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1.
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.  相似文献   

2.
This article presents the findings of two studies that were designed to improve young children's number knowledge through the use of mathematical games. The first study, with 5‐year‐old children (N = 55), involved parents coming into the classroom to play games with small groups of children. The second study, with 7‐year‐old children (N = 128), explored several ways of incorporating games into school mathematics programmes, including parents playing games with the children. Individual task‐based interviews were used to gather data on the children's number knowledge, and detailed observations were made of selected children's experiences during their normal mathematics lessons and while they were playing the mathematical games. The results showed that games appeared to be most effective as a way of enhancing children's learning when a sensitive adult was available to support and extend the children's learning as they played. The factors that appear to be important when involving parents in games sessions at school are discussed.  相似文献   

3.
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4.
Research Findings: Big Math for Little Kids (BMLK) is a mathematics curriculum developed for use with 4- and 5-year-old children. To investigate the BMLK curriculum's effect on children's mathematics knowledge, this cluster-randomized controlled trial randomly assigned child care centers to provide mathematics instruction to children, using either the BMLK mathematics curriculum or the centers’ business-as-usual curriculum, over a 2-year period when children were in prekindergarten and kindergarten. Participants in the study were 762 children and their teachers at 16 publicly subsidized child care centers. The study assessed children's mathematics knowledge using the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B), Direct Mathematics Assessment, a measure of young children's mathematics knowledge that is not aligned with the curriculum. The ECLS-B scores of children in the BMLK group increased significantly more than did those of children in the comparison group. The study also included exploratory analyses to examine whether children in the BMLK group demonstrated evidence of improved mathematical language. Practice or Policy: These results indicate that the BMLK curriculum, which is designed to help teachers use play-based, developmentally appropriate mathematics instruction, has a positive impact on young children's mathematics knowledge as measured by a general mathematics assessment that is not aligned with the curriculum.  相似文献   

5.
As one of the so-called basic skills, 'mathematics' or 'numeracy' is at the top of the list of subjects in adult education programmes. Together with political investment in general and further education, practitioners and theoreticians focus on 'knowing and learning in different contexts'. Jean Lave's theory about 'situated learning' may be regarded as a confrontation with the idea of learning as acquisition of propositional knowledge. One characteristic of adult education in mathematics is that the participants bring with them adult life experience from their everyday and work. Another characteristic is their perspective in educating themselves. There is an apparent contradiction between many adults being blocked in relation to mathematics in formal settings and being competent in their everyday life. It is possible to make sense of this contradiction by analytically expanding the context for knowing and learning mathematics from the participants' experiences and perspectives to also include the adults' dispositions, cf. Pierre Bourdieu's concept of 'habitus' as a guiding principle for practice. By interpreting the account of her life by a 75 year old woman concerning her attitudes to mathematics, the author illustrates and discusses the two analytical concepts ('situated learning' and 'habitus') and their suitability for analysing adults knowing or not-knowing mathematics in different situation contexts. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

6.
This article reports on an analysis of the process in which knowledge to be taught was transposed into knowledge actually taught, concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical praxeology of the two different types of knowledge exposed, in the task as such and in the activity of the classroom. Through the teacher’s explicit process of reasoning, modeling, revising, solving, and repeatedly explaining the task, we found that the transposition of knowledge was seriously affected by the contextualization of the task. Modeling word problems about everyday situations has its limitations and can, as in this case, make the problem unsolvable unless it is accepted as a “textbook task” disguised as real but adjusted to the norms of school mathematics. Such constraints may obscure mathematical ideas afforded by the task. We conclude that learning opportunities embedded in a task do not necessarily surface when a task is treated in a classroom setting.  相似文献   

7.
数学素养是现代社会公民应具备的基本素养,对于个体的终身发展具有重要的意义,应从幼儿园教育阶段就开始培养幼儿的数学素养。让幼儿体验到数学的重要性是促进幼儿数学素养发展的起点。由于幼儿尚不具备抽象思维能力,所以他们通常并不能自发体验到数学的重要性,而需要幼儿园教师的适当引导。教师应遵循兴趣激发原则、基本概念原则、自然引导原则,在幼儿园一日生活、区域游戏、集体教学中让幼儿充分感知和体验数学的重要性。只有引导幼儿体验到数学很重要,才能激发幼儿学习数学的信心与热情,提高幼儿对数学活动的兴趣与参与度,帮助幼儿开启真正愿意学习数学的过程,为幼儿数学素养的终生发展打下良好的基础。  相似文献   

8.
This paper asks what and how some children tell others about themselves and the life they live at home and in school. Drawing on data collected through ethnographic observations, interviews and children's written texts about themselves, the article illustrates the meanings children create and attach to their everyday experience of interactions with adults and other children. Family, friends, pets, school and leisure activities occupy much space in the children's writings. Some of the texts include the placement of self in a positive interpersonal context both at home and at school, with a focus on the importance of these relationships for the children. Some others contain children's negative feelings at home or towards the school. These children blame themselves for their negative feelings in their texts. At the same time, they write about not having a voice when it comes to important decisions concerning their life. They can tell/write it as it is, but they cannot participate in decision-making when it comes to problematic situations.  相似文献   

9.
The first national education goal, school readiness, recognizes a need for young children to be better prepared for entry into elementary school. Many low-income children exhibit a pattern of underachievement in school mathematics. Research has revealed a developmental gap between low-income preschool children and their middle-class peers with respect to the extent of their numerical knowledge. Research has also found that many low-income children do not receive a broad base of support for mathematical development at home or in preschool. In each of two studies, we conducted a bi-generation (parent and child) mathematics intervention with Head Start families. The intervention was designed to enhance parental support for pre-kindergarten children's mathematical development. It was found that low-income parents were willing and able to support this area of their children's development once they were provided with the training to do so. The support that parents provided to their children through the intervention was clearly effective in enhancing the development of children's informal mathematical knowledge. Intervention children developed more extensive mathematical knowledge than a comparison group of low-income children. Thus, an important step toward achieving the school readiness goal can be taken by fostering low- income parents' support for young children's mathematical development.  相似文献   

10.
We adopt a neo-Vygotskian view that a fully concrete scientific concept can only emerge from engaging in practice with systems of theoretical concepts, such as when mathematics is used to make sense of outside school or vocational practices. From this perspective, the literature on mathematics outside school tends to dichotomise in- and out-of-school practice and glamorises the latter as more authentic and situated than academic mathematics. We then examine case study ethnographies of mathematics in which this picture seemed to break down in moments of mathematical problem solving and modelling in practice: (1) when amateur or professional players decided to investigate the mathematics of darts scoring to develop their “outing” strategies and (2) when a prevocational mathematics course task challenged would-be mathematics teachers’ concept of fractions. These examples are used to develop the Vygotskian framework in relation to vocational and workplace mathematics. Finally, we propose that a unified view of mathematics, outside and inside school, on the basis of Vygotsky’s approach to everyday and scientific thought, can usefully orientate further research in vocational mathematics education.  相似文献   

11.
This study explored preschool teachers' beliefs about the appropriateness of early literacy and mathematics education. In all, 60 teachers of 4-year-olds, half working with low-socioeconomic status (SES) children at publicly funded preschools and the other half with middle-SES children at private preschools, were randomly assigned to read either the mathematics or the literacy versions of written vignettes describing issues related to teaching these subjects. Teachers were interviewed individually concerning the vignettes. Analyses showed that teachers of middle-SES children tended to support literacy and mathematics education that respects individual children and their preferences and to oppose classroom use of computers; overall they emphasized nonacademic areas. Teachers of low-SES children tended to focus on literacy and mathematics to prepare children for kindergarten and to support computer use; they showed concern about their students' underdeveloped readiness to learn, particularly literacy. Analyses comparing subject matter showed that for literacy, teachers preferred to gear a curriculum toward children's interests and to allow children to follow their interests in a literacy-rich classroom to promote social competence and positive dispositions toward literacy. For mathematics, teachers preferred to embed mathematics into everyday routines to promote the learning of key knowledge and skills throughout the day. These findings have significant implications for professional development.  相似文献   

12.
The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of children's mathematics skills, but there is limited causal evidence supporting this link. To address this research gap, 47 Head Start children were randomly assigned to a mathematical language intervention group or a business-as-usual group. Over the course of eight weeks, interventionists implemented a dialogic reading intervention focused on quantitative and spatial mathematical language. At posttest, students in the intervention group significantly outperformed the students in the comparison group not only on a mathematical language assessment, but on a mathematical knowledge assessment as well. These findings indicate that increasing children's exposure to mathematical language can positively affect their general mathematics skills. This study is an important first step in providing causal evidence of the importance of early mathematical language for children's general mathematical knowledge and the potential for mathematical language interventions to increase children's overall mathematics abilities.  相似文献   

13.
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14.
This qualitative study examined the relationship between young deaf children's level of mathematics ability ("high" and "low," as defined by test score on the Test of Early Mathematics Ability-3) and opportunities available for the construction of early mathematics knowledge during a problem-solving task implemented by their parents. Findings indicate that the manner in which the mathematically based concepts (number/counting, quantity, time/sequence, and categorization) were incorporated into the activity was more meaningful for children who demonstrated high levels of mathematical ability. In addition, children who demonstrated high levels of mathematical ability experienced a more purposeful use of mediation during activity implementation; however, overall use of mediated learning experience was limited for children from both ability groups.  相似文献   

15.
Current changes, especially the wide application of information technology, in all fields of our life, mean that mathematical knowledge becomes necessary in almost every domain. It implies new expectations for mathematical education. An urgent need of a new mathematical literacy for all—also a new mathematical literacy for engineers—is evident. It is necessary to consider a process of mathematics learning at tertiary level from the epistemological perspective and to investigate students’ ways of mathematical thinking. This epistemological knowledge is especially indispensable when students use information technology. In this article current requirements regarding mathematical education are discussed, especially those for future engineers. Analysis of examples of learning elementary statistics, using graphing calculators as supporting tools, leads to the formulation of essential aims for mathematics educators concerning mathematics teaching for future engineers.  相似文献   

16.
阳明学讲求功夫上身,以突破口耳之学缺乏行动力的局限。只有把良知化成良能,才能在日常生活中随机发用。因此,诚意先于格物,亲民重于新民,每时每刻都得柔心,训练自己的感觉。能力在感觉,意义在感觉。  相似文献   

17.
Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics.  相似文献   

18.
My starting point in this paper is that there is a cultural gap between the mathematics that children do as part of their everyday experience and the mathematics that they learn at school; my thesis is that the computer has (perhaps uniquely) the potential to bridge this divide. The paper will examine the cultural impact-both actual and potential-of the computer on children's mathematical education; at the ways in which the introduction of the computer does and will changes the ambient space in which children learn mathematics.I begin with a brief discussion of the cultural context of mathematics learning and the relationship between informal, everyday mathematical activity, and formal, school mathematies. This perspective leads to a closer examination of what it means to do mathematics, and on the relationship of a technology to the mathematics embedded within a given culture. I discuss the issue of injecting meaning into mathematical activity, and then examine some ways in which the computer might offer a solution to this central problem. Next, I give some examples of the influence of the computer on the culture of the mathematics classroom. Finally, I suggest some of the outstanding issues of research and curriculum development which remain.This paper is based on substantially the same data as is discussed in an article inCultural Dynamics.  相似文献   

19.
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.  相似文献   

20.
In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.  相似文献   

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