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This study investigated the underexplored topic of teacher preparation program admissions processes by interviewing faculty and analyzing program documents. We investigated how 31 K-12 mathematics and science teacher preparation programs (MSTPPs) and faculty attend to diversity, equity, inclusion, and social and racial justice (DEIJ). Specific foci included applicant recruitment and selection, components of applications (e.g., forms, essays, and interviews), and how applicants' DEIJ-related information and orientations factor into admissions. We found that all MSTPPs participating in the study collected information related to DEIJ (e.g., applicants' ethnoracial backgrounds, citizenship), and all interviewed faculty expressed an interest in increasing the diversity of applicants and admitted students. Faculty expressed preferences for applicants who evidenced positive DEIJ orientations, such as recognizing social and ethnoracial injustices, but at the same time, differences were evident in how MSTPPs and faculty attended to DEIJ. Considerations, implications, and dilemmas for teacher preparation programs and faculty are discussed. [ABSTRACT FROM AUTHOR]

This qualitative study examines the information collected about applicants to mathematics or science teacher preparation programs (MSTPPs) and how university faculty perceive and value this information in admissions decisions. Based on document review and interviews with MSTPP faculty and admissions directors, we found that broad measures of mathematics and science content background (e.g., achievement test scores, past mathematics and science courses taken) were used more frequently than information on applicants‐specific mathematics and science content knowledge and dispositions. In many cases, application components (such as interviews and personal essay statements) were perceived by faculty to be conducive to surfacing applicants‐content knowledge and dispositions; however, they were not constructed or employed in a way that afforded the obtainment of this information. We highlight salient examples of MSTPPs‐collection and use of information related to mathematics and science and discuss implications for TPP admissions processes. [ABSTRACT FROM AUTHOR]

STEM education should be grounded in our knowledge of how students think in STEM‐focused learning environments. However, little is currently known regarding specific types of thinking in these contexts. We explore the theoretical notion of STEM Ways of Thinking (SWoT) in interdisciplinary learning situations. Our primary focus is not on the curricular content of STEM education, but rather on the nature of the cognitive activity at play during STEM‐focused activity. We give particular focus to students' claim making and reasoning during interdisciplinary STEM activity. Our framework focuses on the disciplines of science, engineering, and mathematics. While these disciplines have vastly different practices and epistemologies, we argue that claim making and reasoning provide an avenue for considering student thinking at their intersections. A brief literature review of SWoT is provided that illustrates trends and limitations amongst current theories and studies. After a detailed discussion of our own theoretical perspective of SWoT, we provide an illustrative learning segment to explore the explanatory and analytic power of our theoretical perspective. Implications of our work on curriculum and instruction are provided. [ABSTRACT FROM AUTHOR]

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities from multiple courses in the program, we offer general principles of instruction for supporting mathematical inquiry at all grade levels. We contend that an awareness and application of the multiple facets of mathematical knowledge for teaching can be critical to supporting mathematical inquiry across the K-16 spectrum. [ABSTRACT FROM PUBLISHER]

We describe and analyze a professional development (PD) model that involved a partnership among science, mathematics and education university faculty, science and mathematics coordinators, and middle school administrators, teachers, and students. The overarching project goal involved the implementation of interdisciplinary STEM Design Challenges (DCs). The PD model targeted: (a) increasing teachers' content and pedagogical content knowledge in mathematics and science; (b) helping teachers integrate STEM practices into their lessons; and (c) addressing teachers' beliefs about engaging underperforming students in challenging problems. A unique aspect involved low-achieving students and their teachers learning alongside each other as they co-participated in STEM design challenges for one week in the summer. Our analysis focused on what teachers came to value about STEM DCs, and the challenges in and affordances for implementing DCs. Two significant areas of value for the teachers were students' use of scientific, mathematical, and engineering practices and motivation, engagement, and empowerment by all learners. Challenges associated with pedagogy, curriculum, and the traditional structures of the schools were identified. Finally, there were four key affordances: (a) opportunities to construct a vision of STEM education; (b) motivation to implement DCs; (c) ambitious pedagogical tools; and, (d) ongoing support for planning and implementation. This article features a . Please click on the supporting information link below to access. [ABSTRACT FROM AUTHOR]

Two related case studies of secondary mathematics teachers examine the roles and conditions helpful in initiating, directing, and/or supporting teachers' own professional development. Using multiple data sources from school-based and professional settings, we applied analytic induction to identify patterns of similarities and differences in teachers' experiences and developmental trajectories. Findings revealed how the teachers served as brokers in their own development process and how attitude, attention, and awareness played important roles in teacher learning. As the teachers initiated learning processes, they demonstrated awareness of broader educational contexts that support learning by identifying external policies and priorities that aligned with teachers' attitudes. They then used these external priorities as boundary objects to broker for teachers' learning, including other teachers' learning. They attended to learning needs in directing a plan for learning activities, rather than using externally mandated goals for changing practice (e.g., an external focus on improving students' tests scores). These cases suggest that in structuring professional learning, opportunities to self-identify learning needs should be part of the process, and external supports can become more powerful when teachers play a brokering role in relating these supports to their immediate contexts. Further implications for professional development processes are explored. [ABSTRACT FROM AUTHOR]

This article measures and discusses six teacher groups’ (a) time spent working with data and (b) time devoted to particular kinds of inquiry activities, and explores various contextual factors that influence these results. The authors make use of a framework useful in describing and analyzing the stance taken by teachers when they engage with student-learning data. Their findings suggest that most teacher groups spend the vast majority of their time collecting and analyzing data, with little time devoted to exploring potential data sources and reflecting on implications of their data analysis. Furthermore, “time on task” is less important than stance in determining the nature of the inquiry activity. Implications of these results are explored. [ABSTRACT FROM PUBLISHER]

Background/Context: Schools and districts are increasingly emphasizing evidence-based decision making as a means for improving teaching and learning. In response, professional development efforts have shifted toward situated, sustained activities that involve groups of teachers in reflective inquiry about student-learning data, instructional practices, and curricular goals. Although strong evidence exists regarding the benefits of looking at student work, there is little research that investigates how teachers might work together to attain these benefits. Classroom teachers often lack the necessary skills and supports to enact data-based inquiry in a manner that informs and influences classroom practices. Purpose/Objective/Research Question/Focus of Study: In response to a need for specific frameworks to support teachers' collaborative interactions around student-learning data, we have developed a conceptual framework for describing and characterizing key influences on teachers' actions and interactions. The purpose of this article is to fully describe the two dimensions that constitute the framework, illustrate them with examples from multiple cases, and discuss potential implications of the framework on research and practice. Population/Participants/Subjects: This framework was developed from multiyear case analyses of seven professional learning communities (PLCs). The teachers in these PLCs were secondary science and mathematics teachers who were supported by a 3-year professional development project. Research Design: We began to derive this conceptual framework using constant comparison in the development of semiannual case studies. Preliminary results and hypotheses on the specific ways in which teacher groups were interacting as they worked with student-learning data led to the need to better conceptualize what was occurring. Building on others' work related to stance, we used grounded theory methods to construct and refine this framework. Findings/Results: A detailed framework and examples are provided regarding collaborative teacher inquiry groups' inquiry stance along two dimensions: (1) their epistemological stance toward student-learning data, and (2) the nature of their dialogue when using these data in their inquiry process. The first dimension is delineated by four descriptive categories ranging from an improving to a proving stance; the second dimension ranges from sustained negotiation to no negotiation. Conclusions/Recommendations: This analysis of inquiry stance in a collaborative group is valuable in providing a detailed tool for empirical analyses of collaborative teacher development in the context of working with student-learning data. Additionally, it provides practical support for facilitators and school leaders by characterizing fundamental and often hidden influences on PLC processes and outcomes. [ABSTRACT FROM AUTHOR]

The article provides information on the efforts of mathematics teachers to improve their students' mathematical engagement, problem solving and learning. It also presents specific suggestions for supplementing existing curriculum with various mathematics tasks. As part of their initiative plan, the authors agreed to participate in the three-year Partnership for Reform in Secondary Science and Mathematics (PRiSSM) project. Furthermore, they were interested in the increasingly popular use of professional learning communities (PLC) as well as other collaborative teacher development models.

Background/Context: The type of professional development provided for teachers has been undergoing change from a one-time workshop approach to a more embedded, long-term, reflective, and collaborative structure. Although findings on the impact of new forms of professional development (PD) are beginning to emerge in the literature, there is little research on the professional development of those who design and support these PD efforts. Purpose/Focus of Study: To better understand how to support secondary teachers' engagement in collaborative inquiry, a group of 12 professional development providers deliberately set out to use the same processes and structures in their development and implementation of a PD model. This research examines what this group learned about fostering and sustaining a culture of collaborative inquiry and considers how this can inform PD providers' support of teachers' engagement in a collaborative inquiry cycle. Research Design: A narrative case study design was used to examine the evolution of the professional development group from its inception in March 2004 through December 2005, halfway through the project's duration. The particular timeframe was targeted to explore the developmental phase of the group and critical decisions that shaped the group structure and direction. Data Collection and Analysis: Traditional qualitative data sources were collected and analyzed in the construction of the narrative, including interviews with the professional developers, archived documents, and video and audio recordings of meetings. Conclusions/Recommendations: The PD group's focus on how to foster and sustain a culture of collaborative inquiry provides insights into the structures and processes that support this kind of collaborative endeavor. Assuming an inquiry stance toward the work was challenged by the ongoing business of implementing a large-scale project and the demands of people's other work in school districts and universities. Difficulties related to communication between and during meetings also occurred. An explicit reliance on collaborative norms and explicitly using processes such as dialogue structured by protocols, distributing leadership responsibilities, and co-constructing an inquiry focus based on data analysis helped the group develop and maintain an inquiry stance. These findings inform the support of teachers undertaking collaborative inquiry for professional growth. [ABSTRACT FROM AUTHOR]

This article presents five case studies of grade six to grade eight science and mathematics teachers engaged in supported collaborative inquiry. The research focus is on teachers’ growth trajectories related to their participation in professional learning communities supported through a professional development project. There were noticeably different trajectories in the teachers’ progress through the inquiry cycle and a variation in the degree of collaboration in different professional learning communities. Some of the successes and challenges are attributed to the cross-grade, cross-disciplinary nature of the collaboration; others to teachers’ existing relationships with each other prior to the beginning of this professional development project. The case study data indicate that dialogic inquiry grounded in classroom-based data is a key element in teachers’ professional growth. [ABSTRACT FROM AUTHOR]

Discusses the significance of improving the writing prompts for improving student reflection on mathematics in a middle school in Washington. Development and use of writing prompts; Use of the Connected Mathematics Project curriculum and textbook series; Scores of the students before and after the writing responses; Implications for classroom practice.

Presents information on a study that described an instructional approach incorporating simulations and classroom discussions in a differential equations course and the subsequent effects in student learning attitudes and outcomes. Methodology of the study; Results and discussion on the study.

Focuses on middle school algebra education. Overview on algebra as generalized arithmetic; Utilization of the difference of squares; Challenges to developing algebraic understanding in middle school students.

As attention to the development of algebraic understandings at early grade levels increases, theory and empirical support for these efforts are needed. This paper outlines a theoretical perspective for studying student understandings of mathematical operations, with a particular focus on addition. The notion of operation sense is defined using a perspective that incorporates the construction of mental objects. In the context of addition, it is argued that operation sense can be used to describe student development of additive concepts as well as transitions into algebraic ways of thinking. The report of a case study on the development of a young boy is then provided. The investigation attempts to instantiate the framework in regard to student development of an understanding of addition. Evidence was found that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking, including a finite group setting and use of addition on unknown and arbitrary quantities. Limitations of the framework are discussed. [ABSTRACT FROM AUTHOR]

Determines the effect of lateral osteotomy with infracture or outfracture on valve cross-sectional area in both patients and a cadaver. Two parts of the study; How the clinical evaluation was performed on three patients; Case reports on patients with nasal obstruction.

Discusses the sequence of activities in teacher-preparation courses concerning geometric congruence and similarity at Washington State University in Pullman, Washington. Planning and creation of the instruction; Investigation made on the different types of triangles; Assessment of the activity.

This paper presents an alternate perspective for utilizing the action/process/object framework when discussing student development of conceptions of function. After a review of related theories, a property-oriented view of function is described which is based on visual aspects of functional growth. The theory is supported with data on student learning. The property-oriented view of function incorporates and extends previously described frameworks used in analyzing functional understandings, including the covariance and correspondence views (Confrey & Smith, 1991; Thompson, 1994). The property-oriented view differs from the covariance view in that less emphasis is placed on the manner in which the variables are changing and more emphasis is placed on the properties that result from these changes. The property-oriented view differs from a correspondence view in that functional properties such as invertibility and domain give rise to a different kind of thinking about functions than do properties such as symmetry, linearity, continuity, etc. Implications for further research and curriculum development are also provided. [ABSTRACT FROM AUTHOR]

Collaborative inquiry groups, such as professional learning communities and lesson study groups, are proliferating in schools across the United States. In whatever form, the potential for impacting student learning through this collaborative work is expanded or limited by the nature of teachers’ conversations. Polite, congenial conversations remain superficially focused on sharing stories of practice, whereas collegial dialogue probes more deeply into teaching and learning. Examples of talk taken from collaborative teacher inquiry groups are used to illustrate these important differences. Specific recommendations are provided, including the role that teacher leaders can play in adopting and modeling specific strategies that support the use of more substantive professional conversation. [ABSTRACT FROM AUTHOR]