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1.
Bert van Oers 《Educational Studies in Mathematics》2010,74(1):23-37
In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children’s development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early mathematical thinking. In these latter approaches, mathematical development in the early developmental stages is seen as an emerging process in the context of children’s own activities that contributes to meaningful learning and stimulation of children’s cultural identity (Bildung approach). The discussion between the training approach versus the ‘Bildung’ approach is still intemperately going on. In this article, some outcomes of a research programme (based at the Free University Amsterdam) are discussed that present empirical studies and their theoretical background (cultural–historical theory, elaborated in an educational concept called ‘Developmental Education’) that demonstrates the promising potentials of promoting mathematical thinking through supporting young children’s appropriation of schematic representations and notations in the context of play. 相似文献
2.
杜英芳 《天津师范大学学报(基础教育版)》2011,12(1):59-61
中美两国数学教育界对学生数学思维的发展都非常重视。我国学者从形象思维、抽象思维、直觉思维等角度对之进行研究和探索;美国学者从儿童生活实际出发,认为学生数学思维包括：匹配与区分、分类、排序、顺序、建模。在论述思维发展时,都结合学生的实际,以案例的方式进行描述。两国在研究的逻辑方法上存在显著差异。我国研究体现出从一般到特殊的特点,而美国的研究则体现出从特殊到一般的特点。比较两国的研究,吸取各自所长,有利于促进我国基础教育数学课程改革的健康发展。 相似文献
3.
Educators of young children can enhance the development of a problem-solving thought process through daily activities in their
classrooms. An emphasis should be placed on the actual thought process needed to solve problems that occur in everyday living.
Educators can follow simple suggestions to create problem-solving situations for all ages of children. The process of thinking
through a problem and finding a solution is more important than traditional mathematics counting and memorizing useless facts.
Even very young children are capable of a problem-solving process that is on the appropriate developmental level. The problem-solving
process is constructivist in nature, as each individual perceives problems according to her or his background and developmental
levels. Educators need to make a conscious effort to capitalize on all stages of problem-solving thinking to enhance future
mathematical development. 相似文献
4.
数学能力是基础性的认知能力,包括数量、空间和逻辑推理等认知能力。早期数学教育有助于在儿童发育和发展的关键期为儿童奠定认知和神经基础,从而培养儿童抽象而精确的数学思维能力与问题解决能力。脑与认知科学研究表明,儿童生来具有数的概念,体现在两个独立的数的核心表征系统,一是大数系统,模糊估计、粗略表征物体的数量幅度;二是小数系统,精确计数、清晰表征每一个物体。早期数学教育可以借鉴当前丰富的脑与认知科学研究成果,将科学理论和教学实践相结合,利用儿童先天具备的数学潜质,逐渐深入而广泛地培养儿童的数学技能。培养儿童的早期数学能力需要家庭、学校和社会的共同努力。 相似文献
5.
In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of
university calculus students’ collaborative development of mathematical methods for finding the volume of a solid of revolution,
in response to mathematical necessity in problem solving, without prior instruction on solution methods. The second theory
emerges from microlinguistic analysis of students’ mathematical choices and use of warrants in substantial argumentation to
communicate, clarify, and convince others of the validity of their conjectures and mathematical work. Our goal was to illuminate
mathematical argumentation by collaborative groups of calculus students at a qualitative level of detail sufficient to reveal
one view of how these students satisfied the creative drive for mathematical meaning, communication, and accuracy in problem
solving as evidenced in one classroom over several days. 相似文献
6.
Matthew Inglis Juan Pablo Mejia-Ramos Adrian Simpson 《Educational Studies in Mathematics》2007,66(1):3-21
In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted
form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate
mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use
of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role
in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately
match up warrant-types with modal qualifiers. 相似文献
7.
Dimitris Chassapis 《Educational Studies in Mathematics》1998,37(3):275-293
This study focuses on the process by which children develop a formal mathematical concept of the circle by using various instruments
to draw circles within the context of a goal-directed drawing task. Particular attention was given to the transition from
using tracers and templates to using a compass for drawing circles and to the extent to which the use of different drawing
instruments may contribute to the formation of a formally defined mathematical concept of the circle. The critical difference
considered in the study is that the compass, in contrast to circle-drawing tracers or templates, induces by its physical structure
and its functional use the generative features of formal mathematical concepts of the circle, that is, the centre and the
radius. Analysis of the empirical data indicates that the use of the compass in circle drawing structures the circle-drawing
operation in a radically different fashion than circle tracers and templates, and brings into play an action-bound practical
thinking. Such thinking has an overall positive influence on the construction of analytical concepts by children that are
analogous to the formally defined mathematical concepts of the circle.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
8.
9.
《International Journal of Educational Research》2002,37(2):195-210
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
10.
Based on their performance on a standardized achievement test, second-grade children (N = 49) were classified as having mathematics difficulties with normal reading achievement (MD only), both mathematics and reading difficulties (MD/RD), reading difficulties with normal mathematics achievement (RD only) and normal mathematics and reading achievement (NA). Each child was given a series of tasks so that we might assess their thinking across four areas of mathematics: number facts, story problems, place value, and written calculation. Children with MD/RD performed significantly worse than NA children in most areas of mathematical thinking, whereas children with MD only performed worse than NA children only on complex story problems. The MD-only group outperformed the MD/RD group on story problems and written calculation. No significant differences were found between the RD-only and NA groups on any of the tasks. The results suggested that among children with mathematics difficulties, the MD/RD subgroup is distinct from the MD-only subgroup, with the former being characterized by pervasive deficiencies in mathematical thinking and the latter by more specific deficits in problem solving. 相似文献
11.
Ruth M. Steinberg Susan B. Empson Thomas P. Carpenter 《Journal of Mathematics Teacher Education》2004,7(3):237-267
In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's engagement with children's thinking changed dramatically in a period of only a few months; observations and interviews several years later confirm she sustained this change. Our analysis focuses on the mathematical discussions she had with her students, and suggests this talk with children about their thinking in instruction served both as an index of change, and, in combination with other factors, as a mechanism for change. We identified four phases in Ms. Statz's growth toward practical inquiry, distinguished by her use of interactive talk with children. Motivating the evolution of phases were two sorts of mechanisms: scaffolded examination of her students' thinking; and asking and answering questions about individual students' thinking. Processes for generating and testing knowledge about children's thinking ultimately became integrated into Ms. Statz's instructional practices as she created opportunities for herself, and then students, to hear and respond to children's thinking. 相似文献
12.
张同斌 《洛阳工业高等专科学校学报》2009,19(2)
高等数学作为大学生的一门重要基础课程,不仅为专业课提供必要的数学工具,还担负着发展数学思维的作用.因此在高等数学的教学实践中,使学生在学好基本概念、基本理论、运算技能和方法的同时,还应进一步达到培养学生的数学思维能力,优化学生的数学思维品质的目的. 相似文献
13.
Developmental exceptionalities span the range of learning abilities and encompass children with both learning disorders and learning gifts. The purpose of this article is to stimulate thinking about these exceptionalities, particularly the complexities and variations within and across people. Investigators tend to view learning disabilities or abilities, and gifts or high-end exceptionalities, as if they were necessarily and completely independent. This approach has led many in the field to look upon only limited aspects of the exceptional child, culminating in an inability to resolve the great variation and covariation that exists within and across children. Although there are a number of cognitive differences models that correctly advocate for an appreciation of profiles of strengths and weaknesses in the exceptional child, there remains a need for a neuroscientific approach that can help us better understand and accommodate the twice-exceptional individual—one with developmental disorders but also with high skills in the talent, creativity, or intellectual domains. We propose a model that will help us to fully appreciate that the brain that produces developmental learning abilities across the spectrum must be viewed as an integrated and multifaceted organ that is more than a simple reflection of its separate parts or domain-specific symptoms. We use developmental reading disability or dyslexia and the twice-exceptional individual as a means to illustrate how this model can aid in our thinking about these conditions. 相似文献
14.
This paper presents how the medico‐hygienist model of childhood, which had prevailed throughout the nineteenth century, was replaced at the turn of the twentieth century by the novel developmental model, which arose in the first decades of the 1900s and was later systematised by Piaget, Spock, etc. The medico‐hygienist model revolved around core constituents such as regulation, firmness and discipline, standardisation whose historical specificity could be, according to Elias, related to the civilising process. The developmental model, on the other hand, is linked to the systematic scientific investigation of childhood and pertains, foremost, to the proposition that growing up was best figured in the concept of development: the figure of the child as a human who develops consistently in time and space. The key element can be worded as follows: Why is such child maturation almost universally constructed as development? The second crucial idea of the model consists in understanding child development in terms of a (rather linear) sequence of particular stages. The equation of child maturation, both physically and psychologically, with development is crystallised in the figure of a uniform, inevitable and universal sequence of developmental stages and, accordingly, its schedule; therefore, maturation, development, stages and sequences are closely connected to children's socialisation. My aim is to trace developmental thinking in its historical specificity by bringing to light some neglected social processes that contribute to the regulation of children and the transformation of generational relationships. These processes have always occurred in various societies, andyet I am trying to put forward an original perspective that pertains to the intersection of developmental thinking and social change. I attempt here to introduce a historic juncture of developmental thinking and social transformations that moulded children. I also attempt to track down the historical roots of the developmental framework: how it became the central principle by which we think about children today. 相似文献
15.
本文从信息社会对人的数学思维的要求,数学思维在数学学科教育中的价值,及其在素质教育中的地位三个方面阐述了21世纪加强数学思维教育的意义. 相似文献
16.
Primary special school teachers' knowledge and beliefs about supporting learning in numeracy 
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下载免费PDF全文 Lio Moscardini 《Journal of Research in Special Educational Needs》2015,15(1):37-47
This paper presents findings from a qualitative study of a group of 12 teachers in primary special schools in Scotland for children with moderate learning difficulties. It sets out an analysis of classroom observations and interviews that explored teachers' knowledge and beliefs about teaching and learning in mathematics with children with moderate learning difficulties. The teachers were interviewed pre‐ and post‐intervention; this was a research‐based professional development programme in children's mathematical thinking (Cognitively Guided Instruction) which teachers then developed in their classrooms. The findings showed that prior to the professional development, the teachers had a limited knowledge of children's mathematical development with teaching frequently informed by intuitive beliefs and dated and sometimes discredited practices. Most teachers had low expectations of children with learning difficulties. Post‐intervention, the teachers reviewed this stance and affirmed that a deeper understanding of children's mathematical thinking provided a more secure knowledge base for instruction. They also recognised the extent to which learners were constrained by existing classroom practices. The paper argues for the commonality of this knowledge base and considers the problematic nature of viewing such knowledge as sector specific. 相似文献
17.
《Learning and Instruction》2007,17(5):510-531
This paper examines task design that affords deep changes in mathematical thinking in the context of peer interaction. We describe a study in which 60 low-level high-school students solved a proportional reasoning task, the “blocks” task as individuals and/or in dyadic interaction. We show that we could tailor the design of the task in order to create a cognitive conflict among dyads, notwithstanding the strategies used by the students. We show that students' proportional reasoning strategies did not improve as a result of discussion even when guided by an experimenter dedicated at reaching consensus; however the introduction of a hypothesis testing device and the guidance of the experimenter to accommodate divergent views led peers to impressive conceptual change in their discussion and in an individual post-test. Examination of one case of dyadic interaction shows that beyond the value of given characteristics of individuals or of tasks, the process of argumentation that takes place between the peers explains the subsequent gains of the individuals. The conditions under which conceptual change was attained challenge theoretical views on cognitive development and social interactions. 相似文献
18.
We suggest that the assessment of intelligence (a) ought to be tied to measuring basic cognitive components (as opposed to more heterogeneous tasks found on IQ tests and developmental scales); (b) be "contextualized"; and (c) be embedded in developmental theory, unlike current psychometric approaches. As a first step toward thinking about the contextual nature and the developmental course of intelligence, we propose that infants and young children be assessed on four basic information-procesing components that appear to be involved in higher level thinking and reasoning (concept formation, rudimentary counting, visual expectancy, and long-term memory), and that they be followed over time on variants of these measures in order to gain information about rate and quality. 相似文献
19.
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
20.
帮助儿童学会反思——来自心理理论研究的启示 总被引：1，自引：0，他引：1
作为朴素理论的一个核心领域,儿童心理理论研究是目前发展心理学研究中的前沿课题之一.研究表明,儿童不仅能发现人是有心智的,是由各种心理状态构成的,而且能发现可以通过影响一个人的想法而改变他的行为.教育者应该把儿童看成是拥有各种心理状态的、会思考的个体,在教育过程中提供相应的教育策略,帮助儿童成长为真正意义上的能思考、会反思的人. 相似文献