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1.
Cognitive play and mathematical learning in computer microworlds 总被引：1，自引：0，他引：1
Based on the constructivist principle of active learning, we focus on children's transformation of their cognitive play activity into what we regard as independent mathematical activity. We analyze how, in the process of this transformation, children modify their cognitive play activities. For such a modification to occur, we argue that the cognitive play activity has to involve operations of intelligence which yield situations of mathematical schemes.We present two distinctly different cases. If the first case, the medium of the cognitive play activity was a discrete computer microworld. we illustrate how two children transformed the playful activity of making pluralities into situations of their counting schemes. In the second case, the medium was a continuous microworld. We illustrate two children's transformation of the playful activity of making line segments (sticks) into situations of their counting schemes. We explain one child's transformation as a generalizing assimilation because it was immediate and powerful. The transformation made by the other child was more protracted, and social interaction played a prominent role. We specify several types of accommodations induced by this social interaction, accommodations we see as critical for understanding active mathematics learning. Finally, we illustrate how a playful orientation of independent mathematical activity can be inherited from cognitive play. 相似文献
2.
Karina J. Wilkie 《Interactive Learning Environments》2013,21(5):519-535
Recent applications of technology to mathematics education have been designed with cognitive and constructivist theoretical perspectives in mind, viewing mathematical learning as the acquisition of knowledge through the construction of meanings and connections between concepts. With the advent of increasingly flexible communication technologies, there is both the need and opportunity to consider how they might be utilised, particularly since emergent socio-cultural theories advocate learning in mathematics as an inherently social activity where understanding is developed and negotiated collaboratively. The need to examine effective technology-facilitated learning arose in the context of a research project, currently underway in a number of secondary schools in the state of Victoria and funded by the Australian Research Council. It is investigating the learning needs of pupils who are absent from school for prolonged or intermittent periods owing to chronic illness yet continue with their school studies. An emerging understanding of the significant difference between computer-mediated contact for mere information exchange and communication for teaching and learning has led to a consideration of socio-cultural perspectives on effective mathematical learning and a focussed investigation of technologies able to facilitate them. Early data have demonstrated the potential of videoconferencing, online whiteboarding and interactive whiteboard application sharing, but which require particular resources, aligned infrastructure and teacher support. This article explores issues surrounding the use of such technologies for collaborative mathematical learning in a context where online interaction is being considered for the learning support of pupils unable to attend school. 相似文献
3.
Elements of Epistemological Knowledge for Mathematics Teachers 总被引：1，自引：1，他引：0
Heinz Steinbring 《Journal of Mathematics Teacher Education》1998,1(2):157-189
Epistemological knowledge of mathematics in social learning settings is an important type of professional knowledge for mathematics
teachers because it refers to social and interactive processes of communication. This article focuses on one central aspect
of epistemological mathematical knowledge, namely on the problematique of how mathematical signs and symbols gain meaning
in the interactive social processes of teaching and learning. A teaching episode is presented and analyzed from an epistemological
perspective. This analysis leads to the identification of three important components of epistemological knowledge that could
be introduced into the education of mathematics teachers: the developmental nature of mathematical knowledge; interactive
social processes of mathematical communication as autonomous systems; and the interdependence of social and epistemological
constraints in mathematical communication.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
One could focus on many different aspects of improving the quality of mathematics teaching. For a better understanding of children’s mathematical learning processes or teaching and learning in general, reflection on and analysis of concrete classroom situations are of major importance. On the basis of experiences gained in a collaborative research project with elementary school teachers, several ideas about a professional reflection on one’s own instruction activities are explained. The paper focuses on joint reflection between teachers and researchers on the participating teacher’s own classroom interaction by means of concrete examples. It becomes clear that changes of one’s own interaction behavior will take place only in the long-term. Nevertheless such a joint professional reflection should be an essential component of teachers’ professional knowledge in a natural way. 相似文献
5.
美国数学教育家杜宾斯基提出的APOS理论是一种建构主义的数学学习理论,他将数学概念的建构分为Action、Process、Object、Scheme四个阶段.在对该理论的认识基础上,结合高职学生数学学习认知的心理特点,对化工专业高等数学概念的教学进行探讨,并就如何进行数学概念教学设计作了探索,使学生主动建构其概念体系. 相似文献
6.
Fostering Parental Support for Children's Mathematical Development: An Intervention with Head Start Families 总被引：2，自引：0，他引：2
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
7.
Deborah Schifter 《Journal of Mathematics Teacher Education》1998,1(1):55-87
A successful practice grounded in the principles that guide the current mathematics education reform effort requires a qualitatively different and significantly richer understanding of mathematics than most teachers currently possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K-6 teachers' mathematical development, (a) engagement in inquiry into mathematics itself, and (b) investigation of children's mathematical thinking, illustrating how the need for these two kinds of investigations arises in classroom situations and how they can be pursued in a professional development setting. 相似文献
8.
Deaf children tend to fall behind in mathematics at school. This problem may be a direct result of particular experiences in the classroom; for example, deaf children may find it hard to follow teachers' presentations of basic, but nevertheless quite abstract, mathematical ideas. Another possibility is that the problem starts before school: They may either be worse than hearing children at early, nonlinguistic number representations, they may be behind in learning the culturally transmitted number string, or both. This may result in deaf children failing to develop informal problem-solving strategies, which prepare most children for the more formal learning of number and arithmetic that they will have to do at school. We compared 3- and 4-year-old deaf and hearing children's ability to remember and to reproduce the number of items in a set of objects. In one condition, we presented all the items together in a spatial array; in another, we presented them one at a time in a temporal sequence. Deaf children performed as well as the hearing children in the temporal tasks, but outperformed their hearing counterparts in the spatial task. These results suggest that preschool deaf children's number representation is at least as advanced as that of hearing children, and that they are actually better than hearing children at representing the number of objects in spatial arrays. We conclude that deaf children's difficulties with mathematical learning are not a consequence of a delay in number representation. We also conclude that deaf children should benefit from mathematical instruction that emphasizes spatial representation. 相似文献
9.
论中小学“数学情境与提出问题”的数学学习 总被引：24，自引：30，他引：24
创新源于问题，问题源于情境，在中小学数学教育中，应着力抓住创设数学情境与提出数学问题的“情境－问题”学习链，努力培养学生的创新意识和实践能力，以利于我国创造型人才的成长。 相似文献
10.
Richard Noss 《Educational Studies in Mathematics》1988,19(2):251-268
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
11.
12.
In recent years the interest in preschool mathematics has increased. However, studies seldom focus on children under the age of three and research is scarce on the early use of mathematics observed in natural settings. This article reports a study of mathematical possibilities during diaper changing in a preschool setting. A diaper change can be a communicative moment when the child can experience mathematics with a professional preschool teacher, but it can also be a moment of mechanical routine with no pedagogical context. The intention of the study presented here was to investigate the mathematical potential preschool teachers described in relation to diaper changing and to examine the ways this potential was put into action. Both similarities and differences emerged regarding the mathematical potential preschool teachers described in relation to diaper changing and the mathematical content that they were observed to communicate. The results show that it is possible to communicate mathematical content in a pedagogical way during diaper changes, making this routine a learning opportunity for children. However, the results also show variations in the observed range and context of such communication, and therefore the potential for mathematical learning during diaper changes seems to differ widely. 相似文献
13.
Stefanie Rach Aiso Heinze 《International Journal of Science and Mathematics Education》2017,15(7):1343-1363
Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students’ learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 first-semester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students’ abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed. 相似文献
14.
Jill Adler 《Journal of Mathematics Teacher Education》2000,3(3):205-224
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
15.
Although studies on students’ difficulties in producing mathematical proofs have been carried out in different countries,
few research workers have focussed their attention on the identification of mathematical proof schemes in university students.
This information is potentially useful for secondary school teachers and university lecturers. In this article, we study mathematical
proof schemes of students starting their studies at the University of Córdoba (Spain) and we relate these schemes to the meanings
of mathematical proof in different institutional contexts: daily life, experimental sciences, professional mathematics, logic
and foundations of mathematics. The main conclusion of our research is the difficulty of the deductive mathematical proof
for these students. Moreover, we suggest that the different institutional meanings of proof might help to explain this difficulty.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
One could focus on many different aspects of improving the quality of mathematics teaching. For a better understanding of
children’s mathematical learning processes or teaching and learning in general, reflection on and analysis of concrete classroom
situations are of major importance. On the basis of experiences gained in a collaborative research project with elementary
school teachers, several ideas about a professional reflection on one’s own instruction activities are explained. The paper
focuses on joint reflection between teachers and researchers on the participating teacher’s own classroom interaction by means
of concrete examples. It becomes clear that changes of one’s own interaction behavior will take place only in the long-term.
Nevertheless such a joint professional reflection should be an essential component of teachers’ professional knowledge in
a natural way.
An erratum to this article can be found at 相似文献
17.
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
18.
Mathematics learning and practice in and out of school: A framework for connecting these experiences
Joanna O. Masingila Susana Davidenko Ewa Prus-Wisniowska 《Educational Studies in Mathematics》1996,31(1-2):175-200
A variety of researchers in the last fifteen years have described how people learn and use mathematics in out-of-school situations. These researchers have found that mathematics learning and practice in and out of school differ in a number of ways. In this paper we examine and discuss these differences while maintaining the position that while some differences may be inherent, many differences can be narrowed so that mathematics learning and practice in school and out of school can build on each other and be connected. Before discussing a framework that we think sheds some light on connecting these experiences, we present some research from several of our studies that illustrates some of the differences between in-school and out-of-school mathematics practice and lays the groundwork for the discussion of the framework.We then discuss Saxe's (1991) research framework for gaining insight into the interplay between sociocultural and cognitive development processes through the analysis of practice participation (p. 13). Although Saxe's framework is a method for studying the interplay between sociocultural and cognitive development processes, we propose that it may be helpful in working towards connecting in-school and out-of-school mathematics learning and practice. Thus, we discuss the framework with illustrations from our own research, and then elaborate on ways to make this interplay between in-school and out-of-school contexts more deliberate. 相似文献
19.
This study examined elementary school children's beliefs about learning and assessed the influences of such beliefs on their understanding of science texts. Eighty-three children, 46 from Grade 4 and 37 from Grade 6, were administered a questionnaire on children's implicit notions of learning. Children were also asked to read a science text and complete several tasks that assessed their understanding of text information. Results indicated that older children were more likely to hold constructivist views of learning, and they also performed better than younger children on the text-processing tasks. As well, children's views of learning were significantly related to depth of text understanding when age effects were controlled. This study extends current research on epistemological beliefs of university and high school students. Implications of children's beliefs about learning and their roles in knowledge construction are discussed. Copyright 2001 Academic Press. 相似文献
20.
Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon meeting of these two communities, who have very different perspectives on mathematics and its teaching. The instructors had no experience in primary school teaching, and their professed goal was to deepen the teachers’ understanding of the mathematics they teach, while teachers were expecting the course to be pedagogically relevant for their teaching. Surprisingly, despite this mismatch in expectations, the course was considered a success by teachers and instructors alike. In our study, we analyzed a lesson on division with remainder for teachers of grades 3–6, taught by the professor. The framework used for the data analysis was mathematical discourse for teaching, a discursive adaptation of the well-known mathematical knowledge for teaching framework. Our analysis focuses on the nature of the interactions between the parties and the learning opportunities they afforded. We show how different concerns, which might have hindered communication, in fact fueled discussions, leading to understandings of the topic and its teaching that were new to all the parties involved. The findings point to a feasible model for professional development where mathematicians may contribute to the education of practicing teachers, while they are gaining new insights themselves. 相似文献