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.

Measurement of affect during simulation-based training

Training designed to support and strengthen higher-order mental abilities now often involves immersion in Virtual Reality where dangerous real world scenarios can be safely replicated. However despite the growing popularity of advanced training simulations, methods for evaluating their use rely heavily on subjective measures or analysis of final outcomes. Without dynamic, objective performance measures the outcome of training in terms of impact on cognitive skills and ability to transfer newly acquired skills to the real world is unknown. The relationship between affective intensity and cognitive learning provides a potential new approach to ensure the processing of cognitions which occur prior to final outcomes, such as problem-solving and decision-making, are adequately evaluated. This paper describes the technical aspects of pilot work recently undertaken to develop a new measurement tool designed to objectively track individual affect levels during simulation-based training.

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.

Hydrogen bonding in proton-transfer compounds of 5-sulfosalicylic acid with a series of aliphatic nitrogen Lewis bases

The crystal structures of the proton-transfer compounds of 5-sulfosalicylic acid (3-carboxy-4-hydroxybenzenesulfonic acid) with the aliphatic nitrogen Lewis bases, hydroxylamine, triethylamine, pyrrolidine, morpholine, N-methylmorpholine and piperazine, viz. hydroxyammonium 3-carboxy-4-hydroxybenzenesulfonate (1), triethylaminium 3-carboxy-4-hydroxybenzenesulfonate (2), pyrrolidinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (3), morpholinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (4), N-methylmorpholinium 3-carboxy-4-hydroxybenzenesulfonate monohydrate (5) and piperazine-1,4-diium bis(3-carboxy-4-hydroxybenzenesulfonate) hexahydrate (6) have been determined and their comparative structural features and hydrogen-bonding patterns described. Crystals of 4 are triclinic, space group P-1 while the remainder are monoclinic with space group either P21/c (1 - 3) or P21/n (5, 6). Unit cell dimensions and contents are: for 1, a = 5.0156(3), b = 10.5738(6), c = 18.4785(9) Å, β = 96.412(5)o, Z = 4; for 2, a = 8.4998(4), b = 12.3832(6), c = 15.4875(9) Å, β = 102.411(5)o, Z = 4; for 3, a = 6.8755(2), b = 15.5217(4), c = 12.8335(3) Å, β = 92.074(2)o, Z = 4; for 4, a = 6.8397(2), b = 12.9756(5), c = 15.8216(6) Å, α = 90.833(3), β = 95.949(3), γ = 92.505(3)o, Z = 4; for 5, a = 7.0529(3), b = 13.8487(7), c = 15.6448(6) Å, β = 90.190(6)o, Z = 4; for 6, a = 7.0561(2), b = 15.9311(4), c = 12.2102(3) Å, β = 100.858(3)o, Z = 2. The hydrogen bonding generates structures which are either two-dimensional (2 and 5) or three-dimensional (1, 3, 4 and 6). Compound 6 represents the third reported structure of a salt of 5-sulfosalicylic acid having a dicationic piperazine species.

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.

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?