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.

Using picture books in the Secondary English classroom

This Chapter explores how teachers can use children's picture books in the Secondary English classroom.

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.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Presentations in English : find your voice as a presenter

With estimates of more than thirty million given each day, presentations have become an integral part of modern society. They can signify the difference between gaining or losing a job, or being successful or unsuccessful at university and a future career. Presentations in English, combining a 128-page book and DVD, is an innovative and complete course aimed specifically at non-native speakers of English.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Medienvermittelte transnationale Öffentlichkeiten im Zeitalter praktischer Hybridisierung (English title: Mediated transnational publics in environments of practical hybridisation)

This article is concerned with the repercussions of societal change on transnational media. It offers a new understanding of multilingual programming strategies by examining “Radio MultiKulti” (RM), a public service radio station discontinued from 1/1/2009 by Rundfunk Berlin-Brandenburg. In its fourteen years of existence, “RM” had to implement a well-intended and politically-motivated logic of ‘multiethnic, intercultural service station’. However, as we demonstrate, such a direction, despite some achievements, has resulted in the constraints to RM’s journalistic activities and language policy, drawing criticism for the station’s economic viability. This paper proposes that multilingual media services are to be framed by the concept of practical hybridity that allows a necessary responsiveness towards an ever-changing media environment, at the moment within digital culture. Our approach draws on Mikhail Bakhtin’s and Yuri Lotman’s theoretical approaches to hybridity, as well as in-depth interviews conducted with “RM” staff from 2005 onwards, further interviews with key agents outside RM and a continuous monitoring of the public debate which culminated at the end of 2008 in the controversial decision to close the radio station. Against this background, the concluding remarks are meant to contribute to the scholarly debate on hybridization as well as to inform multilingual media policy in the 21st century.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Questions of English : ethics, aesthetics, rhetoric, and the formation of the subject in England, Australia and the United States

The impact and content of English as a subject on the curriculum is once more the subject of lively debate. Questions of English sets out to map the development of English as a subject and how it has come to encompass the diversity of ideas that currently characterise it. Drawing on a combination of historical analysis and recent research findings Robin Peel, Annette Patterson and Jeanne Gerlach bring together and compare important new insights on curriculum development and teaching practice from England, Australia and the United States. They also discuss the development of teacher training, highlighting the variety of ways in which teachers build their own beliefs and knowledge about English.