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1.
The purpose of this exploratory study was to use a teaching as problem solving perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning teachers of secondary school mathematics. A metacognitive framework was developed to examine the thoughts of teachers before, during and after lesson enactments. Data were obtained through observations, lesson plans, videotapes, and audiotapes of structured interviews during the course of one semester. Data analysis suggests that the metacognition of teachers plays a well-defined role in classroom practice. These findings provide useful insights for researchers and teacher educators in their preservice and inservice mathematics programs.  相似文献   

2.
This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.  相似文献   

3.
Research that aimed to examine teachers’ experiences whilst implementing a reform approach to mathematics teaching in an Irish primary school forms the basis of this paper. In particular, factors that contributed to changing mathematics practice in this case study school are outlined. The school engaged in professional development (PD) that focused on using an instructional framework [Hiebert, J., T. P. Carpenter, E. Fennema, K. C. Fuson, D. Wearne, H. Murray, A. Olivier, and P. Human. 1997. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth: Heinemann] in the school-identified strand units of length and weight. Four classes were tracked throughout the study and each class acted as a sub-case within the larger study. Data collected through lesson observations, teacher interviews, pupil work samples, and pupil focus group interviews were used to compare teachers’ experiences and to identify what supported and enabled them to change their practice, in addition to highlighting challenges that may have prevented such change. Findings were that shifts in practice were evident to different degrees in the four classes during the study. In relation to enabling factors, findings suggest that tailored PD, and the use and refinement of an instructional framework contributed to enabling teachers in changing their mathematics teaching. In particular, teachers reported that the 4Ts instructional framework was a very useful tool in supporting them to change mathematics teaching.  相似文献   

4.
In this paper we try to characterize the pedagogical approaches that mathematics teachers are developing to meet the challenges posed by education reforms. A key aspect is the identification of the perspectives that underlie those pedagogical approaches, using the term perspective to include a broad pedagogical structure composed of multiple conceptions that are related to some aspects of a teacher’s practice. Through the study of the practice of a secondary mathematics teacher, we try to explore how his/her pedagogical approaches on mathematics, mathematics learning, and mathematics teaching are related to the relational architecture that is established in the classroom during the development of an instructional unit of similarity at a secondary school level, and we examine if that relationship can be explained in terms of the underlying perspective. The results of the study have shown the characteristics of that relationship, and the important role that the teacher’s knowledge of the students’ difficulties plays both in making decisions and in developing the teachers’ actions.  相似文献   

5.
In this study, we investigated the impact of teaming school-based instructional coaches with science or mathematics middle school teachers to build a community of practice around inquiry instruction. This professional development model began with a 2-week summer institute and continued with four follow-up sessions during the academic school year for the teacher and instructional coach participants. The teachers’ participation in this professional development program with (1) content instruction through inquiry lessons, (2) practice teaching to middle school students, and (3) coach-led reflection improved their understanding of inquiry-based practices and the quality of their classroom inquiry implementation. Professional development experiences that prepare teachers and coaches simultaneously in inquiry and content may help build a shared language for reform and accelerate inquiry instructional changes.  相似文献   

6.
This article presents a conceptual framework for studying the relationship between cognition and instructional practices of preservice secondary mathematics teachers. It describes how the framework was used as a basis for activities in which preservice teachers engaged in structured reflection on their teaching as a means towards their professional growth. The approach required student teachers to engage in both prelesson and postlesson reflective activities. These activities are described, and details of two cases are given. This article demonstrates how this approach can facilitate the progression of preservice teachers' pedagogical techniques and conceptions. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

7.
How do we support students through their difficult transition to secondary school? Perceived value for and perceived ability to be successful during secondary school are a crucial part of any answer to this question. These perceptions and their interaction with classroom instruction are at the heart of many issues students face in this challenging new learning environment. Seeking to address these issues head-on, the current study modelled the shared role of motivation (intrinsic/extrinsic) and self-efficacy beliefs within mathematics, native and foreign language achievement across first-year secondary school studies at six schools in Japan. Modelling included pre-post subject achievement and students' instructional experiences. Longitudinal latent structural equation modelling was undertaken for each of the subjects to examine the interplay between students' motivational and instructional experiences across one academic year. Findings support the shared role of intrinsic motivation and self-efficacy within achievement (βs = 0.1–0.24), and reciprocal relationships between perceptions of instruction and students’ motivations/beliefs (βs = 0.15–0.21). Results also suggest different patterns of motivation-belief and motivation/belief-instruction interconnections across the three subjects of study researched. The pervasive role of instructional experiences for students' motivation-beliefs (from teaching to self-efficacy and intrinsic motivation, βs = 0.14–0.21) highlight the powerful role of teachers in these critical environments. Implications for theory and practice arising from the results and the integrative model utilised are discussed.  相似文献   

8.
Abstract. This article presents three in‐depth case studies focused on supporting students with learning challenges to learn math strategically. Participants were three eighth‐grade students enrolled in a learning assistance classroom who were of at least average intelligence but who were performing significantly below grade level in mathematics. These case studies document the processes by which these students were supported to self‐regulate their learning in mathematics more effectively. We begin by outlining important instructional foci in mathematics education for intermediate or secondary students with learning disabilities, along with what research indicates are effective instructional processes. In that context, we introduce the theoretical principles underlying the instructional model used here—Strategic Content Learning (SCL). Based on analyses of case study data, we describe how SCL instruction was structured to promote strategic learning. Throughout the discussion, intervention processes are described in sufficient detail to be of use to practitioners.  相似文献   

9.
In the research reported in this article, we sought to understand the instructional practices of 26 secondary teachers from one district who use a problems-based mathematics textbook series (Core-Plus). Further, we wanted to examine beliefs that may be associated with their instructional practices. After analyzing data from classroom observations, our findings indicated that the teachers’ instructional practices fell along a wide continuum of lesson implementation. Analysis of interview data suggested that teachers’ beliefs with regard to students’ ability to do mathematics were associated with their level of lesson implementation. Teachers also differed, by level of instructional practices, in their beliefs about appropriateness of the textbook series for all students. Results strongly support the need for professional development for teachers implementing a problems-based, reform mathematics curriculum. Further, findings indicate that the professional development be designed to meet the diverse nature of teacher needs.  相似文献   

10.

This paper describes a partnership between a university and an urban school district, formed with a goal of preparing mathematics teacher leaders to conduct professional development (PD) at their schools. The university and district partners worked together to achieve the district’s mission of providing every student with high-quality instruction and equitable learning opportunities in mathematics by building the district’s capacity to conduct school-based PD for mathematics teachers. Given the power of school-based subject-specific PD for improving instructional quality, we worked with Teacher Leaders from participating schools to prepare and support them to lead PD workshops at their schools. In this paper, we examine how Teacher Leaders learn and adapt key elements of a PD model over three school years through the lenses of Prediger et al.’s Three-Tetrahedron-Model (2019) and the university’s Learning to Lead model. Over 3 years, we see that Teacher Leaders use the key structures of the PD model; make adaptations in response to school goals, interests, and priorities; and gain confidence in their work with colleagues. By viewing the adaptations through the lens of pedagogies of practice as well as the relationships illustrated by the 3-T model, this work offers insights into the complexities of teacher leadership development.

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11.
Instructional practice plays a significant role in understanding teachers’ pedagogical content knowledge (PCK). The aim of the study reported on was to compare mathematics and technology pre-service teachers’ knowledge of PCK. The study used a case study approach of five mathematics and five technology pre-service teachers with a total of ten. Data was collected in seven public schools around Gauteng province in South Africa. The observation technique was employed in order to understand students’ classroom practice, using a video camera to capture the setting. One lesson of 45 minutes presented by each pre-service teacher, rendering a total of ten lessons, was observed. The study adapted the theoretical framework of PCK (Shulman 1987). The study scrutinised the data based on the qualitative content analysis method and found that most pre-service teachers in both mathematics and technology possess a limited knowledge of PCK. In both subjects, most of the pre-service teachers’ classroom practice did not exhibit comprehensive knowledge of the subject matter or knowledge of the learners. However, the difference is that only mathematics pre-service teachers have some knowledge of assessment. The data also indicate that “9E” instructional practice can be a valuable tool to enhance field-specific PCK within the field of mathematics and technology education subjects. Therefore, the study proposes further investigation of the “9E” instructional model that could be used as field-specific PCK within the fields of mathematics, science and technology.  相似文献   

12.
This teacher development study closely examined a teacher's practice for the purpose of understanding how she selected and implemented instructional materials, and correspondingly how these processes changed as she developed her problem‐based practice throughout a school year. Data sources included over 20 hours of planning and analysis meetings with the teacher and 27 video‐taped lessons with discussions before and after each lesson. Through qualitative analysis we examined the data for: students' cognitive demand for curricular materials the teacher selected and implemented; teacher's beliefs and practices for students' engagement in mathematical thinking; and teacher's and students' communication about mathematics during instruction. We found that the teacher shifted her views and use of instructional materials as she changed her practice towards more problem‐based approaches. The teacher moved from closely following her traditional, district‐adopted textbook to selecting problem‐based tasks from outside resources to build a curriculum. Simultaneously, she changed her practice to focus more on students' engagement in mathematical thinking and their communication about mathematics as part of learning. During this shift in practice, the teacher began to reify instructional materials, viewing them as instruments of her practice to meet students' needs. The process of shifting her views was gradual over the school year and involved substantial analysis and reflection on practice from the teacher. Implications include that teachers and teacher educators may need to devote more attention and support for teachers to use instructional materials to support instruction, rather than materials to prescribe instruction. This use of instructional materials may be an important part of transforming practice overall.  相似文献   

13.
Future teachers often claim that advanced undergraduate courses, even those that attempt to connect to school mathematics, are not useful for their teaching. This paper proposes a new way of designing advanced undergraduate content courses for secondary teachers. The model involves beginning with an analysis of the curriculum and practices of school mathematics and its teaching, and then using those to build up to the advanced mathematics – in this case, real analysis. After developing definitions, examples, theorems, and proofs, the model then reconnects to practice, asking the teachers to translate ideas from real analysis in ways that are appropriate for teaching high school content to students. To illustrate the model, we provide and discuss two example tasks.  相似文献   

14.
Professional Conversations and Professional Growth   总被引：1，自引：0，他引：1  
A professional development program for 18 teachers was conducted over a two-year period. The participating teachers taught in intermediate schools (students aged 11–13) and secondary schools. The teachers worked collaboratively to improve their mathematics teaching, with encouragement to reflect on their practice but with minimal instruction from the researchers. Results, as defined by change in teaching practices, beliefs, and reflections, and student achievement, indicated that the collaborative program was particularly useful for experienced secondary school teachers but less useful for intermediate school teachers. We concluded that this type of professional development was most useful for teachers who had sufficient knowledge of mathematics; these teachers were able to focus on pedagogy and to draw connections between aspects of the mathematics they taught, without recourse to a specialist's advice. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

15.
In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.  相似文献   

16.
This study presents an analysis of whether geometry teachers create opportunities for student discussion when engaging students in proving as revealed through the use of a multimedia survey instrument. We presented 42 secondary mathematics teachers with 8 multimedia narratives set in the situation of doing proofs in high school geometry and asked them to choose what they would do next, presenting options that included a normative instructional action which closed off discussion and less typical actions that encouraged student discussion. Our analysis provides insight into the professional obligations that teachers use to justify their departure from the norm in order to encourage student talk as well as the background variables that are associated with such decisions. We found that while secondary mathematics teachers frequently chose to promote discussion in their classrooms, the rationale that they chose for this decision and the reasons they might choose not to immediately encourage discussion differed according to the amount of experience they had teaching geometry. We use these differences to illustrate how the professional obligations can be used to better understand how teacher decisions are rationalized at the level of the instructional situation.  相似文献   

17.
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.  相似文献   

18.
Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student arguments and provide feedback to students based on those validations. Prior research has demonstrated several weaknesses teachers have with respect to proof validation, but little research has investigated instructional sequences aimed to improve this skill. In this article, we present the results from the implementation of such an instructional sequence. A sample of 34 prospective secondary mathematics teachers (PSMTs) validated twelve mathematical arguments written by high school students. They provided a numeric score as well as a short paragraph of written feedback, indicating the strengths and weaknesses of each argument. The results provide insight into the errors to which PSMTs attend when validating mathematical arguments. In particular, PSMTs’ written feedback indicated that they were aware of the limitations of inductive argumentation. However, PSMTs had a superficial understanding of the “proof by contradiction” mode of argumentation, and their attendance to particular errors seemed to be mediated by the mode of argument representation (e.g., symbolic, verbal). We discuss implications of these findings for mathematics teacher education.  相似文献   

19.
For this study, Prospects, a data set on schools and students in the United States collected during the early 1990s, was used to examine the effects of instructional and school organizational characteristics on the longitudinal mathematics and reading achievements of students from either a first- or third-grade cohort. Three schooling models were tested using hierarchical linear modeling (HLM) while controlling for parental socioeconomic (SES) status. Factors and variables that represented instructional and school features were derived from teacher and principal responses to survey items. These features had direct and interactive effects on mathematics achievement, supporting both an environmental and interactive model of schooling. Further, schools characterized by teacher collegiality, support for innovation, principal leadership, goal agreement, and community support contained teachers who employed important instructional strategies more effectively, and students who had the highest mathematics gains over the observed period.  相似文献   

20.
Teacher efficacy in a particular content area is seen as an important factor shaping teaching practice and student learning in the Western literature. However, inadequate efforts have been made to examine this assumption empirically. Drawing on the Trends of International Mathematics and Science Study (TIMSS) 2011 mathematics teachers’ data at the eighth grade level, this study examines the relationship between teacher efficacy in teaching mathematics and teachers’ mathematical instructional practices in five Asian countries/regions. Guided with Bandura’s social cognitive theory, this study finds that overall teachers in the five countries/regions reported much lower teacher efficacy in teaching mathematics and lower levels of instructional practices than the international norms. The relationship between teacher efficacy and instructional practices varied within these countries/regions. Teacher efficacies in teaching mathematics are not always statistically and positively related to their instructional practices in engaging students. Together, these findings challenge the theoretical assumption about the positive relationship between teacher efficacy and instructional practices. Possible reasons of these findings and future directions are discussed.  相似文献   

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