Reshaping expectations for web-based collaborative learning

We offered an experimental graduate course built around a World Wide Web-based collaborative learning experience; five graduate students participated. The World Wide Web served as the primary platform on which knowledge was compiled, shared, and synthesized. We built a WWW-based annotated bibliography and synthesized information from several disciplines. Net Forum-based discussions included student responses to questions posed by the instructors and by other students. The Web was valued most as a tool for information dispersal. As a result, students learned more from their peers than they had in other courses. However, students found brainstorming and conversation using Net Forum, a list server, and electronic mail cumbersome and intimidating. Participants noted a need for personal contact to develop the sense of community critical to fruitful collaboration. Complex issues were brought to closure in several face-to-face meetings. In future offerings, we envision an extended course that begins with community-building meetings (live or video) before migrating to intense WEb-based collaboration. We will use the Web\u27s text and image capabilities for sharing complex information over long distances and time periods, and we will downplay the expectation of immediate response and focus instead on considered response. We will use Web-based conferencing technology for brainstorming and real-time interaction among participants. Institutions may have to increase flexibility in the timing and structure of courses to facilitate inter-institutional offerings

Service-Learning in One State: Results of the North Carolina Service-Learning Inventory

Recent years have seen greatly expanded interest in service-learning among educators at both the K-12 and college levels. By most accounts, the initiation of service-learning programs and courses has come about in response to a recognized need to provide more effective citizenship education and to do a better job of preparing young people to be active members of their communities (see, for example, Barber). What is less clear, however, is the overall shape and substance of these programs. Because service-learning usually has a strong local component, not very much is known of the broader patterns and trends at the national and state levels

Some extremal properties of the solutions of ordinary differential equations systems

Based on variables doubling procedure the extremals flow immersion into the trajectories bunch has been considered. The conditions for existence of extremals have been obtained. The Lyapunov function for a doubled linearized system has been constructed

Illustrations of irreducibility and tops of umbrellas in the PostScript methodology

Sierpi´nski carpets and similar objects, irreducible and indecomposable continua are visually realized based on the PostScript language. Algorithmic problems associated with rendering effects and the presence of tops of umbrellas and irreducible points have been solved within the PostScript language methodology

An investigation into students' understandings of linear relationships when using dynamic mathematical software as an exploration tool

Numerous studies have provided substantial evidence of the benefits of technology when learning mathematical concepts. Despite this evidence, various factors inhibit successful implementation and navigation of technology. As a result, when students require technology to further develop their understanding of concepts, they may fall short because they lack the consolidated skills enabling them to competently advance. This study investigated students' understandings of Linear Relationships concepts using the dynamic software GeoGebra. The purpose was to identify developmental hurdles and issues that could be addressed by teachers in their teaching sequence. The design involved a tightly focused investigation of the understanding of Linear Relationships concepts through analysing the students' responses during the unit. Empirical evidence is provided to explain the difficulties faced by students when using technology to support their understanding of Linear Relationships. This evidence has theoretical and practical implications for the instruction of the Linear Relationships unit and the incorporation of GeoGebra as a pedagogical tool. The theoretical base for this study was the van Hiele Teaching Phases and the SOLO model. The five Teaching Phases that form part of the van Hiele Theory presented a framework for teaching and learning in which to sequence Linear Relationships activities that facilitate students' cognitive development for the transition between van Hiele levels. While the Teaching Phases have been widely studied, particularly with respect to Geometry, this study extends research by utilising activities for the teaching sequence aligned with the Teaching Phases, and based on the Linear Relationships unit for the Australian Curriculum Stage 5.3 (approximately 14–16 years old) incorporating GeoGebra as a technological tool to support understanding. To provide a deeper insight with which to view students' understandings of Linear Relationships concepts, the SOLO model was used as an analytical tool. Qualitative data was collected during the investigation. This comprised three Google Form Tests: a Pre-test, an End of Topic test, and a Delayed Post-test, to provide the main set of data, along with video and audio footage, photographs and workbook samples. The tests were completed by 26 students from a Year 9 Stage 5.3 class (approximately 14–16 years old), all from one secondary school. A central finding of this study is the identification of the developmental pathway for Linear Relationships concepts. This pathway characterises student growth in understanding and recognised two cycles of responses within the concrete symbolic SOLO mode. Whilst first cycle responses indicated possible levels of support from the ikonic mode, students were mainly operating within the concrete symbolic mode. This study also identified student difficulties associated with dynamic technology, such as GeoGebra, when used to support the understanding of Linear Relationships concepts. The research highlights the difficulties students encounter when attempting to utilise technology to develop conceptual understanding with mathematical topics such as Linear Relationships. Hence, the characterisation of a developmental pathway for conceptual understanding of Linear Relationships provides a valuable tool for teaching. In addition, this study highlights the use of the SOLO model as an interpretive tool for research in Mathematics education and the van Hiele Teaching Phases as a pedagogical tool for developing comprehensive learning experiences

Education for Sustainability and Pre-service Teacher Education

Aspects of environment are common topics in Australian primary schools. However Education for Sustainability (EfS), where students actively investigate the underlying causes of unsustainable practices and actively plan for and instigate change, is less well understood and less commonly practised. It cannot be assumed that pre-service teachers have the knowledge, skills and desire to incorporate EfS, as advocated in Australian policies, into their repertoires of practice, or, that they will acquire those skills as they gain teaching experience. Therefore for EfS to become an integral component of the primary school experience, carefully planned rather than ad hoc preparation for EfS is necessary in pre-service teacher education. This essentially qualitative study describes how a one semester final year pre-service primary teacher unit in EfS was shaped, and reports on how a cohort of pre-service teachers responded, particularly in terms of how well prepared they felt to engage with EfS in future teaching. Although motivation and confidence to engage with EfS varied across the cohort, pre-service teacher education appeared to make a positive contribution to both. In a longitudinal design, five teachers who had participated in the EfS unit became the focus of individual case studies early in their teaching careers. Each case study investigated ways in which the beginning teacher engaged with EfS, linking teaching decisions to pre-service teacher education. The constructivist approach adopted by the tutors was particularly valued by the early career teachers. They appreciated various modes of experiential learning including engagement with the kinds of teaching strategies advocated in EfS and a strong orientation to the curriculum requirements of primary school. However the extent to which each early career teacher implemented EfS was tempered not only by personal skill and motivation, but also by work situations which did not necessarily support EfS endeavours. Whilst pre-service teacher education has a vital role in the promulgation of EfS in schools, and this study shows that it can be effective in advancing the desires of beginning teachers to do something for the environment, there are broad implications for the institutions that so heavily impact on the capacity of school systems and university systems to act in EfS

An Investigation into Students' Understandings of Class Inclusion Concepts in Geometry

This study investigated students' understandings of class inclusion concepts in Geometry. The purpose was to identify a developmental pathway leading to an understanding of the interrelationships among two-dimensional figures and their properties. The design involved a tightly focused investigation of the manner in which geometrical class inclusion concepts evolve, in particular, relationships among triangle and quadrilateral figures, and relationships among their properties. Empirical evidence is provided to explain the difficulties students face in understanding of class inclusion notions. This evidence has theoretical as well as practical implications

A Developmental Perspective on Community Service in Adolescence

A substantial number of U.S. adolescents currently participate in community service and there is increased national interest in service programs. This article assesses the assumption of developmental benefits to service participants by critically reviewing 44 empirical studies. It offers a theoretical framework for understanding the findings by connecting them to identity development and delineating three pertinent concepts: agency, social relatedness, and moral-political awareness. These concepts are applied to studies that investigate: ( 1) the characteristics and motivations of participants, ( 2) the effects of service, and ( 3) the process of service. The findings support the conclusion that service activities which provide opportunities for intense experiences and social interactions are often associated with prosocial development. The findings also point to the need for more studies focused on particular service programs and on relationships between service providers and those served