共查询到20条相似文献，搜索用时 46 毫秒
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Raymond Duval 《Educational Studies in Mathematics》2006,61(1-2):103-131
To understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes. What are the cognitive systems that are required to give access to mathematical objects? Are these systems common to all processes of knowledge or, on the contrary, some of them are specific to mathematical activity? Starting from the paramount importance of semiotic representation for any mathematical activity, we put forward a classification of the various registers of semiotic representations that are mobilized in mathematical processes. Thus, we can reveal two types of transformation of semiotic representations: treatment and conversion. These two types correspond to quite different cognitive processes. They are two separate sources of incomprehension in the learning of mathematics. If treatment is the more important from a mathematical point of view, conversion is basically the deciding factor for learning. Supporting empirical data, at any level of curriculum and for any area of mathematics, can be widely and methodologically gathered: some empirical evidence is presented in this paper. 相似文献
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This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In
the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction
between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on
both time and motion—hence, on physical interpretations of mathematical abstractions—which are dimensions of thinking that
are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk
contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide
an essential mediating role between the two. 相似文献
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The theoretical background and different methods ofconcept mapping for use in teaching and in research on learning processes are discussed. Two mathematical projects, one on fractions and one on geometry, are presented in more detail. In the first one special characteristics of concept maps were elaborated. In the second one concept mapping allowed students' individual understanding to be monitored over time and provided information about students' conceptual understanding that would not have been obtained using other methods. Regarding the students' individual concept maps in more detail there were some additional findings: (i) The characteristics of the maps change remarkably from fourth grade to sixth grade; (ii) There is some evidence that prior knowledge related to some mathematical topics plays a very important role in students' learning behaviour and in their achievement; (iii) Concept maps provide information about how individual students relate concepts to form organised conceptual frameworks; (iv) Long-term difficulties with specific concepts are able to be traced. These findings are discussed with regard to results of other studies as well as to their implications for the teaching of mathematics in the classroom. 相似文献
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Philip C. Clarkson 《Educational Studies in Mathematics》1992,23(4):417-429
It is argued that bilingual students should not be categorized as a unidimensional group. Their level of competence in each language is important if academic activity is considered. As an example of this, results from the present study indicate that Papua New Guinea bilingual students competent in both their languages scored significantly higher on two different types of mathematical tests compared to collegues who had low competence in their languages. Further, there was some indication that bilingual students competent in both languages performed better than monolingual students, even though the monolingual students attended schools that had many more teaching resources. Such results were seen as support for the new Papua New Guinea govemment policy of using students' original languages in school. The use of the students' original languages may also open the way for easier access to traditional mathematical concepts in classrooms. 相似文献
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Luis Radford 《Educational Studies in Mathematics》2000,42(3):237-268
The purpose of this article, which is part of a longitudinal classroom research about students' algebraic symbolizations,
is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the
algebraic generalization of patterns and(2) to provide accounts about the students' emergent algebraic thinking. The research
draws from Vygotsky's historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov's theory
of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered
as a sign-mediated cognitive praxis. Within this theoretical framework, the students' algebraic activity is investigated in the interaction of the individual's
subjectivity and the social means of semiotic objectification. An ethnographic qualitative methodology, supported by historic,
epistemological research, ensured the design and interpretation of a set of teaching activities. The paper focuses on the
discussion held by a small group of students of which an interpretative, situated discourse analysis is provided. The results
shed some light on the students' production of (oral and written) signs and their meanings as they engage in the construction
of expressions of mathematical generality and on the social nature of their emergent algebraic thinking.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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Mariana Montiel Miguel R. Wilhelmi Draga Vidakovic Iwan Elstak 《Educational Studies in Mathematics》2009,72(2):139-160
The main objective of this paper is to apply the onto-semiotic approach to analyze the mathematical concept of different coordinate
systems, as well as some situations and university students’ actions related to these coordinate systems. The identification
of objects that emerge from the mathematical activity and a first intent to describe an epistemic network that relates to
this activity were carried out. Multivariate calculus students’ responses to questions involving single and multivariate functions
in polar, cylindrical, and spherical coordinates were used to classify semiotic functions that relate the different mathematical
objects. 相似文献
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In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
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Maura Iori 《Educational Studies in Mathematics》2018,98(1):95-113
While many semiotic and cognitive studies on learning mathematics have focused primarily on students, this study focuses mainly on teachers, by seeking to bring to light their awareness of the semiotic and cognitive aspects of learning mathematics. The aim is to highlight the degree of awareness that teachers show about: (1) the distinction between what the institution (school, university, society, etc.) proposes as a mathematical object (not in itself but as the content to be learned) and one of its semiotic representations; (2) the different aspects of a semiotic representation that the student able to handle the representation and the student who handles the representation with difficulty may focus on; (3) the semiotic conflicts generated by the contents of semiotic representations that are similar to each other in some respect. For this purpose, in this study, the semio-cognitive approach introduced by Raymond Duval was complemented with the semiotic-interpretative approach of the Peircean tradition. By embracing the pragmatist research paradigm, the methodology was based on the research questions, which guided the selection of the research methods within a qualitatively driven mixed methods design. The research results clearly show the need for a review of professional teacher training programs, as regards the role the semiotic handling plays in the cognitive construction of the mathematical objects and the learning assessment. 相似文献
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George Santi 《Educational Studies in Mathematics》2011,77(2-3):285-311
The objective of this paper is to study students?? difficulties when they have to ascribe the same meaning to different representations of the same mathematical object. We address two theoretical tools that are at the core of Radford??s cultural semiotic and Godino??s onto-semiotic approaches: objectification and the semiotic function. The analysis of a teaching experiment involving high school students working on the tangent, shows how students?? difficulties in ascribing sense to different representations of a common mathematical object can be traced back to the kind of objectification processes and semiotic functions they are able to establish. 相似文献
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Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics (Chevallard 19:221–266, 1999), in combination with semiotic aspects from the instrumental approach to tool use. The analysis we present is based on interviews carried out with a 10th grade student who participated in our research. Our findings highlight the mathematical knowledge (technological discourse) constructed in the process of confronting, differentiating, and articulating the several mathematical techniques and theoretical ideas (pertaining to the numeric perspective and the syntactic perspective on algebraic equivalence) related to the designed equivalence tasks. 相似文献
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分析了数学概念的特点及其学习的主要影响因素,认为不正确的概念意象和薄弱的抽象概括能力是阻碍学生数学概念学习的主要原因;提出了营造概念学习情境、计算机图形培育概念直觉、突出概念本质属性、强化概念之间普遍联系等教学策略。 相似文献
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数学问题解决及其教学 总被引：11，自引：0，他引：11
刘元宗 《课程.教材.教法》2004,(2)
数学问题是以数学为内容,或者虽不以数学为内容,但必须运用数学概念、理论或方法才能解决的问题。它来源于人类的生产、生活实践,来源于人们了解自然、认识自然的科技活动。问题解决中的“问题”主要是指那些非常规的,或者条件不充分、结论不确定的开放性、探究性问题,其设计要遵循可行性、渐进性、应用性等原则。问题解决教学要通过创设情境来激发学生的求知欲望,使学生亲身体验和感受分析问题、解决问题的全过程,从而培养使用数学的意识、探索精神和实际操作能力。教学中,要注重发挥学生的主体作用和教师主导作用,二者相辅相成,不可偏废。 相似文献
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Yusuke Shinno 《International Journal of Science and Mathematics Education》2018,16(2):295-314
This paper reports on combining semiotic and discursive approaches to reification in classroom interactions. It focuses on the discursive characteristics and semiotic processes involved in the teaching and learning of square roots in a ninth grade classroom in Japan. The purpose of this study is to characterize the development of mathematical discourses in a series of mathematics lessons in terms of the commognitive framework and the model of semiotic chaining. To achieve this objective, the notion of reification is revisited from cognitive, semiotic, and discursive points of view, and classroom activities are observed and analysed in terms of the combined theoretical framework. The results suggest that the model of semiotic chaining is not incommensurable with a strong discursive approach and the changes of meta-discursive rules—an essential aspect of the reification of new signifiers—that take place in the phases of the learning of addition on square roots. 相似文献
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Lulu Healy Solange Hassan Ahmad Ali Fernandes 《Educational Studies in Mathematics》2011,77(2-3):157-174
In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the appropriation of practices associated with the sets of artefacts that have historically come to represent the body of knowledge we call mathematics. This process of appropriation involves a coordination of a variety of the semiotic resources??spoken and written languages, mathematical representation systems, drawings, gestures and the like??through which mathematical objects and relationships might be experienced and expressed. To highlight the connections between perceptual activities and cultural concepts in the meanings associated with this process, we concentrate on learners who do not have access to the visual field. More specifically, we present three examples of gesture use in the practices of blind mathematics students??all involving the exploration of geometrical objects and relationships. On the basis of our analysis of these examples, we argue that gestures are illustrative of imagined reenactions of previously experienced activities and that they emerge in instructional situations as embodied abstractions, serving a central role in the sense-making practices associated with the appropriation of mathematical meanings. 相似文献
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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