Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Curriculum alignment: Exploring student perception of learning achievement measures

The importance of constructively aligned curriculum is well understood in higher education. Based on the principles of constructive alignment, this research considers whether student perception of learning achievement measures can be used to gain insights into how course activities and pedagogy are assisting or hindering students in accomplishing course learning goals. Students in a Marketing Principles course were asked to complete a voluntary survey rating their own progress on the intended learning goals for the course. Student perceptions of learning achievement were correlated with actual student learning, as measured by grade, suggesting that student perceptions of learning achievement measures are suitable for higher educators. Student perception of learning achievement measures provide an alternate means to understand whether students are learning what was intended, which is particularly useful for educators faced with large classes and associated restrictions on assessment. Further, these measures enable educators to simultaneously gather evidence to document the impact of teaching innovations on student learning. Further implications for faculty and future research are offered.

Promoting student learning with online videos : a research agenda

Gen Y students are digital natives (Prensky 2001) who learn in complex and diverse ways, with a variety of learning styles apparent in any given course. This paper proposes a web 2.0 conceptual learning solution–online student videos–to respond to different learning styles that exist in the classroom.

Enhancing the use of Internet and Web services for quality learning : an action research

Internet and Web services have been used in both teaching and learning and are gaining popularity in today’s world. E-Learning is becoming popular and considered the latest advance in technology based learning. Despite the potential advantages for learning in a small country like Bhutan, there is lack of eServices at the Paro College of Education. This study investigated students’ attitudes towards online communities and frequency of access to the Internet, and how students locate and use different sources of information in their project tasks. Since improvement was at the heart of this research, an action research approach was used. Based on the idea of purposeful sampling, a semi-structured interview and observations were used as data collection instruments. 10 randomly selected students (5 girls and 5 boys) participated in this research as the controlled group. The study findings indicated that there is a lack of educational information technology services, such as e-learning at the college. Internet connection being very slow was the main barrier to learning using e-learning or accessing Internet resources. There is a strong relationship between the quality of written task and the source of the information, and between Web searching and learning. The source of information used in assignments and project work is limited to books in the library which are often outdated and of poor quality. Project tasks submitted by most of the students were of poor quality.

Faculty and students’ awareness and challenges of e-learning in a college of education

This study explored the use of e-learning by student teachers and faculty members at the Paro College of Education, Royal University of Bhutan. It provides an overview of the current status of e-learning at the College including the challenges faced by both faculty members and students teachers, and the influence of ICT resources on the use of e-learning by the lecturers and student teachers. The results indicated that there exist challenges in exercising e-learning at the College for teaching and learning. The data indicated that the Internet connection is slow and revealed that most of the lecturers have average computer competency. This study strongly recommends that the College develops a strategic plan for ICT infrastructure and resources that includes policy and guidelines for use. This study also suggests that lecturers and student teachers use freely available e-learning management software.

Case study of collaborative learning in two contexts : what do students gain?

This book presents important research advances in the study of teaching and teacher research as well as a review of motivation in education; mentoring; an evaluation of online learning; educational change and computer-assisted teaching.

Three primary school students’ cognition about 3D rotation in a virtual reality learning environment

This paper reports on three primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Departures from tradition : the early years learning framework for Australia

In 2009, the Commonwealth Government of Australia published the first national learning framework for use with children aged birth to five years. The framework marks a departure from tradition in that it emphasizes intentional teaching, learning as well as child development, a particular type of play-based learning, outcomes, and equity. This article analyzes aspects of the document that depart from well established approaches to early childhood education in Australia and identifies challenges for educators who are required to use the document. It concludes that ongoing and supportive professional learning opportunities must accompany the introduction and enactment of the document.

Finding the remote: Immersive learning in an outback community

Real-world design education projects present particular challenges when in a place remote from and distinctively different to students’ familiar territory. The teaching challenge is to assist students to translate the skills they learn at university into an entirely new context, facilitating a project they will learn from, and the community will value. In 2008 QUT design and engineering students undertook a project called Linking Karumba for this remote Queensland town. They engaged with a landscape, climate and community dramatically different from their base in urban Brisbane, and in a fortnight produced locally responsive strategic planning options. The theoretical approach to this was twofold: they needed to make a rapid shift along a continuum from being “outsiders” towards becoming “insiders” (Relph 1976), and to create designs responsive to local distinctiveness (Cumberlidge and Musgrave 2007). This paper outlines Linking Karumba’s teaching strategy via an analogy with the “immersion” method in bilingual education. Three teaching methods were adopted. Firstly, the overall framework drew on Brockbank and McGill (1998), and Thomas’ (2006a) approaches to student reflective practice. Within this, Girot’s “Four Trace Concepts” (1999) inspired exercises for finding Karumba and moving toward insideness; and a program of community engagement sought immersion in local distinctiveness, and “conversation” between the differing forms of knowledge and capacities embedded within the community and students (Armstrong 1999, Thomas 2006). The responsiveness of the student work to the character of Karumba’s culture and environment indicated remarkable levels of immersion, and the community highly valued the project outcomes: four strategic planning options which attracted $830 000 in state government funding for implementation.

Executive function effects and numerical development in children : behavioural and ERP evidence from a numerical Stroop paradigm

Most research on numerical development in children is behavioural, focusing on accuracy and response time in different problem formats. However, Temple and Posner (1998) used ERPs and the numerical distance task with 5-year-olds to show that the development of numerical representations is difficult to disentangle from the development of the executive components of response organization and execution. Here we use the numerical Stroop paradigm (NSP) and ERPs to study possible executive interference in numerical processing tasks in 6–8-year-old children. In the NSP, the numerical magnitude of the digits is task-relevant and the physical size of the digits is task-irrelevant. We show that younger children are highly susceptible to interference from irrelevant physical information such as digit size, but that access to the numerical representation is almost as fast in young children as in adults. We argue that the developmental trajectories for executive function and numerical processing may act together to determine numerical development in young children.

Paving for diverse pathways : using industry-linked learning to support Performing Arts students in their transition to protean careers

Statistics presented in Australia Council reports such as Don’t Give Up Your Day Job (2003), and Artswork: A Report On Australians Working in the Arts 1 and 2 (1997, 2005), and in other studies on destinations for Performing Arts graduates, demonstrate the diversity of post-graduation pathways for our students, the prevalence of protean careers, and the challenges in developing a sense of professional identity in a context where a portfolio of work across performance making, producing, administration and teaching can make it difficult for young artists to establish career status and capital in conventional terms (cf. Dawn Bennett, “Academy and the Real World: Developing Realistic Notions of Career in the Performing Arts”, Arts & Humanities in Higher Education, 8.3, 2009). In this panel, academics from around Australia will consider the ways in which Drama, Theatre and Performance Studies as a discipline is deploying a variety of practical, professional and work-integrated teaching and learning activities – including performance-making projects, industry projects, industry placements and student-initiated projects – to connect students with the networks, industries and professional pathways that will support their progression into their career. The panellists include Bree Hadley (Queensland University of Technology), Meredith Rogers (La Trobe University), Janys Hayes (Woolongong University) and Teresa Izzard (Curtin University). The panelists will present insights into the activities they have found successful, and address a range of questions, including: How do we introduce students to performance-making and / or producing models they will be able to employ in their future practice, particularly in light of the increasingly limited funds, time and resources available to support students’ participation in full-scale productions under the stewardship of professional artists?; How and when do we introduce students to industry networks?; How do we cater for graduates who will work as performers, writers, directors or administrators in the non-subsidised sector, the subsidised sector, community arts and education?; How do we category cater for graduates who will go on to pursue their work in a practice-as-research context in a Higher Degree?; How do we assist graduates in developing a professional identity? How do we assist graduates in developing physical, professional and personal resilience?; How do we retain our connections with graduates as part of their life-long learning?; Do practices and processes need to differ for city or regionally based / theoretically or practically based degree programs?; How do our teaching and learning activities align with emergent policy and industrial frameworks such as the shift to the “Producer Model” in Performing Arts funding, or the new mentorship, project, production and enterprise development opportunities under the Australia Council for the Arts’ new Opportunities for Young and Emerging Artists policy framework?

Working together for Toby : early childhood student teachers engaging in collaborative problem-based learning around child abuse and neglect

Early childhood teacher education programs have a responsibility, amongst many, to prepare teachers for decision-making on real world issues, such as child abuse and neglect. Their repertoire of skills can be enhanced by engaging with others, either face-to-face or online, in authentic problem-based learning. This paper draws on a study of early childhood student teachers who engaged in an authentic learning experience, which was to consider and to suggest how they would act upon a real-life case of child abuse encountered in an early childhood classroom in Queensland. This was the case of Toby (a pseudonym), who was suspected of being physically abused at home. Students drew upon relevant legislation, policy and resource materials to tackle Toby’s case. The paper provides evidence of students grappling with the complexity of a child abuse case and establishing, through collaboration with others, a proactive course of action. The paper has a dual focus. First, it discusses the pedagogical context in which early childhood student teachers deal with issues of child abuse and neglect in the course of their teacher education program. Second, it examines evidence of students engaging in collaborative problem-solving around issues of child abuse and neglect and teachers’ responsibilities, both legal and professional, to the children and families they work with. Early childhood policy-makers, practitioners and teacher educators are challenged to consider how early childhood teachers are best equipped to deal with child protection and early intervention.

Nonverbal Learning Disability explained : the link to shunted hydrocephalus

A Nonverbal Learning Disability is believed to be caused by damage, disorder or destruction of neuronal white matter in the brain’s right hemisphere and may be seen in persons experiencing a wide range of neurological diseases such as hydrocephalus and other types of brain injury (Harnadek & Rourke 1994). This article probes the relationship between shunted hydrocephalus and Nonverbal Learning Disability. Description of hydrocephalus and intelligence associated with hydrocephalus concludes with explication of the ‘final common pathway’ that links residual damage caused by the hydrocephalic condition to a Nonverbal Learning Disability (Rourke & Del Dotto 1994, p. 37). The paper seeks to assist teachers, teacher aides, psychologists, guidance officers, support workers, parents and disability service providers whose role is to understand and advocate for individuals with shunted hydrocephalus and spina bifida.

Creating global networks through an online engineering graduate program

Internationally the railway industry is facing a severe shortage of engineers with high level, relevant, profession and technical knowledge and abilities, in particular amongst engineers involved in the design, construction and maintenance of railway infrastructure. A unique graduate level program has been created to meet that global need via a fully online, distance education format. The development and operation of this Master of Engineering degree is proposed as a model of the process needed for the industry-relevance, flexible delivery, international networking, and professional development required for a successful graduate engineering program in the 21st century. In particular, the paper demonstrates how a mix of new and more familiar technologies are utilised through a variety of tasks to overcome the huge distances and multiple time zones that separate the participants across a growing number of countries, successfully achieving close and sustained interaction amongst the participants and railway experts.