The didactical challenge of symbolic calculators guin dominique ruthven kenneth trouche luc
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Thus, this chapter will define aspects of representational competence, modes of representations, and the role of a representational competence theoretical framework in science education research and practice. Esta perspectiva está en la base de las propuestas de Vérillon y Rabardel 1995 que se han utilizado recientemente para desarrollar la teoría de la génesis instrumental con la que se busca caracterizar el aprendizaje de artefactos en entornos tecnológicos Guin, Trouche y Ruthven, 2005. We will briefly describe the methodology and the main results in relation to the phenomena previously mentioned. In this chapter, we study more precisely their learning processes related to their use of symbolic calculators. Barbeau Humanities, Social Science and Law Springer East Asian Social Movements Jeffrey Broadbent, Vicky Brockman Humanities, Social Science and Law Springer Learning and Instructional Technologies for the 21st Century Leslie Moller, Jason Bond Huett, Douglas M.

These two questions are investigated through the design, implementation and analysis of the outcomes of two online in-service courses for mathematics teachers. They take into account individual and social processes of the mathematical instrument construction from a given artifact. That is, guiding the students to think of the concept, in terms of finding areas of bound regions by using the idea of approximation and limit visually, dealing with numeric and algebraic representations, and construing geometric representations of the concept. Proceedings of the 28 th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Just as expertise in playing a piano relies on the interanimation of finger movements and perceived sounds, the authors argue that mathematical expertise involves the systematic interpenetration of perceptual and motor aspects of playing mathematical instruments. What does the sum of those areas represent when the number of simple figures increases? The students in the project had been using Derive for one or two years, respectively. Responsibility: Dominique Guin, Kenneth Ruthven, Luc Trouche editors.

The fulfilment of these two requirements is illustrated for tasks from the upper secondary education concerning functions, equations and inequalities. While computational technologies are transforming the professional practice of mathematics, as yet they have had little impact on school mathematics. Il insiste en particulier sur deux points: l'importance de la notion de schème pour analyser l'action instrumentée, pour mettre en relation le geste et la pensèe; l'importance de la notion de métaconnaissance pour analyser les différences de comportements des élèves. Results of this analysis have an influence on the design of problem situations. A result is the enrichment of multiple views of algebra and changing classroom dynamics.

Jones Humanities, Social Science and Law Springer Non-Native Language Teachers Enric Llurda Humanities, Social Science and Law Springer Inner Speech — L2 María C. We developed our research in the context of a functional teacher-training program in which future teachers are expected to transform a set of didactical notions into instruments that could be useful in the teaching practice. Abstract In this study, we attempt to identify some examples of key moments in the learning of isometries with students who are 14 and 15 years old. A return to these basic issues can also shed light on the difficulties students encounter in learning mathematics. This article reports part of a research project that attempts to identify the elements of an online course that promote the emergence of teachers' reflections.

First of all, we pinpoint the didactic phenomena taking place in the experiments; subsequently, we suggest a new theoretical approach aimed at giving a better description, for each student, of the transformation of a technical tool into an instrument for mathematical work. We reflect on the contribution that this complementarity makes to the discussion on the articulation of theoretical frameworks. Decker Humanities, Social Science and Law Springer The Criminology of White-Collar Crime Sally S. The E-mail message field is required. En tercer lugar, nos fijamos en los aspectos de gestión del tutor, que tiene que ir creando la necesidad de que los alumnos sigan un proceso de matematización vertical García, s. Bruinsma Humanities, Social Science and Law Springer Violence in Europe Sophie Body-Gendrot, Pieter Spierenburg Humanities, Social Science and Law Springer Duverger's Law of Plurality Voting Shaun Bowler, André Blais, Bernard Grofman Humanities, Social Science and Law Springer Teaching Mathematical Reasoning in Secondary School Classrooms Karin Brodie Humanities, Social Science and Law Springer Games: Purpose and Potential in Education Christopher Thomas Miller Humanities, Social Science and Law Springer Substance Abusing Inmates Lior Gideon Humanities, Social Science and Law Springer Constructing Knowledge for Teaching Secondary Mathematics Orit Zaslavsky, Peter Sullivan Humanities, Social Science and Law Springer Stifling Political Competition James T. The research process is on the conceptualization of the notion of limit by means of the discrete continuous interplay.

The second review focuses on clarifying how the concept of reflection is defined in the research literature and why it is considered as particularly relevant to the professional development of mathematics teachers. And, what type of reasoning do students develop about the concept as a result of using Derive software? The findings may lead to an examination of the current situation in differential equation classrooms to ensure a balance between procedural, conceptual, and technological knowledge with mathematical thinking approach. What does it mean for a function to be nonnegative and continuous on one given interval? Hence, they were familiar with the software and the laptops: in terms of instrumental genesis like it is referred in Trouche, 2005 , the students had already accomplished the generation of a number of the Derive commands and other computer facilities as instruments for their work with mathematics. Hoffmann, Johannes Lenhard, Falk Seeger Humanities, Social Science and Law Springer Barriers and Biases in Computer-Mediated Knowledge Communication Rainer Bromme, Friedrich W. The concept of documentational genesis can be considered as an analogy of the concept of instrumental genesis Rabardel, 1995; Trouche, 2005b into the field of mathematics teacher education. The discrepancy between technology as a support for visual perception but a tool that cannot support theconception of approaching infinities, makes the study of asymptotes an intriguing domain for investigating what is being manipulated with software and how.

Drawing on a substantial program of French innovation and research, as well as closely related studies from Australia and the Netherlands, it provides rich illustrations of the many aspects of technology integration and of the ways in which these are shaped at different levels of the educational institution. This study documents the type of mathematical competence that first year university students develop as a result of working on series of problems that involve definite integral concepts. This typology indicates that the more complex the environment, the more diverse the work methods, and, consequently, the more necessary the intervention of the teacher in order to assist instrumental genesis. This paper reviews efforts to use digital tools in teachers' and pupils' work and problem solving in mathematics within the frame of two research and development projects in six lower secondary schools in Norway. Didactic art was meant both to entertain and to instruct. Not only has this facilitated the application of established methods of mathematical and statistical analysis but it has stimulated the development of innovative approaches.

The most salient results of the study indicate that a majority of students were able 1 to cope with partial data about functions e. It is more complex when described in terms of the relationships among these three dimensions. This study describes learning advanced mathematics that occurs through constructing qualitative reasoning methods using graphic technology. Nelson Humanities, Social Science and Law Springer International Handbook of Juvenile Justice Josine Junger-Tas, Scott. The appearance of ever more powerful and portable computational tools has certainly given rise to continuing research and development activity at all levels of mathematical education.

Nuestro interés se centra en las funciones epistémica, heurística y pragmática de los organizadores del currículo Trouche, 2005a p. Around the 19th century the term didactic came to also be used as a criticism for work that appears to be overly burdened with instructive, factual, or otherwise educational information, to the detriment of the enjoyment of the reader. An instrumental approach to mathematics learning in symbolic calculator environments; 7. The insight gained suggests that both approaches were needed to get the full picture of the development. En este trabajo caracterizamos el aprendizaje del futuro profesor de matemáticas sobre la noción de objetivo. Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement the authors call perceptuomotor integration. We assume an instrumental mediation view of learning and propose conceptual and methodological tools for exploring learning processes organized around three dimensions that we call meaning, technical use and practical use of a didactical notion.