基于学习进阶的幼儿教师数学核心经验模型建构

幼儿教师数学核心经验主要是指教师在教学实践中形成的数学领域至关重要的概念、能力或技能,对于幼儿的数学学习和教师的数学教学具有至关重要的作用。幼儿教师作为基本的学习者,其专业发展过程符合学习进阶的各项准则,不同职业发展阶段的幼儿教师有着各自不同的进阶轨迹。学习进阶强调学习是一种不断积累和发展的过程,并倡导为不同阶段的学习者设计不同的进阶框架,这为有效推动幼儿教师数学核心经验的发展提供了充分的理论参考。本研究在厘清幼儿教师数学核心经验内涵与结构的基础上,依据学习进阶的主要观点,建构幼儿教师数学核心经验的经验模型,并提出相应的教师培养策略,主要包括加强数学核心经验的学习共同体建设、制订数学核心经验的阶梯式成长方案和完善数学核心经验的质量监测指标。     

Under-threes’ mathematical learning – teachers’ perspectives

This project highlights preschool teachers’ views of toddlers’ learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1–3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data were collected through interviews with six preschool teachers working in four different preschools. The data show that the teachers emphasize the body as very important for the learning process, which means that for these children, it is not a matter of simply talking about mathematical concepts, but experiencing them bodily. The teachers also report that they now pay more attention than previously to what material the children use and how they interact with it. They are more aware of how they organize and offer the various materials in the preschool and how this influences the way children use them and, consequently, their learning processes.     

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for meaningful and developmentally appropriate mathematics experiences for young children in diverse early learning settings. Instructional and curricular methods inspired by the Reggio Emilia Approach are described as effective ways to teach number concepts to young children from preschool through primary age. Strategies for teachers of young learners are presented in order to strengthen the mathematics curriculum in contemporary early learning settings. The authors’ analysis and recommendations are informed by their extensive experiences including studies in Reggio Emilia early childhood settings (infant toddler, preschool, and primary schools) and their work in early childhood teacher education at their respective universities.     

基于MQI评估系统的大班数学集体活动质量分析及其启示

数学是学前儿童学习和入学准备的重要领域,也是学前教育质量监测的重要方面。MQI评估系统作为一种评估数学课堂教学质量的框架,体现了最新数学教育观念,突出了数学的学科特性和认知要求,强调儿童的主动参与和生成性的教学过程,可同时对教师的教和儿童的学进行评估。本研究使用MQI评估系统对我国幼儿园大班数学集体活动的质量进行考察,结果表明除数学意义建构和数学语言之外,数学丰富度领域各维度表现水平不高;教师对儿童行为进行处理和反馈的水平较低;大多数活动片段中不存在数学表达和语言上的错误及不严密性问题;儿童参与有意义的解释或者提问和推理较少,参与活动的认知要求不高。幼儿园大班数学集体活动质量受到集体教学中"教"与"学"的关系、教师对数学领域知识和儿童数学发展目标的认知、教师评价儿童数学思维的能力及师幼互动技巧、教师培训与考核的侧重点等因素的影响。我国学前教育界应重视数学教育活动的过程性质量,关注儿童数学学习过程性能力的发展,并应在借鉴MQI评估系统的基础上开发适合我国幼儿园数学教育实践的质量评估系统。     

Exploring the role of computer-based assessment in diagnosing children’s mathematical errors in primary education in Ireland

Concern about children’s mathematics performance in Ireland and elsewhere has prompted a range of responses from researchers, policymakers, educators and the media. While policy-level responses in Ireland include revising curricula and implementing a numeracy strategy that calls for increased tuition hours, teachers have also drawn on a wide array of resources in mediating curriculum-based mathematical knowledge, concepts and skills for the children in their classes. In the classroom context, formative assessment tools can be of particular value. This paper explores the potential role for one such tool, a computer-based assessment (CBA), in supporting the teaching and learning of mathematics at primary level. That test requires children to respond to open-format items, and the study illustrates how traditional error-analysis techniques are combined with the affordances of CBAs to enable automated scoring of responses. Discussion focuses on the positive role that digitally mediated error-analysis approaches can play in helping teachers understand better and address the challenges being faced by children in relation to mathematics in the middle grades of primary school. Suggestions for further research are highlighted.     

Curriculum spaces for connecting to children’s multiple mathematical knowledge bases

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.     

Effects of a Pre-Kindergarten Mathematics Intervention: A Randomized Experiment

Abstract

Research indicates that a socioeconomic status-related gap in mathematical knowledge appears early and widens during early childhood. Young children from economically disadvantaged families receive less support for mathematical development both at home and in preschool. Consequently, children from different socioeconomic backgrounds enter elementary school at different levels of readiness to learn a standards-based mathematics curriculum. One approach to closing this gap is the development and implementation of effective mathematics curricula for public preschool programs enrolling economically disadvantaged children. A randomized controlled trial was conducted in 40 Head Start and state preschool classrooms, with 278 children, to determine whether a pre-kindergarten mathematics intervention was effective. Intervention teachers received training that enabled them to implement with fidelity, and a large majority of parents regularly used math activities teachers sent home. Intervention and control groups did not differ on math assessments at pretest; however, gain scores of intervention children were significantly greater than those of control children at posttest. Thus, the intervention reduced the gap in children's early mathematical knowledge.     

Increasing Teacher Mathematical Talk During Shared Book Reading in the Preschool Classroom: A Pilot Study

Research Findings: Shared book reading provides opportunities for adults to engage in literacy-related interactions with children in meaningful ways. Research has examined various dimensions of adult and child behavior during shared book-reading interactions with some focus on how book type affects the reading experience. Little research, however, has examined systematically the use of shared book reading in a mathematical context. Thus, the purpose of the study was twofold: (a) to examine the effect of book type on teacher use of mathematical talk during shared book reading in preschool classrooms and (b) to examine the effect of training teachers specifically to use mathematical talk during shared book reading. A multielement design with 2 female preschool teachers who taught in inclusion classrooms in an urban school district was used. Results generally indicated that the use of mathematical storybooks resulted in increased teacher mathematical talk compared to the use of nonmathematical storybooks. Training and instructional supports resulted in an increase in mathematical talk over that achieved by mathematical storybooks alone. Practice or Policy: Because shared book reading is a common practice in preschool classrooms, strategically choosing books to address mathematical skills can increase attention to mathematics throughout daily routines and provide a means of increasing teacher mathematical talk.     

Young Children's Exposure to Mathematics: The Child Care Context

Four preschool teachers from two preschool settings were observed to explore the contribution of child care experiences on the development of young children's understanding of mathematics. Teachers were also interviewed regarding their attitudes and beliefs about the importance of early education, children's understanding of mathematics prior to formal schooling, and their role in facilitating mathematical knowledge. Although the programs and teachers differed in terms of program orientation, teaching style, student participation, and interactions with students, the programs did not differ in terms of the amount or content of mathematics presented to children. During the classroom observations that were conducted, very little mathematics was presented in any of the classrooms either directly or indirectly to students. In contrast, teachers said that they believed that mathematics was important and that they engaged in mathematical discussions in their classroom interactions. Discussion of the lack of math presented in the classroom and the discrepancy of teachers' beliefs and teaching behaviors are discussed.     

Meaning and Money

This paper examines how the inclusion of everyday mathematics into classroom instruction can make mathematics more meaningful to students. The concept of mathematical meaningfulness is reviewed and then compared to the experiences of children learning about money at home and at school. The empirical study used interviews and observations to determine what activities Hawaiian children from preschool through second grade did with money at home, while shopping and during classroom lessons. The interview data are used to show what kinds of knowledge children derived from these experiences at different ages. This everyday knowledge is compared to what children were expected to learn about money in school. The data support the conclusion that certain kinds of differences between everyday and school mathematics can make the inclusion of everyday mathematical topics in classrooms problematic. The paper concludes with a discussion of how everyday mathematics can be more profitably included in the curriculum, with examples from several mathematics programs.     

The preparation experiences of elementary mathematics specialists: examining influences on beliefs,content knowledge,and teaching practices

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (n = 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.     

Linguistic Invention and Semantic Warrant Production: Elementary Teachers’ Interpretation of Graphs

In this qualitative study of mathematical discourse between elementary teachers, we examined linguistic invention and semantic warrant production as participants made successive attempts to communicate mathematical ideas. Linguistic invention is a creative practice of describing mathematics in terms of personal experience. We introduce semantic warrant production, which emerged as part of our analysis of substantial arguments produced by teachers learning mathematics. Participants engaged in linguistic invention and semantic warrant production to convince themselves and others of the validity of their mathematical inferences about a graph of rate of change versus time. Personal experiences that are taken-as-shared in a learning community can support accurate mathematical inference if connections between conventional language, common experiences, and mathematical representations are made explicit by learners.     

Catching the moments – coteaching to stimulate science in the preschool context

An important task for the preschool teacher is to create meaningful learning situations where children have opportunities to experience science. However, many teachers have both weak subject knowledge and a lack of confidence to teach science. The aim of the project presented in this article was to capture how nine preschool teachers developed their learning of and self-confidence in teaching science during a two-year professional development (PD) project while coplanning, coteaching, and coreflecting on their teaching activities. During the project, the preschool teachers’ self-confidence and attitudes played an important role for the their approach to science activities. Their collaborative learning and reflection became important for their PD and for the way science phenomena were included in the preschool context. As such, the project is based on opportunities for preschool teachers to develop their ideas about science and to reframe their work with the aim to stimulate children’s curiosity for science.     

Connecting with the horizon: developing teachers’ appreciation of mathematical structure

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.     

From activity to transdisciplinarity and back again – preschool teachers’ reasoning about pedagogical goals

This study presents an analysis of preschool teachers’ reasoning about pedagogical goals. Of specific interest is how teachers in a Swedish and a Finnish context describe goals for children’s learning and how they describe them implementing these goals into their practice. The research question is thus: How are pedagogical goals perceived and enacted, in the thematic-oriented and play-based pedagogical practice of preschool? In-depth interviews were conducted with six preschool teachers, of which three expressed learning goals guiding their pedagogical work. The Variation Theory of learning is the guiding principle throughout the analysis, and reveals indirect and direct objects of learning and content for learning described by the three teachers. A deeper analysis of the features of these provides a comprehensive picture of pedagogical goals that are intertwined and move between activity goals, working goals and transdisciplinary goals. These results contribute to our understanding of the characteristics of preschool pedagogy and the complex pedagogical practice preschool entails.     

Preschool – an arena for children’s learning of social and cognitive knowledge

The aim is to investigate Swedish preschool teachers’ accounts of children’s learning in relation to the goals in the Swedish preschool curriculum. The research question is: “What do preschool teachers see as fundamental aspects of learning in preschool practice?” The study is based on interactionist perspectives founded in Urie Bronfenbrenner’s ecological systems theory in which individuals and environment influence each other in a dynamic, reciprocal interaction. The data consist of interviews. The results show two themes that describe what teachers express as fundamental learning aspects in preschool practice: children’s learning of social knowledge and children’s learning of social and cognitive knowledge as integrated. The results show that some preschool teachers view social knowledge as fundamental to children’s learning. Others have a broader learning-oriented approach, which is grounded in the Swedish preschool curriculum and in modern theories of learning. This is an integrated learning approach, which is assumed to promote children’s learning and development in a long-term perspective.     

由家长对学前儿童数学教育观念的调查所引发的思考

本文针对家长关于学前儿童数学教育的一些误区,探讨了学前阶段儿童教育的核心价值、教育方法及其重要意义,期望能帮助家长及教师树立正确教育观念,为幼儿今后的数学学习打下良好的基础。     

Powerful teaching in preschool – a study of goal-oriented activities for conceptual learning

This article reports on a small-scale investigation of how teachers organise goal-oriented learning in Swedish preschools. The revised Swedish curriculum (National Agency for Education 2011) highlights the need for children to develop their mathematics skills through activities that integrate play and learning. This study investigates how different types of activities contribute to children developing their understanding of the concepts ‘half’ and ‘double’. Three preschool teachers participated in a developmental project in which they conduct teaching in accordance with the Variation Theory of Learning. The pedagogical contexts they bring into being reveal important insights for early childhood education. The pedagogical context that can be realised in the planned activities limits or favours the learning process and the success of the theoretical aspirations for the session. This article discusses the idea of ‘teaching’ and how to facilitate conceptual development in a goal-oriented but child-centred practice. The main results show that play is central in early childhood education, and that problem-solving as a means for mathematics education needs to be problematised and used with sensitivity to the children's intentions and perspectives.     

Is It DAP? American Preschool Teachers’ Views on the Developmental Appropriateness of a Preschool Math Lesson from China

Planned instruction is an important teaching form in early childhood mathematics education, but some educators are concerned about its developmental appropriateness. The present study was undertaken to address this issue. One hundred and seven American preschool teachers participated in the study: They watched a video-taped math lesson that was conducted in a 4-year-olds’ classroom in China and answered video-cued questions in a questionnaire. A mix of qualitative and quantitative methods was used in analyzing the data. Research Findings: Results show that on average, participants rated the quality and developmental appropriateness of the lesson as high. They acknowledged children’s active learning, teacher’s careful preparation, and use of different learning methods. But, they also identified inadequate elements such as lack of peer interactions and lesson differentiation. Practice or Policy: A relief of American preschool teachers’ current beliefs regarding the developmental appropriateness of math lessons provides critical reference for professional preparation/development programs. American preschool teachers’ high value of children’s active learning in a planned math lesson and their appreciation of teacher’s skillful guidance imply an imperative need to promote American preschool teachers’ pedagogical knowledge and skills in teaching mathematics to young children.     

Child Voice: How Immigrant Children Enlightened Their Teachers with a Camera

Changes in global patterns of residence mean that preschool teachers welcome immigrant children and families into preschools in increasing numbers. Many teachers report both anticipation and apprehension about having immigrant children in the classroom. Apprehension is related to concerns about a lack of enough knowledge about languages and cultures to sensitively work with children and families. To overcome apprehensions and challenges, teachers are encouraged to learn from the work of other adults. This study builds upon research that suggests that teachers can also look to the children as a source of knowledge. The purpose of this study was to explore how preschool immigrant children might use a disposable camera to communicate with their teachers. The participants of this qualitative study were immigrant and native-born students in a local preschool. Each child was given a disposable camera, instruction about taking photographs and the request to take pictures of what was important to them. Data were collected by recording each child telling the teacher about the pictures. Data were analyzed for themes, patterns and categories. Findings indicated that the messages that the children conveyed to their teachers included important information about language development and family cultural identity. Findings also identify teacher strategies that helped and hindered child ability to communicate during the photo-narration process. An implication of the study was a shift of child agency within the teacher child relationship during photo-narration activity.