Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

Evaluation of the "reconceptualising early mathematics learning" project

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ assessment and a Pattern and Structure Assessment (PASA) interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a relatively short period of time.

A conceptual model for reflecting on expected learning vs. demonstrated student performance

Educators are faced with many challenging questions in designing an effective curriculum. What prerequisite knowledge do students have before commencing a new subject? At what level of mastery? What is the spread of capabilities between bare-passing students vs. the top performing group? How does the intended learning specification compare to student performance at the end of a subject? In this paper we present a conceptual model that helps in answering some of these questions. It has the following main capabilities: capturing the learning specification in terms of syllabus topics and outcomes; capturing mastery levels to model progression; capturing the minimal vs. aspirational learning design; capturing confidence and reliability metrics for each of these mappings; and finally, comparing and reflecting on the learning specification against actual student performance. We present a web-based implementation of the model, and validate it by mapping the final exams from four programming subjects against the ACM/IEEE CS2013 topics and outcomes, using Bloom's Taxonomy as the mastery scale. We then import the itemised exam grades from 632 students across the four subjects and compare the demonstrated student performance against the expected learning for each of these. Key contributions of this work are the validated conceptual model for capturing and comparing expected learning vs. demonstrated performance, and a web-based implementation of this model, which is made freely available online as a community resource.

Checking-in at the library : designing an ambient media system for social learning and collaboration opportunities

The knowledge economy of the 21st century requires skills such as creativity, critical thinking, problem solving, communication and collaboration (Partnership for 21st century skills, 2011) – skills that cannot easily be learnt from books, but rather through learning-by-doing and social interaction. Big ideas and disruptive innovation often result from collaboration between individuals from diverse backgrounds and areas of expertise. Public libraries, as facilitators of education and knowledge, have been actively seeking responses to such changing needs of the general public...

Learning beyond books : strategies for ambient media to improve libraries and collaboration spaces as interfaces for social learning

With the advent of digital media and online information resources, public libraries as physical destinations for information access are being increasingly challenged. As a response, many libraries follow the trend of removing bookshelves in order to provide more floorspace for social interaction and collaboration. Such spaces follow a Commons 2.0 model: they are designed to support collaborative work and social learning. The acquisition of skills and knowledge is facilitated as a result of being surrounded by and interacting with a community of likeminded others. Based on the results of a case study on a Commons 2.0 library space, this paper describes several issues of collaboration and social learning in public library settings. Acknowledging the significance of the architectural characteristics of the physical space, we discuss opportunities for ambient media to better reflect the social attributes of the library as a place; i.e. amplify the sense of other co-present library visitors and provide opportunities for shared encounters and conversations, which would remain invisible otherwise. We present the design of a user check-in system for improving the library as a physical destination for social learning, sharing, and inspiration for and by the community.

STALKERBOT : learning to navigate dynamic human environments by following people

Service robots that operate in human environments will accomplish tasks most efficiently and least disruptively if they have the capability to mimic and understand the motion patterns of the people in their workspace. This work demonstrates how a robot can create a humancentric navigational map online, and that this map re ects changes in the environment that trigger altered motion patterns of people. An RGBD sensor mounted on the robot is used to detect and track people moving through the environment. The trajectories are clustered online and organised into a tree-like probabilistic data structure which can be used to detect anomalous trajectories. A costmap is reverse engineered from the clustered trajectories that can then inform the robot's onboard planning process. Results show that the resultant paths taken by the robot mimic expected human behaviour and can allow the robot to respond to altered human motion behaviours in the environment.

Locally weighted learning model predictivek control for elastic joint robots

This paper proposes an efficient and online learning control system that uses the successful Model Predictive Control (MPC) method in a model based locally weighted learning framework. The new approach named Locally Weighted Learning Model Predictive Control (LWL-MPC) has been proposed as a solution to learn to control complex and nonlinear Elastic Joint Robots (EJR). Elastic Joint Robots are generally difficult to learn to control due to their elastic properties preventing standard model learning techniques from being used, such as learning computed torque control. This paper demonstrates the capability of LWL-MPC to perform online and incremental learning while controlling the joint positions of a real three Degree of Freedom (DoF) EJR. An experiment on a real EJR is presented and LWL-MPC is shown to successfully learn to control the system to follow two different figure of eight trajectories.

Predicting the localized surface plasmon resonances of spherical nanoparticles on substrate : electrostatic eigenmode method

We present experimental results that demonstrate that the wavelength of the fundamental localised surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple, one line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined, and the role of local environment refractive indices on the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.

Understanding QC and EQA : an authentic learning model for undergraduate students (Conference Abstract)

Introduction QC and EQA are integral to good pathology laboratory practice. Medical Laboratory Science students undertake a project exploring internal QC and EQA procedures used in chemical pathology laboratories. Each student represents an individual lab and the class group represents the peer group of labs performing the same assay using the same method. Methods Using a manual BCG assay for serum albumin, normal and abnormal controls are run with a patient sample over 7 weeks. The QC results are assessed each week using calculated z-scores and both 2S & 3S control rules to determine whether a run is ‘in control’. At the end of the 7 weeks a completed LJ chart is assessed using the Westgard Multirules. Students investigate causes of error and the implications for both lab practice and patient care if runs are not ‘in control’. Twice in the 7 weeks two EQA samples (with target values unknown) are assayed alongside the weekly QC and patient samples. Results from each student are collated and form the basis of an EQA program. ALP are provided and students complete a Youden Plot, which is used to analyse the performance of each ‘lab’ and the method to identify bias. Students explore the concept of possible clinical implications of a biased method and address the actions that should be taken if a lab is not in consensus with the peer group. Conclusion This project is a model of ‘real world’ practice in which student demonstrate an understanding of the importance of QC procedures in a pathology laboratory, apply and interpret statistics and QC rules and charts, apply critical thinking and analytical skills to quality performance data to make recommendations for further practice and improve their technical competence and confidence.

Governance of learning mechanisms : evidence from construction firms

The focus of knowledge management (KM) in the construction industry is moving towards capability building for value creation. The study reported by this paper is motivated by recent assertions about the genesis and evolution of knowledge management capability (KMC) in the strategic management field. It attempts to shed light on the governance of learning mechanisms that develop KMC within the context of construction firms. A questionnaire survey was administered to a sample of construction contractors operating in the very dynamic Hong Kong market to elicit opinions on the learning mechanisms and business outcomes of targeted firms. On the basis of a total of 149 usable responses, structural equation modeling (SEM) analysis identified relationships among knowledge-governance mechanisms, knowledge processes, and business performance, thereby supporting the existence of strategic learning loops. The study findings provide evidence from the construction context for capability assertions that knowledge-governance mechanisms and processes form learning mechanisms that carry out strategic learning to create value, effect performance outcomes, and ultimately drive the evolution of KMC. The findings imply that it is feasible for managing construction firms to govern learning mechanisms through managing the capability-based holistic KM system, thereby reconfiguring KMC to match needs in the dynamic market environment over time.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

Collaborative research into the affordances of place for primary school children’s literacy learning

In the context of culturally diverse high poverty areas of Australia, we have conducted collaborative research with teachers and students in a primary school for more than a decade. Teachers have been exploring the affordances of place‐based pedagogies (Gruenewald & Smith, 2008) for the development of students’ spatial literacies and their understandings of the politics of places and built environments (Comber, Nixon, Ashmore, Loo & Cook, 2006; Comber, Thomson and Wells, 2001). This paper reports on a project in which the affordances of placedbased pedagogy are being explored through teacher inquiries and classroom‐based design experiments (Cobb, Confrey, di Sessa, Lehrer & Schauble, 2003). Located within a large‐scale urban renewal project in which houses are being demolished and families relocated, the original school has been replaced by a larger school that serves a population from a wider area. In this paper we draw on the study to consider the challenges of working with teachers and primary school students to study innovative ideas and practices in educational research. Specifically we consider issues raised by collaborative studies of the affordances of cross curricular projects focusing on social and environmental change to engage students in academic learning and expand their literate repertoires in a changing policy climate.

Games for change and transformative learning : an ethnographic case study

This thesis aims to contribute to a better understanding of how serious games/games for change function as learning frameworks for transformative learning in an educational setting. This study illustrates how the meaning-making processes and learning with and through computer gameplay are highly contingent, and are significantly influenced by the uncertainties of the situational context. The study focuses on SCAPE, a simulation game that addresses urban planning and sustainability. SCAPE is based on the real-world scenario of Kelvin Grove Urban Village, an inner city redevelopment area in Brisbane, Queensland, Australia. The game is embedded within an educational program, and I thus account for the various gameplay experiences of different school classes participating in this program. The networks emerging from the interactions between students/players, educators, facilitators, the technology, the researcher, as well as the setting, result in unanticipated, controversial, and sometimes unintended gameplay experiences and outcomes. To unpack play, transformative learning and games, this study adopts an ecological approach that considers the magic circle of gameplay in its wider context. Using Actor-Network Theory as the ontological lens for inquiry, the methods for investigation include an extensive literature review, ethnographic participant observation of SCAPE, as well as student and teacher questionnaires, finishing with interviews with the designers and facilitators of SCAPE. Altogether, these methods address my research aim to better understand how the heterogeneous actors engage in the relationships in and around gameplay, and illustrate how their conflicting understandings enable, shape or constrain the (transformative) learning experience. To disentangle these complexities, my focus continuously shifts between the following modes of inquiry into the aims „h To describe and analyse the game as a designed artefact. „h To examine the gameplay experiences of players/students and account for how these experiences are constituted in the relationships of the network. „h To trace the meaning-making processes emerging from the various relations of players/students, facilitators, teachers, designers, technology, researcher, and setting, and consider how the boundaries of the respective ecology are configured and negotiated. „h To draw out the implications for the wider research area of game-based learning by using the simulation game SCAPE as an example for introducing gameplay to educational settings. Accounting in detail for five school classes, these accounts represent, each in its own right, distinct and sometimes controversial forms of engagement in gameplay. The practices and negotiations of all the assembled human and non-human actors highlight the contingent nature of gameplay and learning. In their sum, they offer distinct but by no means exhaustive examples of the various relationships that emerge from the different assemblages of human and non-human actors. This thesis, hence, illustrates that game-based learning in an educational setting is accompanied by considerable unpredictability and uncertainty. As ordinary life spills and leaks into gameplay experiences, group dynamics and the negotiations of technology, I argue that overly deterministic assertions of the game¡¦s intention, as well as a too narrowly defined understanding of the transformative learning outcome, can constrain our inquiries and hinder efforts to further elucidate and understand the evolving uncertainties around game-based learning. Instead, this thesis posits that playing and transformative learning are relational effects of the respective ecology, where all actors are networked in their (partial) enrolment in the process of translation. This study thus attempts to foreground the rich opportunities for exploring how game-based learning is assembled as a network of practices.