Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

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.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Seeing is understanding : the effect of visualisation in understanding programming concepts

How and why visualisations support learning was the subject of this qualitative instrumental collective case study. Five computer programming languages (PHP, Visual Basic, Alice, GameMaker, and RoboLab) supporting differing degrees of visualisation were used as cases to explore the effectiveness of software visualisation to develop fundamental computer programming concepts (sequence, iteration, selection, and modularity). Cognitive theories of visual and auditory processing, cognitive load, and mental models provided a framework in which student cognitive development was tracked and measured by thirty-one 15-17 year old students drawn from a Queensland metropolitan secondary private girls’ school, as active participants in the research. Seventeen findings in three sections increase our understanding of the effects of visualisation on the learning process. The study extended the use of mental model theory to track the learning process, and demonstrated application of student research based metacognitive analysis on individual and peer cognitive development as a means to support research and as an approach to teaching. The findings also forward an explanation for failures in previous software visualisation studies, in particular the study has demonstrated that for the cases examined, where complex concepts are being developed, the mixing of auditory (or text) and visual elements can result in excessive cognitive load and impede learning. This finding provides a framework for selecting the most appropriate instructional programming language based on the cognitive complexity of the concepts under study.

Assessment in education : principles, policy and practice

The English examination system provides a market in which a limited number of providers are accredited to offer curriculum-based examinations in many subject areas and at several levels. The most significant are the General Certificate of Secondary Education (GCSE) and the General Certificate of Education, Advanced (A level). Because these examinations are used for high-stakes purposes, including higher education and employment selection for individuals and programme evaluation for institutions, it is desired that scores from various exams be ‘comparable’ in several respects: across syllabuses and examination boards within a subject area, across years, and even across subject areas. Just how to accomplish this goal has been a topic of continual research and debate for over 50 years, through many changes of examination and institutional structures. But ever year, tens of thousands of scores must be reported, and every year, users expect them to ‘be comparable’ and use them as if they are.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

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.

Designing for engagement : building IT systems

Context The School of Information Technology at QUT has recently undertaken a major restructuring of their Bachelor of Information Technology (BIT) course. Some of the aims of this restructuring include a reduction in first year attrition and to provide an attractive degree course that meets both student and industry expectations. Emphasis has been placed on the first semester in the context of retaining students by introducing a set of four units that complement one another and provide introductory material on technology, programming and related skills, and generic skills that will aid the students throughout their undergraduate course and in their careers. This discussion relates to one of these four fist semester units, namely Building IT Systems. The aim of this unit is to create small Information Technology (IT) systems that use programming or scripting, databases as either standalone applications or web applications. In the prior history of teaching introductory computer programming at QUT, programming has been taught as a stand alone subject and integration of computer applications with other systems such as databases and networks was not undertaken until students had been given a thorough grounding in those topics as well. Feedback has indicated that students do not believe that working with a database requires programming skills. In fact, the teaching of the building blocks of computer applications have been compartmentalized and taught in isolation from each other. The teaching of introductory computer programming has been an industry requirement of IT degree courses as many jobs require at least some knowledge of the topic. Yet, computer programming is not a skill that all students have equal capabilities of learning (Bruce et al., 2004) and this is clearly shown by the volume of publications dedicated to this topic in the literature over a broad period of time (Eckerdal & Berglund, 2005; Mayer, 1981; Winslow, 1996). The teaching of this introductory material has been done pretty much the same way over the past thirty years. During this period of time that introductory computer programming courses have been taught at QUT, a number of different programming languages and programming paradigms have been used and different approaches to teaching and learning have been attempted in an effort to find the golden thread that would allow students to learn this complex topic. Unfortunately, computer programming is not a skill that can be learnt in one semester. Some basics can be learnt but it can take many years to master (Norvig, 2001). Faculty data typically has shown a bimodal distribution of results for students undertaking introductory programming courses with a high proportion of students receiving a high mark and a high proportion of students receiving a low or failing mark. This indicates that there are students who understand and excel with the introductory material while there is another group who struggle to understand the concepts and practices required to be able to translate a specification or problem statement into a computer program that achieves what is being requested. The consequence of a large group of students failing the introductory programming course has been a high level of attrition amongst first year students. This attrition level does not provide good continuity in student numbers in later years of the degree program and the current approach is not seen as sustainable.

Using Media Technologies in English

English has long been the subject where print text has reigned supreme. Increasingly in our networked and electronically connected world, however, we can be using digital technologies to create and respond to texts studied in English classrooms. The current approach to English includes the concept of ‘multiliteracies,’ which suggests that print texts alone are necessary but not sufficient’ (E.Q, 2000) and that literacy includes the flexible and sustainable mastery of a repertoire of practices. This also includes the decoding and deployment of media technologies (E.Q, 2000). This has become more possible in Australia as secondary students have increasing access to computers and online platforms at home and at school. With the advent of web 2.0., with its interactive platforms and free media making software, teachers and students can use this software to access information and emerging online literature in English covering a range of text types and new forms for authentic audiences and contexts. This chapter is concerned with responding to literary and mediated texts through the use of technologies. If we remain open to trying out new textual forms and see our digital ‘native students’ (Prensky, 2007) as our best resource, we can move beyond technophobia, become digital travellers’ ourselves and embrace new digital forms in our classrooms.

Wrapped fragments : Drapery, the eighteenth century portrait bust and the male subject

The depiction of drapery (generalised cloth as opposed to clothing) is a well-established convention of Neo-Classical sculpture and is often downplayed by art historians as of purely rhetorical value. It can be argued however that sculpted drapery has served a spectrum of expressive ends, the variety and complexity of which are well illustrated by a study of its use in portrait sculpture. For the Neo-Classical portrait bust, drapery had substantial iconographic and political meaning, signifying the new Enlightenment notions of masculine authority. Within the portrait bust, drapery also served highly strategic aesthetic purposes, alleviating the abruptness of the truncated format and the compromising visual consequences of the “cropped” body. With reference to Joseph Nollekens’ portraits of English statesman Charles James Fox and the author’s own sculptural practice, this paper analyses the Neo-Classical use of drapery to propose that rendered fabric, far from mere stylistic flourish, is a highly charged visual signifier with much scope for exploration in contemporary sculptural practice.

Teachers making connections : online communities as a source of professional learning

The impact of the Internet on our lives has been pervasive. People are increasingly turning to the social interaction available on the Internet to satisfy their needs, whether these are professional or personal. The Internet offers users fast access to social contacts such as online chat groups and discussion lists,helping us to make connections with others. Online communities are being increasingly used by teachers for professional support, guidance and inspiration. These are often organised around subject areas and offer teachers opportunities to develop both personally and professionally. Online communities may present as a source of continuous professional development for teachers as they are able to deliver authentic and personalised opportunities for learning. This paper will present the findings of a study that was conducted on three online communities for teachers. It will explore the nature of online community membership and offer some conclusions regarding their potential as a source of professional learning for teachers.

High quality/high equity systems of education: Curriculum, teachers and reform in the search for equitable outcomes for all students

The issue of what an effective high quality / high equity education system might look like remains contested. Indeed there is more educational commentary on those systems that do not achieve this goal (see for example Luke & Woods, 2009 for a detailed review of the No Child Left Behind policy initiatives put forward in the United States under the Bush Administration) than there is detailed consideration of what such a system might enact and represent. A long held critique of socio cultural and critical perspectives in education has been their focus on deconstruction to the supposed detriment of reconstructive work. This critique is less warranted in recent times based on work in the field, especially the plethora of qualitative research focusing on case studies of ‘best practice’. However it certainly remains the case that there is more work to be done in investigating the characteristics of a socially just system. This issue of Point and Counterpoint aims to progress such a discussion. Several of the authors call for a reconfiguration of the use of large scale comparative assessment measures and all suggest new ways of thinking about quality and equity for school systems. Each of the papers tackles different aspects of the problematic of how to achieve high equity without compromising quality within a large education system. They each take a reconstructive focus, highlighting ways forward for education systems in Australia and beyond. While each paper investigates different aspects of the issue, the clearly stated objective of seeking to delineate and articulate characteristics of socially just education is consistent throughout the issue.