Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Peace education

There are various understandings of peace education. What might be called maximalist peace education refers to educating students towards personal fulfilment and the creation of a just and co-operative society. What might be called minimalist peace education refers to educating students to avoid war, militarism and arms races. Peace education is only now being formally accepted as an integral part of educational endeavour, and an important part of this acceptance is recognition in international pronouncements and instruments, emphasizing the importance of a culture of peace and the right to peace. In terms of methodology, peace education includes curriculum, structures and process, and personal leadership. This last element is clearly the most challenging of all.

Third space in cyberspace : Indigenous youth, new technologies and literacies

This chapter analyses the affordances and constraints of an online literacy program designed for Indigenous Australian youth through a partnership between the Indigenous community, university staff and local schools. The after-school program sought to build on the cultural resources and experiences of the young people through a dialogic process of planning, negotiating, implementing, reflecting, and renegotiating the program with participants and a range of stakeholders. In the majority of cases, students presented themselves as part of pervasive global popular cultures, often hot-linking their webpages to pop icons and local sports stars. Elders regarded their competency as a potential cultural tool and community resource.

The arobase in the libr@ry : new political economies of children’s literatures and literacies

This essay--part of a special issue on the work of Gunther Kress--uses the idea of affordances and constraints to explore the (im)possibilities of new environments for engaging with literature written for children (see Kress, 2003). In particular, it examines a festival of children's literature from an Australian education context that occurs online. The festival is part of a technologically mediated library space designated by the term libr@ry (Kapitzke & Bruce, 2006). The @ symbol (French word "arobase") inserted into the word library indicates that technological mediation has a history, an established set of social practices, and a political economy, which even chatrooms with "real" authors may alter but not fully supplant.

New routes for the field trip

As with the broader field of education research, most writing on the subject of school excursions and field trips has centred around progressive/humanist concerns for building pupil’s self-esteem and for the development of the ‘whole child’. Such research has also stressed the importance of a broad, grounded, and experiential curriculum - as exemplified by subjects containing these extra-school activities - as well as the possibility of strengthening the relationship between student and teacher. Arguing that this approach to the field trip is both exhausted of ideas and conceptually flawed, this paper proposes some alternate routes into the area for the prospective researcher. First, it is argued that by historicising the subject matter, it can be seen that school excursions are not simply the product of the contemporary humanist desire for diverse and fulfilling educational experiences, rather they can, in part, be traced to eighteenth century beliefs among the English gentry that travel formed a crucial component of a good education, to the advent of an affordable public rail system, and to school tours associated with the Temperance movement. Second, field trips can be understood from within the associated framework of concerns over the governance of tourism and the organisation of disciplinary apparatuses for the production of an educated and regulated citizenry. Far from being a simple learning experience, museums and art galleries form part of a complex of disciplinary and power relations designed to produce a populace with very specific capacities, aspirations and styles of public conduct. Finally, rather than allowing children ‘freedom’ from the constraints of the classroom, on the contrary, through the medium of the field-trip, children can become accustomed to having their activities governed in the broader domain of the generalised community . School excursions thereby constitute an effective tactic through which young people have their conduct managed, and their social and scholastic identities shaped and administered.

A re-assessment of the debate over sex education

The intention of this paper is to call into question the apparent dichotomy between left and right wing positions concerning the implementation of sex education in Queensland Schools. By adopting a more historicised approach, it is suggested that these positions are part of dual and supplementary strategies which work through specific problematisations associated with youth. Accordingly, the emphasis should be shifted from generalised depictions of the adolescent/youth to more focused accounts, questioning how teaching children to manage their sex became a governmental imperative.

Historical timelines : analyzing multimodal text design

The recent focus on literacy in Social Studies has been on linguistic design, particularly that related to the grammar of written and spoken text. When students are expected to produce complex hybridized genres such as timelines, a focus on the teaching and learning of linguistic design is necessary but not sufficient to complete the task. Theorizations of new literacies identify five interrelated meaning making designs for text deconstruction and reproduction: linguistic, spatial, visual, gestural, and audio design. Honing in on the complexity of timelines, this paper casts a lens on the linguistic, visual, spatial, and gestural designs of three pairs of primary school aged Social Studies learners. Drawing on a functional metalanguage, we analyze the linguistic, visual, spatial, and gestural designs of their work. We also offer suggestions of their effect, and from there consider the importance of explicit instruction in text design choices for this Social Studies task. We conclude the analysis by suggesting the foci of explicit instruction for future lessons.