Formative assessment and the role of teachers' content area

Professional development (PD) programs focused on increasing teachers' use of formative assessment generally provide a framework designed to help teachers understand the breadth and complexity of formative assessment, while advocating for teacher choice with respect to the specific implementation. This study examined the implementation patterns of 82 high school mathematics and science teachers to understand whether implementation approaches differed by content area. Results suggested that mathematics and science teachers significantly increased their self‐reported practice of formative assessment, in similar ways; however, the specific approaches that mathematics and science teachers chose to operationalize on a daily basis differed. These findings have implications for the design of PD and future research efforts.     

The Indiana Science Initiative: Lessons from a Classroom Observation Study

The Indiana Science Initiative (ISI) is a systemic effort to reform K–8 science education. The program provides teachers with professional development, reform‐oriented science modules, and materials support. To examine the impact of the initiative's professional development, a participant observation study was conducted in the program's pilot year. Five teachers in grades 3–6 were observed and interviewed as they implemented the ISI‐provided modules. Analysis of the observation data revealed that the teachers incorporated each of the features of inquiry science instruction. However, they did not consistently teach in a way that was aligned with the intent of the ISI. Examination of interview data provided insight into influences on teachers' use of inquiry with the ISI‐provided modules. These data revealed that teachers were aware of the intent of the ISI and attempted to align their instruction. However, teachers were influenced by their perceptions of students' behavior and abilities as well as timing and the appropriate level of teacher control needed to facilitate science instruction. The research suggests that professional development activities should prepare teachers to help learners evaluate explanations against alternatives, connect explanations to scientific knowledge, and provide strategies to address teachers' perceptions of students, timing, and teacher control.     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations? (c) How do the participants draw upon these perspectives when designing a lesson? The participants identified five characteristics that are needed for realistic contexts: providing entry points to mathematics, using “catchy” and “youthful” contexts, selecting personal contexts for the students, using contexts that are not “too fake” or “forced,” and connecting to the lesson's mathematical content. These characteristics largely relate to the institutional, interpersonal, and individual obligations with some connections with the disciplinary obligation. The participants considered these characteristics when identifying a realistic context for a problem‐based lesson. The context promoted mathematical connections. In addition, the teachers varied the context to increase the relevance for their students. The study has implications for supporting teachers' implementation of problem‐based instruction by attending to teachers' perspectives regarding the obligations shaping their work.     

Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert‐scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open‐ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.     

Rural teacher leadership in science and mathematics

This study adds to our understanding of science and mathematics teacher leadership in rural schools. Through In Vivo and Concept coding of teacher interviews, we investigated 20 secondary science and mathematics teachers' perceptions of rural teacher leadership during their participation in a three-year professional development program. As the teachers developed as teacher leaders, they broadened their focus from improving their own students' learning to sharing new knowledge learned through the program with other teachers both informally and formally. We compared our program components to the Teacher Leader Model Standards and added an emphasis on the importance of disciplinary content knowledge. We also identified patterns in science and mathematics teacher leadership that are contextually connected to teachers' instruction in rural high poverty schools. Rural teacher leadership included the importance of building strong teacher–student relationships, providing new academic opportunities for students, encouraging students' success, and building community connections.     

Conditions and decisions of urban elementary teachers regarding instruction of STEM curriculum

The study was situated in a National Science Foundation supported Math Science Partnership between a private university and an urban school district. This study sought to understand the decision‐making process of elementary teachers as they implement an integrated science, technology, engineering, and mathematics (STEM) curriculum in their classrooms and the interactions that occur between the teachers and curriculum during that process. This qualitative study utilized a comparative case study approach to understanding the decision‐making process of three elementary teachers enacting the same lesson. Analysis of the interactions revealed that the teachers' perceptions of student ability, their pedagogical design capacity, and time were influences that impacted implementation. These findings have implications for STEM‐focused professional development of elementary teachers.     

A High‐Quality Professional Development for Teachers of Grades 3–6 for Implementing Engineering into Classrooms

With the increasing emphasis on integrating engineering into K‐12 classrooms to help meet the needs of our complex and multidisciplinary society, there is an urgent need to investigate teachers' engineering‐focused professional development experiences as they relate to teacher learning, implementation, and student achievement. This study addresses this need by examining the effects of a professional development program focused on engineering integration, and how teachers chose to implement engineering in their classrooms as a result of the professional development. 198 teachers in grades 3–6 from 43 schools in 17 districts participated in a yearlong professional development program designed to help integrate the new state science standards, with a focus on engineering, into their teaching. Posters including lesson plans and student artifacts were used to assess teachers' engineering practices and the implementation in their classrooms. Results indicated that the majority of the teachers who participated in the professional development were able to effectively implement engineering design lessons in their classrooms suggesting that the teachers' success in implementing engineering lessons in their classroom was closely related to the structure of the professional development program.     

Math Autobiographies: A Window into Teachers' Identities as Mathematics Learners

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.     

An Emergent Framework: Views of Mathematical Processes

The findings reported in this paper were generated from a case study of teacher leaders at a state‐level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine participants who were then interviewed and observed as they presented a session at the conference. Participants' statements revealed differences in their views of mathematical processes. The analysis led to an emergent framework for views of mathematical processes that includes three levels: participatory, experiential, and sense‐making. Implications are shared for mathematics methods instructors, professional learning, and research. Discussion also relates the framework to the Standards for Mathematical Practice.     

Using Teacher Portfolios to Enrich the Methods Course Experiences of Prospective Mathematics Teachers

This paper illustrates ways to employ teacher portfolios to improve the quality of methods course experiences for prospective mathematics teachers. Based upon research conducted in an undergraduate teacher preparation program, this case study describes how the author used teacher portfolios to mentor prospective teachers in new ways. The case describes the author's experiences through a case study of his assessment of and response to one prospective teacher's portfolio. This portfolio illustrated themes that were present in other teachers' portfolios, but did so in ways that highlighted strategies for change to the methods course. Through the lens of this teacher's portfolio the author identified specific ways that the prospective teacher's beliefs were impacting her teaching practice, a result that enabled him to better help all of the teachers in the methods course reflect on their teaching. By providing a detailed account of the feedback process that led to this result, this paper illustrates how mathematics teacher educators can use prospective teachers' portfolios to enrich the quality of their methods courses.     

Assessing Preservice Teachers' Beliefs about the Teaching and Learning of Mathematics and Science

With increased study of teachers' beliefs about science and mathematics teaching in recent years, there is a need for instruments that assess beliefs in both content areas. Moreover, early field experiences in schools and professional development efforts may influence the beliefs that preservice and in‐service teachers develop, and instruments for this purpose are limited. This article describes the development and validation of the Confidence, Commitment, Collaboration, and Student thinking in Mathematics and Science (CCCSMS) beliefs scales, a set of 10 six‐item scales. Collectively, these scales measure teachers' self‐confidence in doing and teaching science and mathematics, confidence in understanding children's thinking and building models of that thinking, commitment to teaching science and mathematics from a standards‐based perspective, and commitment to collaborating with peers. The scales represent an efficient and effective way of assessing beliefs of large groups. Although this article focuses predominantly on development of the scales, results from initial use indicate that there are positive correlations between beliefs related to mathematics and beliefs related to science, but the correlations are low enough to show that many teachers think differently about the two subjects.     

Self‐Directed Teacher Learning in Collaborative Contexts

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.     

Measuring K‐8 Teachers' Perceptions of Discourse Use in Their Mathematics Classes

This article documents the development and use of a survey instrument designed to measure K‐8 mathematics teachers ‘perceptions about discourse in mathematics classes. In particular, the 5‐point Likert‐type survey sought to address teachers ‘perceptions of their use of dialogic (dialogue to construct new meaning), univocal (conveying information), and general discourse in their mathematics classes. Factor analysis revealed three reliable factors that were compatible with the original constructs, these include: dialogic discourse (α₃= .67), univocal discourse (α₁= .83), and general discourse (α₂= .68). These results suggest a framework that could be used to uncover K‐8 teachers' perceptions of their use of discourse in mathematics instruction, especially if there is interest in tendencies toward univocal or dialogic discourse. In addition to research implications, the survey could be used to inform the design and implementation of teacher professional development that focuses on discourse in mathematics instruction.     

Teacher Mentoring as a Community Effort

This article presents the findings from a study of a mentoring program for novice mathematics and science teachers, which was provided by their teacher education program. This study reports the findings of interviews with novice math and science teachers, their mentors, and the mentoring program administrators to explore stakeholder perceptions of mentoring support. Findings suggest the importance of using multiple mentoring strategies to develop, support, and retain high‐quality math and science teachers in the teaching profession. This study contributes to what is known about the role that teacher education programs may play in mentoring novice math and science teachers who have graduated from their programs.     

Prospective Teachers' Perspectives on Mathematics Teaching and Learning: Lens for Interpreting Experiences in a Standards‐Based Mathematics Course

In a mathematics course for prospective elementary teachers, we strove to model standards‐based pedagogy. However, an end‐of‐class reflection revealed the prospective teachers were considering incorporating standards‐based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon, Tzur, Heinz, Kinzel, and Smith to examine the prospective teachers' perspectives on mathematics teaching and learning and to address two research questions. What perspectives on the learning and teaching of mathematics do prospective elementary teachers hold? How do their perspectives impact their perception of standards‐based instruction in a mathematics course and their future teaching plans? Qualitative analyses of reflections from 106 prospective teachers revealed that they viewed mathematics as a logical domain representative of an objective reality. Their instructional preferences included providing firsthand opportunities for elementary students to perceive mathematics. They did not take into account the impact of a student's conceptions upon what is learned. Thus, the prospective teachers plan to incorporate standards‐based strategies to provide active experiences for their future elementary students, but they fail to base such strategies upon students' current mathematical conceptions. Throughout, the need to address prospective teachers' underlying perspectives of mathematics teaching and learning is stressed.