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1.
The goal of this study was to reach a better understanding of the intuitive decisions teachers make when designing a technology-rich learning environment. A multiple case-study design was employed to examine what kinds of factors (external priorities, existing orientations or practical concerns) influence design interactions of teams of kindergarten teachers. This study combines semi-structured interview data on teachers’ existing orientations with analysis of teachers’ design discussions during the design of learning material for a technology-rich learning environment. Three teams of teachers voluntarily participated. Findings on the existing orientations suggest that knowledge and beliefs about teaching and learning related to knowledge and beliefs on technology and early literacy. The analysis of teachers’ discussions revealed that the process could be characterized to a large extent as brainstorms; and that problems are not addressed in-depth. Rather they are resolved through brainstorming, and most argumentation falls in the realm of practical concerns: how to organize learning activities and how to respond to contingencies. The findings of this study suggest that teachers’ explicated design reasoning is mostly influenced by practical concerns, yet their own knowledge and beliefs play an important role at the start of the design process. However, these existing orientations as well as the practical concerns that emerge during the conversation tend to be narrow in scope. Theoretical and practical implications are discussed in light of how this study provides understanding of how to support these teachers.  相似文献   

2.
In order to understand how prospective teachers develop knowledge for teaching, researchers must identify the types of knowledge that are integral to effective science teaching. This case study investigated how 4 prospective secondary biology teachers’ science teaching orientations, knowledge of science learners, and knowledge of instructional sequence, developed during a post-baccalaureate teacher education program. Data sources included a lesson planning task and two interview-observation cycles during the participants’ year-long internship. Over the course of a year, the participants’ science teaching orientations were based primarily on their K-16 learning experiences, and were robust and highly resistant to change. The prospective teachers became more aware of student learning difficulties, and therefore, developed more elaborated knowledge of the requirements of learning. They consistently sequenced instruction in ways that gave priority to transmitting information to students. Prospective teachers’ development of knowledge of student understanding of science and instructional sequence were congruent with their science teaching orientations. Implications are given for teacher education and future research.  相似文献   

3.
In this study, five elementary teachers and a university researcher developed and implemented problem‐based learning (PBL) experiences in the context of science teaching and learning. Collaborative inquiry was adopted as a methodology, while a variety of qualitative methods were used to examine the engagement and development of teachers’ pedagogical content knowledge (PCK). A PCK model is used as a framework to examine teachers’ professional knowledge growth in areas such as orientations to teaching science, knowledge of science curriculum, knowledge of students’ understanding of science, knowledge of assessment, and knowledge of instructional strategies. Implications for how teachers may be supported when adopting instructional innovations are discussed.  相似文献   

4.
This study examines how various teacher characteristics and contextual factors are related to early primary teachers’ beliefs about mathematical teaching and learning and teachers’ attitudes toward their own learning of mathematics. A total of 396 early primary teachers across Nebraska participated in the study. Teacher characteristics and contextual factors were grouped into four sets: teacher professional background, teacher mathematical knowledge for teaching, teaching contexts, and students’ experiences. Multiple regression analyses were conducted with each set of predictors separately, as well as with all four sets together. The results showed significant relationships between teachers’ mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics. Teacher certification level, the number of college math courses taken, and perceived support from colleagues and administrators were also related to some aspects of teachers’ mathematical beliefs and attitudes. The findings suggest the potential role of teachers’ mathematical knowledge for teaching in improving teachers’ mathematical beliefs and attitudes.  相似文献   

5.
This investigation describes secondary mathematics teachers’ learning and instructional change following their participation in a professional development workshop, the Enhancing Secondary Mathematics Teacher Preparation Project (ESP) (2004–2005), specifically focused on the selection and implementation of cognitively challenging mathematical tasks. Data consist of a pre/post-assessment of teachers’ knowledge of the cognitive demands of mathematical tasks and videotaped discussions and written artifacts from the professional development sessions. A mixed methods approach was used to identify connections between teachers’ learning and their experiences in the ESP workshop. Results indicate that ESP teachers developed new ideas about the influence of mathematical tasks on students’ learning. Increases in teachers’ knowledge of the cognitive demands of mathematical tasks were closely linked to ideas represented in frameworks and discussions from the ESP workshop and to teachers’ experiences in solving challenging mathematical tasks as learners.  相似文献   

6.
The research study this article is based on aims to implement research knowledge to teaching, that is, the concept of critical aspects and dimensions of variation used in the variation theory. To do this, the researchers worked with willing teachers to explore how to make mathematics teaching more effective. This paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding of subtraction as well as their learning of it. The students’ tests, examinations of students’ mathematical work, the teachers’ lessons plan and reports of the instructions for lessons form the data base for the article. The analysis indicates that one of the critical aspects in the process of implementation of the variation theory in the teachers’ practice was to identify the critical aspects in students’ learning. Another critical aspect in the implementation of the variation theory was to open up dimensions of variation in the identified critical aspects of the students. By giving teachers the possibility to develop the ability to identify critical aspects in students’ learning, dimensions of variation are opened up in these aspects, and by applying this knowledge in the daily teaching, they have the possibility to improve students’ learning. The findings suggest that developing an understanding of the students’ critical aspects can be a productive basis in helping teachers make fundamental changes in their instructions and improve students’ learning.  相似文献   

7.
Thematic work that integrates different knowledge areas is considered suitable for developing young children’s knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers’ work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive mathematics learning and teaching integrated with art. Data for analysis were collected from a questionnaire answered by 27 early childhood teachers from Finland and Sweden. Influenced by a sociocultural theoretical framework, the analysis concerns the teachers’ expressed goals for learning and their strategies for achieving these goals. The analysis reveals qualitatively different approaches to the learning goals addressed by the teachers – process-oriented, product-oriented, development-oriented and providing awareness – which, respectively, seem to generate different meanings of mathematical learning integrated with art. This study offers an overview of teachers’ approaches to teaching mathematics and art in thematic work, and of how different approaches may influence what mathematical meaning is offered to children to explore.  相似文献   

8.
This exploratory study of elementary school science examines questions central to policy, practice and research on formative assessment: What is the quality of teachers’ content-pedagogical and assessment knowledge? What is the relationship between teacher knowledge and assessment practice? What is the relationship between teacher knowledge, assessment practice and student learning? Drawing on multiple measures, hierarchical linear modelling and path analysis, results suggest that despite weaknesses in teachers’ content-pedagogical and assessment knowledge, teachers’ formative assessment practices are positively related to student learning. Relationships between teachers’ knowledge and assessment practices are mixed. Findings underscore both the potential and challenge of bringing effective formative practice to fruition as well as the need for continued research.  相似文献   

9.
The nature of science (NOS) has become a central goal of science education in many countries. This study sought an understanding of the extent to which a nature of science course (NOSC), designed according to the conceptualization of pedagogical content knowledge (PCK) for teaching nature of science (NOS), affects in-service science teachers’ understanding and learning of NOS, and their orientations towards teaching it. A qualitative research approach was employed as a research methodology, drawing upon pre- and post-instruction NOS questionnaires, field notes, and in-service teachers’ weekly journal entries and assignments. Open-ended NOS questionnaires, used to assess participants’ understandings of NOS, were analysed and categorized as either informed, partially informed and naive. Other qualitative data were analysed through an inductive process to identify ways in-service teachers engaged and learned in the NOSC. The results indicate that at the beginning of the course, a majority of the in-service science teachers held naive understandings of NOS, particularly with respect to the definition of science, scientific inquiry, and differences between laws and theories. They viewed implicit project-based science and science process skills as goals of NOS instruction. By engaging in the course, the in-service science teachers developed an understanding of NOS and orientations to teaching NOS based on various elements, especially reflective and explicit instruction, role modelling, and content- and non-content embedded instruction. The aim of this study is to help science teacher educators, consider how to support and develop science teachers’ understandings of NOS while being mindful of PCK for NOS, and develop methods for teaching NOS frameworks.  相似文献   

10.
Statistics is an increasingly important component of the mathematics curriculum. StatSmart was a project intended to influence middle-years students’ learning outcomes in statistics through the provision of appropriate professional learning opportunities and technology to teachers. Participating students in grade 5/6 to grade 9 undertook three tests, a pre-test, a post-test and a longitudinal retention test over a period of 2 years. Their teachers completed a survey that included items measuring pedagogical content knowledge (PCK) for teaching statistics. Despite the development of valid instruments to measure both student and teacher content knowledge and teachers’ PCK, linking teachers’ knowledge directly to students’ learning outcomes has proved elusive. Multilevel modelling of results from 789 students for whom there were 3 completed tests and measures from their teachers indicated that students’ outcomes were influenced positively by their initial teacher’s PCK. Extended participation of teachers in the project also appeared to reduce negative effects of changing teachers.  相似文献   

11.
This article contributes to the discussion on mathematics teacher reflection. Reflection was included in a study of the didactisation practices of primary school mathematics teachers as one of nine didactisation practices. The study involved five volunteer primary school mathematics teachers. A qualitative design-research approach was designed which employed model-eliciting tasks to create new experiences for teachers. This article reports on the nature and development of mathematics teacher reflection. Teacher reflection was gauged at various times during the programme through written responses to open-ended reflective questionnaires. Teachers were involved in three types of sessions for a period of one year: 1) modelling sessions whereby they collaboratively solved a mathematical modelling task; 2) observing primary school students/learners solve the same problems; and 3) sessions discussing traditional and problem-centred teaching and learning. It was found that modelling tasks provided reflective platforms and a window to teacher resources, orientations and goals. It is recommended that further research into mathematics teacher reflection be conducted where teachers specifically implement modelling in their own classrooms.  相似文献   

12.
数学问题解决能力的高低直接影响到学生学习数学的效率、学习兴趣、学习成绩以及学生学习潜力的开发。传统的数学教学方式容易使学生形成固定的思维模式,不利于创造性思维的培养。基于控制论的数学测试系统,将资源科学归类,提供教师辅导和及时诊断服务,注重学科知识的应用和学生间协作意识的培养。利用该数学测试系统,学生可以及时获得反馈,明晰自己的学习状态和问题;教师可以根据学习过程中学习者的变化状态,不断调整数学训练的内容和方式,制定最佳的教学方案,使学生在控制模型下,不断提高数学问题的解决能力。  相似文献   

13.
Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children’s multiple mathematical knowledge bases (MMKB), including children’s mathematical thinking and children’s home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children’s MMKB in instruction may be to scaffold teachers’ noticing of potential spaces in elementary mathematics curriculum materials for connecting to children’s MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children’s MMKB.  相似文献   

14.
As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.  相似文献   

15.
The activity of reasoning-and-proving is at the heart of mathematical sense making and is important for all students’ learning as early as the elementary grades. Yet, reasoning-and-proving tends to have a marginal place in elementary school classrooms. This situation can be partly attributed to the fact that many (prospective) elementary teachers have (1) weak mathematical (subject matter) knowledge about reasoning-and-proving and (2) counterproductive beliefs about its teaching. Following up on an intervention study that helped a group of prospective elementary teachers make significant progress in overcoming these two major obstacles to teaching reasoning-and-proving, we examined the challenges that three of them identified that they faced as they planned and taught lessons related to reasoning-and-proving in their mentor teachers’ classrooms. Our findings contribute to research knowledge about major factors (other than the well-known factors related to teachers’ mathematical knowledge and beliefs) that deserve attention by teacher education programs in preparing prospective teachers to teach reasoning-and-proving.  相似文献   

16.
In this study, 12 pre-service mathematics teachers worked in teams to develop their knowledge and skills in using teacher-led spreadsheet demonstrations to help students explore mathematics concepts, stimulate discussions and perform authentic tasks through activity-based lessons. Pre-service teachers’ lesson plans, their instruction of the lessons designed, experiences and lesson enactment outcomes were examined. The pre-service teachers in the study were able to develop and demonstrate their knowledge and skill adequately in designing and enacting activity-based mathematical lessons supported with spreadsheets. The results also showed that the pre-service teachers’ use of the spreadsheet as an instructional tool promoted student in-depth mathematical concept formation and an activity-based learning approach to make lessons less teacher centred and more interactive.  相似文献   

17.
This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students’ learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers’ knowledge of their students’ understanding of certain mathematical concepts is fairly limited. It then goes on to discuss this phenomenon in terms of a process that can hinder rather than promote learning. The research illuminates the position of teachers who appear to lack certain detailed information about their students which, it can be argued, could inform more effective teaching strategies. The paper concludes by exploring possible implications for similar situations where learning could be enhanced by more effective classroom assessment strategies and their use to inform future teaching and learning activities.  相似文献   

18.
The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers’ knowledge. It is aimed at exploring the development of teachers’ mathematical and pedagogical conceptions associated with systematic employment of multiple-solution tasks (MSTs) in a “problem-solving” course for prospective mathematics teachers (PMTs). Our attention to teachers’ mathematical conceptions focused on the development of PMTs’ problem-solving competences. Our attention to teachers’ meta-mathematical and pedagogical conceptions focused on changes in teachers’ views concerning the level of interest and level of difficulty of the mathematical tasks. We differentiated between the systematic and craft modes of professional development integrated in the course. Systematic mode involved problem-solving sessions and reflective discussions on collective solution spaces. Craft mode involved interviewing school students. The study demonstrates the effectiveness of MSTs for PMTs’ professional development.  相似文献   

19.
Drawing strategies are widely used as a powerful tool for promoting students’ learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students’ modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students’ performance. We complemented the quantitative approach with a qualitative in-depth analysis of students’ drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed.  相似文献   

20.
Despite multiculturalism being discussed in teacher education, teachers still often feel insecure in the classroom around developing meaningful practices. This might be due to several issues about how preservice teachers are taught. In this article, modelling culturally responsive pedagogy is demonstrated as a promising strategy in shaping preservice teachers’ learning experiences and facilitating the finding of pedagogical responses in their future work. The article examines preservice teachers’ awareness of modelling as a teaching strategy in a multicultural education course in Finland, and the ways in which they connected the modelled strategy to their own learning and intentions for future teaching. A total of 246 reflective learning journals were analysed qualitatively, using a constant comparison approach. The results indicate that preservice teachers recognised and reflected on modelling culturally responsive pedagogy. They highlighted several aspects of the culturally responsive activities, environment and teacher educator behaviours modelled for them. For some preservice teachers, this recognition stayed at the level of personal awareness of own learning on the course, but for others these revelations were springboards to start forming ideas about future teaching practice. Preservice teachers articulated their intentions about the kind of teachers they would like to become, their principles in teaching, as well as specific teaching/learning activities. We present how the modelling of culturally responsive pedagogy strategies allowed preservice teachers to self-reflect, critique and connect their own learning experiences to future practice. Therefore, modelling culturally responsive pedagogy is argued to be a fruitful strategy in teacher education.  相似文献   

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