K-5 teachers to self-report their science instruction. The items on the IPL-S are grouped into scales measuring five dimensions of science instruction: "Low-level Sense-making," "High-level Sense-making," "Communication," "Integrated Practices," and "Basic Practices." As part of the current validation study, 206 elementary teachers completed 4137 daily log entries. The purpose of this paper is to provide evidence of validity for the IPL-S's scales, including (a) support for the theoretical framework; (b) cognitive interviews with logging teachers; (c) item descriptive statistics; (d) comparisons of 28 pairs of teacher and rater logs; and (e) an examination of the internal structure of the IPL-S. We present evidence to describe the extent to which the items and the scales are completed accurately by teachers and differentiate various types of science instructional strategies employed by teachers. Finally, we point to several practical implications of our work and potential uses for the IPL-S. Overall, results provide neutral to positive support for the validity of the groupings of items or scales.

The purpose of this qualitative study was to investigate the contributions of pre-service teachers' memories of science and science education, combined with their experiences in a STEM-focused teacher preparation programme, to their developing identities as elementary school teachers of science. Data collected over three years include a series of interviews and observations of science teaching during elementary teacher preparation and the first year of teaching. Grounded within a theoretical framework of identity and using a case-study research design, we examined experiences that contributed to the participants' identity development, focusing on key themes from teacher interviews: "memories of science and science instruction," "STEM-focused teacher preparation programme," "field experiences," "first year of teaching," and "views of effective science instruction." Findings indicate the importance of exposure to reform strategies during teacher preparation and are summarised in main assertions and discussed along with implications for teacher preparation and research.

This study examined preservice elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course focused on grades 3-5. The preservice teachers (n = 48) completed an assessment before and after the course's unit on the teaching and learning of fractions. Specifically, the preservice teachers were asked to explain why the traditional algorithms for multiplication and division of fractions work. Additionally, they were asked to identify errors in students' work and provide rationales for why the strategies were faulty. All responses on the pre- and post-assessments were coded using an existing framework for the assessment of understanding. Paired t-tests indicated a statistically significant improvement on most items on the assessment and on the total test score. However, an in-depth analysis of how the scores changed gave insights into the proportion of preservice teachers who demonstrated no change, improvement, or regression on each question. The percent of teachers improving on each question ranged from 33% to 46%. Implications for mathematics teacher education programs and future research are discussed.

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the presentation of two teaching vignettes, we highlight key features of mathematics instruction that seem to differentiate students' OTL. These features are nested under four key dimensions in our OTL framework: "the teacher's mathematical knowledge for teaching" ("MKT"), how "time" is utilized in the lesson, the mathematical "tasks" implemented with students, and the nature of the mathematical "talk" in which students engage. We discuss implications for the use of the framework as well as its shortcomings.

The work of instructional coaches, both general and discipline-specific, has become increasingly important as more schools rely on their leadership for improvements in teaching and learning. Much of their work hinges upon their effective communication with teachers and school administrators. This article outlines five practices for instructional coaches to use in order to achieve and maintain effective communication; these five practices draw upon the author's prior work as an instructional coach and upon her own research. The practices are presented by sharing the voices of three mathematics instructional coaches, their teacher colleagues, and their school administrators.

Equality is such an important concept for children to develop. In this article it is argued that a precise definition is needed to ensure that students are provided with a consistent "picture" of what it is that equality really means.

There has been a spike in negative comments about mathematics and standards since the implementation of the Common Core State Standards. Regardless of whether the comments are fueled by social media or traditional media, educators need to be armed with strategies for helping parents understand, navigate, and embrace the Common Core's mathematics content and practices. In this article, the author outlines three strategies and accompanying action steps that can help school leaders and teachers to be proactive rather than reactive when addressing parent concerns about the Common Core math standards. While the examples in this article are embedded in elementary mathematics, the strategies and action steps apply to all K-12 settings.

To address shortfalls in the preparation and achievement of U.S. students in STEM fields (science, technology, engineering, and mathematics), instruction in these areas must begin in the elementary grades, as early as kindergarten (American Association of Colleges for Teacher Education, 2007; Natural Academy of Sciences, 2007; National Research Council, 2000). The urgent need for improvement in the teaching of STEM content to young children led one university in the Southeast to create a STEM-focused elementary teacher preparation program. This exemplary program--called ATOMS (Accomplished Teachers of Mathematics and Science)--is characterized by four key features: program coherence; rigor in the general education program; innovative, conceptually focused methods courses; and extensive fieldwork aligned with coursework. This article describes the features of this highly scalable program in detail, illustrated through participant reflections and contextualized in the research literature on effective teacher education programs.

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to improve their practice. To address this problem, the Mathematics Scan (M-Scan), an observation tool to measure the quality of mathematics instruction, was developed. To introduce educators (including teachers, mathematics specialists, instructional coaches, and administrators) to the M-Scan framework, the authors first describe the development of the M-Scan. Next, they outline the eight dimensions of classroom instruction in the M-Scan that comprise a high-quality mathematics lesson and describe a model lesson to make the framework and its dimensions concrete. Finally, they summarize the M-Scan dimensions in a table that can be used for reflection after a lesson, making suggestions for how to integrate dimensions of the M-Scan into daily practice. (Contains 2 tables.)