La matemática escolar y los estadios de desarrollo

RESUMEN

En este artículo se plantea la relación entre la teoría piagetiana del desarrollo cognitivo con las matemáticas escolares. En el aprendizaje de las matemáticas se deben tener en cuenta las limitaciones en las capacidades cognitivas del niño en los diferentes estadios del desarrollo. Es necesario haber logrado un cierto automatismo en las operaciones típicas de un nivel de desarrollo para poder avanzar al siguiente nivel. Parece que el modelo del procesamiento de la información constituye un marco fructífero de estudio y de investigación en este campo. Se analiza el desarrollo cognitivo en relación con algunos conceptos matemáticos, la capacidad del niño para manejar estos conceptos y las implicaciones en la enseñanza de las matemáticas.     

Telematics-Supported Education for Traditional Universities in Europe

Telematics is the combination of information technology and communication technology. Telematics applications to support educational delivery and participation in traditional European universities are rapidly becoming part of the educational setting. Sometimes they are used specifically to increase distance flexibility in participation, but this is not their only value. Telematics applications are also associated with other forms of flexibility, as well as with heightened efficiency and enrichment of the learning process, both for those in full-time traditional attendance and those participating in increasingly variable ways. In this paper, we first give an overview of the pressures for change in traditional universities in Europe and then define the change domain as involving much more than distance. Then, an overview of a variety of ways that telematics applications are being used in traditional universities in Europe will be given, including categories relating to various aspects of the course-participation experience in the individual course (such as aspects relating to lectures, self-study, and project-type group work). This will be followed by examples of new forms of course organization involving one or more institutions and also of new forms of activities in which traditional universities are becoming involved outside of their core business of mainstream course delivery. The impact on a particular institution, the University of Twente in The Netherlands, will be discussed in more detail. Issues demanding serious attention include staff and student engagement and support and technical decisions relating to the infrastructure and interface of the technology needed to make the new flexibilities possible. These are described and illustrated with examples. The difficulties in supporting this evolution in traditional universities with cost-effectiveness analysis are also noted. Finally, a reflection is made on the changing state of the division between traditional universities and universities organized around distance and open delivery. In some ways, this division is rapidly loosing meaningfulness, but certain differences that are more profound than “distance” still remain.     

Images in mirrors: Recollections,alternative explanations and modes of cognitive functioning

Students' conceptions of how objects are seen directly, and in mirrors, were explored in an analysis of their written and drawn responses to common visual phenomena depicted in cartoons with brief text. Students in Grades K-10 (n=214) completed a questionnaire and some were interviewed. Evidence was sought to support an hypothesis for increasingly sophisticated responses related to the concepts of sight, light, reflection and image. The developmental model used in this analysis was the updated SOLO Taxonomy (Biggs & Collis, 1991; Collis & Biggs 1991). It appears from the results that different modes of functioning can interfere to produce factually incorrect recollections of experience particularly in the age group 7 to 13 years approximately. Also, this is associated with the common spurious conception that mirrors have a lateral inversion property. Explanations involving light were extremely rare and its role related to the production of an image ‘in the mirror’ but not to the perception of an image in the eyes. Specializations: science education, students' understandings of phenomena in science. Specializations: cognitive development, evaluation, mathematics and science education. Specializations: mathematics education, students' understanding of chance and data concepts.     

Learning productivity: a case analysis of the 'e-BOSNO' course for manager teams

Action learning in a workplace context, focused on projects relating to real business needs, is the basis of the management seminars offered by the BOSNO (in Dutch, ‘BedrijfsOpleiding voor Samenwerkende Nederlandse Ondernemingen’[Company training for Dutch companies working in cooperation with each other]) consortium in The Netherlands. In the seminars, managers from participating companies work in teams on multiple‐step problem analysis and solution strategies, supported by workplace coaches. The teams also interact with each other so that peer learning is stimulated. To extend the BOSNO management seminar model in both depth and flexibility, a new approach called e‐BOSNO was designed in which a web‐based learning support environment played a critical role. This paper describes the e‐BOSNO design process and gives results from the first cycle of e‐BOSNO. The results showed the participants to be much more active and interactive than in previous e‐BOSNO seminars, even though there were fewer face‐to‐face meetings. Workplace‐oriented learning occurred and was shared in a way which makes it available for reuse in subsequent e‐BOSNO seminars.     

Visual processing during mathematical problem solving

This study investigated, in the context of mathematical problem solving by secondary school students, the nature of the visual schemata which Johnson (1987) hypothesises mediate between logical propositional structures and rich specific visual images. Four groups of grade 10 students were studied, representing all combinations of high and low operational ability in mathematics (equivalent to Johnson's logical propositional structures) and high and low vividness of visual imagery (corresponding to Johnson's rich images). The results suggested first, that success at problem solving was related to logical operational ability, but not to vividness of visual imagery. Second, a variety of visually based strategies were used during problem solving which differed in their level of generality and abstraction, and use of these strategies appeared related to either logical operational ability or vividness of visual imagery, depending on their level of abstraction. The results supported Presmeg's (1992b) continuum of abstraction of image schemata.Throughout the paper, the first High or Low denotes logical operational ability, and the second, vividness of visual imagery.     

E-learning by design

Teachers in higher education throughout the world are making use of course-management systems (CMS) to support their courses. None of these teachers grew up with using a CMS; they must themselves learn how to use them effectively at the same time that they are using them with their students. While institutions commonly provide some sort of introductory workshop for CMS use, these workshops have limitations in terms of their transfer value into practice. In this paper we discuss an example of embedded justin-time support within the CMS itself to help teachers learn how to use a CMS efficiently but also so that both they and their students can take on new roles in the learning process. A new form of computer-based support for teaching and learning has emerged since the late 1990s. It is a system of integrated tools that makes use of both database and web functionalities in order to make a web environment available to support a course or learning event. One name for such a system is a course-management system (CMS). Course-management systems are new tools for teachers and thus teachers must learn how to use them in a technical sense as well as in a meaningful sense. By meaningful, we mean not only to increase the efficiency of participating in a course but also to enrich and extend learning processes.     

Network Applications for Group-Based Learning: Is More Better?

Group-based learning is being introduced into many settings in higher education. Is this a sustainable development with respect to the resources required? Under what conditions can group-based learning be applied successfully in distance education and in increasingly flexible campus-based learning? Can networked support facilitate and enrich courses where group-based learning is applied? These questions formed the basis of the motivation for the research project whose main results are presented here. The goals set for the research were the identification of problems associated with the planning, operationalisation, and monitoring of group tasks in group-based learning in higher education, and the identification of networked support options which, in combination with appropriate instructional decisions, have the potential to remedy these problems. The solutions identified were tested in the context of three case studies.