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.

Adaptive teachers embracing new ways of learning with robotics in Chinese schools

In July 2010, China announced the “National Plan for Medium and Long-term Education Reform and Development(2010-2020)” (PRC 2010). The Plan calls for an education system that: • promotes an integrated development which harnesses everyone’s talent; • combines learning and thinking; unifies knowledge and practice; • allows teachers to teach according to individuals’ needs; and • reforms education quality evaluation and personnel evaluation systems focusing on performance including character, knowledge, ability and other factors. This paper discusses the design and implementation of a Professional Learning Program (PLP) undertaken by 432 primary, middle and high school teachers in China. The aim of this initiative was to develop adaptive expertise in using technology that facilitated innovative science and technology teaching and learning as envisaged by the Chinese Ministry of Education’s (2010-2020) education reforms. Key principles derived from literature about professional learning and scaffolding of learning informed the design of the PLP. The analysis of data revealed that the participants had made substantial progress towards the development of adaptive expertise. This was manifested not only by advances in the participants’ repertoires of Subject Matter Knowledge and Pedagogical Content Knowledge but also in changes to their levels of confidence and identities as teachers. It was found that through time the participants had coalesced into a professional learning community that readily engaged in the sharing, peer review, reuse and adaption, and collaborative design of innovative science and technology learning and assessment activities.

Principles of motor learning in ecological dynamics : a comment on functions of learning and the acquisition of motor skills (with reference to sport)

This paper provides a commentary on the contribution by Dr Chow who questioned whether the functions of learning are general across all categories of tasks or whether there are some task-particular aspects to the functions of learning in relation to task type. Specifically, they queried whether principles and practice for the acquisition of sport skills are different than what they are for musical, industrial, military and human factors skills. In this commentary we argue that ecological dynamics contains general principles of motor learning that can be instantiated in specific performance contexts to underpin learning design. In this proposal, we highlight the importance of conducting skill acquisition research in sport, rather than relying on empirical outcomes of research from a variety of different performance contexts. Here we discuss how task constraints of different performance contexts (sport, industry, military, music) provide different specific information sources that individuals use to couple their actions when performing and acquiring skills. We conclude by suggesting that his relationship between performance task constraints and learning processes might help explain the traditional emphasis on performance curves and performance outcomes to infer motor learning.

Something’s coming, something good: Identifying TPACK competence in pre-service teachers’ analyses of learning objects

There is a song at the beginning of the musical, West Side Story, where the character Tony sings that “something’s coming, something good.” The song is an anthem of optimism, brimming with promise. This paper is about the long-held promise of information and communication technology (ICT) to transform teaching and learning, to modernise the learning environment of the classroom, and to create a new digital pedagogy. But much of our experience to date in the schooling sector tells more of resistance and reaction than revolution, of more of the same but with a computer in the corner and of ICT activities as unwelcome time-fillers/time-wasters. Recently, a group of pre-service teachers in a postgraduate primary education degree in an Australian university were introduced to learning objects in an ICT immersion program. Their analyses and related responses, as recorded in online journals, have here been interpreted in terms of TPACK (Technological Pedagogical and Content Knowledge). Against contemporary observation, these students generally displayed high levels of competence and highly positive dispositions of students to the integration of ICT in their future classrooms. In short, they displayed the same optimism and confidence as the fictional “Tony” in believing that something good was coming.

Impact of extracellular matrix derived from osteoarthritis subchondral bone osteoblasts on osteocytes : role of integrinβ1 and focal adhesion kinase signaling cues

INTRODUCTION: Our recent study indicated that subchondral bone pathogenesis in osteoarthritis (OA) is associated with osteocyte morphology and phenotypic abnormalities. However, the mechanism underlying this abnormality needs to be identified. In this study we investigated the effect of extracellular matrix (ECM) produced from normal and OA bone on osteocytic cells function. METHODS: De-cellularized matrices, resembling the bone provisional ECM secreted from primary human subchondral bone osteoblasts (SBOs) of normal and OA patients were used as a model to study the effect on osteocytic cells. Osteocytic cells (MLOY4 osteocyte cell line) cultured on normal and OA derived ECMs were analyzed by confocal microscopy, scanning electron microscopy (SEM), cell attachment assays, zymography, apoptosis assays, qRT-PCR and western blotting. The role of integrinβ1 and focal adhesion kinase (FAK) signaling pathways during these interactions were monitored using appropriate blocking antibodies. RESULTS: The ECM produced by OA SBOs contained less mineral content, showed altered organization of matrix proteins and matrix structure compared with the matrices produced by normal SBOs. Culture of osteocytic cells on these defective OA ECM resulted in a decrease of integrinβ1 expression and the de-activation of FAK cell signaling pathway, which subsequently affected the initial osteocytic cell's attachment and functions including morphological abnormalities of cytoskeletal structures, focal adhesions, increased apoptosis, altered osteocyte specific gene expression and increased Matrix metalloproteinases (MMP-2) and -9 expression. CONCLUSION: This study provides new insights in understanding how altered OA bone matrix can lead to the abnormal osteocyte phenotypic changes, which is typical in OA pathogenesis.

Teachers as researchers : a ‘fair dinkum’ learning legacy

As we encounter a policy landscape where increasingly the education lexicon includes keywords such as data, evidence, quality, standards, it is interesting to revisit Garth Boomer's contribution regarding teachers as researchers. As an early-career classroom teacher in the mid-1970s, I was inspired by Boomer's provocation to engage with research as a practitioner seeking evidence of learning (or not learning). Since that time, convinced of the power of teacher research in enhancing both student and teacher learning, I have devoted a good deal of my academic life to finding ways of supporting teachers to engage in research - from finding funds to facilitate teacher-researcher networks, through designing research projects with teacher-researchers as key collaborators, to embedding practitioner inquiry in university courses wherever possible pre- and in-service.

Identification and elimination of a matrix-induced systematic error in LA–ICP–MS 206Pb/238U dating of zircon

Black et al. (2004) identified a systematic difference between LA–ICP–MS and TIMS measurements of 206Pb/238U in zircons, which they correlated with the incompatible trace element content of the zircon. We show that the offset between the LA–ICP–MS and TIMS measured 206Pb/238U correlates more strongly with the total radiogenic Pb than with any incompatible trace element. This suggests that the cause of the 206Pb/238U offset is related to differences in the radiation damage (alpha dose) between the reference and unknowns. We test this hypothesis in two ways. First, we show that there is a strong correlation between the difference in the LA–ICP–MS and TIMS measured 206Pb/238U and the difference in the alpha dose received by unknown and reference zircons. The LA–ICP–MS ages for the zircons we have dated can be as much as 5.1% younger than their TIMS age to 2.1% older, depending on whether the unknown or reference received the higher alpha dose. Second, we show that by annealing both reference and unknown zircons at 850 °C for 48 h in air we can eliminate the alpha-dose-induced differences in measured 206Pb/238U. This was achieved by analyzing six reference zircons a minimum of 16 times in two round robin experiments: the first consisting of unannealed zircons and the second of annealed grains. The maximum offset between the LA–ICP–MS and TIMS measured 206Pb/238U for the unannealed zircons was 2.3%, which reduced to 0.5% for the annealed grains, as predicted by within-session precision based on counting statistics. Annealing unknown zircons and references to the same state prior to analysis holds the promise of reducing the 3% external error for the measurement of 206Pb/238U of zircon by LA–ICP–MS, indicated by Klötzli et al. (2009), to better than 1%, but more analyses of annealed zircons by other laboratories are required to evaluate the true potential of the annealing method.

Toward biomimetic materials in bone regeneration : functional behavior of mesenchymal stem cells on a broad spectrum of extracellular matrix components

Bone defect treatments can be augmented by mesenchymal stem cell (MSC) based therapies. MSC interaction with the extracellular matrix (ECM) of the surrounding tissue regulates their functional behavior. Understanding of these specific regulatory mechanisms is essential for the therapeutic stimulation of MSC in vivo. However, these interactions are presently only partially understood. This study examined in parallel, for the first time, the effects on the functional behavior of MSCs of 13 ECM components from bone, cartilage and hematoma compared to a control protein, and hence draws conclusions for rational biomaterial design. ECM components specifically modulated MSC adhesion, migration, proliferation, and osteogenic differentiation, for example, fibronectin facilitated migration, adhesion, and proliferation, but not osteogenic differentiation, whereas fibrinogen enhanced adhesion and proliferation, but not migration. Subsequently, the integrin expression pattern of MSCs was determined and related to the cell behavior on specific ECM components. Finally, on this basis, peptide sequences are reported for the potential stimulation of MSC functions. Based on the results of this study, ECM component coatings could be designed to specifically guide cell functions.

Elements of Better Assessment for the Improvement of Learning

Building a community of shared practice at the classroom level calls for clarity about the important assessment capabilities and dispositions of teachers, especially when teachers are expected to take a direct focus on learning. In this chapter, we present new ways of thinking about teachers’ assessment literacies, offering a formulation of better assessment for the improvement of learning, including three elements, namely (i) assessment criteria and standards; (ii) the teacher’s professional judgment; and (iii) social moderation. The potential of the first element lies in teachers’ classroom practices that deliberately embed assessment criteria and standards in pedagogy in productive ways. The second element involves the engagement of teachers and students in judgment practice, that develops the understanding that judgment involves more than the application of explicit or stated criteria. More fundamental is the matter of how teachers bring to bear stated features of quality and other intellectual and experiential resources in arriving at judgment. That is to say, they range across and orient to explicit (stated), tacit (unstated) and meta-criteria in judgment making. These insights have direct relevance to teachers’ efforts to develop students’ own evaluative experience, especially as this involves students working with stated features of quality for self-assessment and peer-assessment purposes. Further, practices for social moderation are discussed, giving examples of good practice in moderation, how teachers experience moderation and the potential benefits of various types.

Evidence of effectiveness : high level synthesis of research to prevent obesity and increase physical activity in children

Background Prevention of childhood obesity is a public health priority for Malaysia and many other countries. Physical activity for children is also decreasing at an alarming rate. Both conditions are associated with non-communicable diseases and with significant morbidity and mortality in later life. Systematic reviews of public health interventions provide a useful summary to inform public health practice by combining the results of a range of research studies on a specific intervention into a single report. Systematic reviews are deemed most valuable for health program development and evidence based practice. Unfortunately, many policy makers and practitioners are simply unaware of the evidence: which strategies which are most likely to provide benefit; and which strategies are known to be harmful or useless. This presentation provides a “birds eye” overview based upon recent (since 2007 to present) high quality systematic reviews of public health interventions. Method HealthEvidece.org and the Cochrane Library were searched for systematic reviews which evaluated interventions targeting obesity prevention and increasing physical activity for children. The findings of the included reviews were themed and summarized. Results Seven reviews were identified addressing obesity in the early years, and fifteen reviews addressing obesity more broadly in childhood. Additional reviews were identified aimed at increasing physical activity. The synthesis shows several strategies to be effective, however many popular strategies clearly are not. Several of the reviews were inconclusive due to an absence of robust primary studies. Amongst the findings, interventions undertaken in the school setting appear very promising. Conclusions There is significant evidence from systematic reviews to guide public health practice and policy, and to inform future research.

The power of naming : the multifaceted value of learning students’ names

The modern day Australian law school is expected to educate and engage law students. Ideally law school will instil a sense of passion (or at least appreciation) for the law, promote a positive professional identity, foster a sense of community, and provide general support to law students. Collectively, the Australian legal academy is struggling with these goals. Significant numbers of students feel isolated, disconnected and unengaged throughout their tertiary legal education. Teaching students from increasingly diverse backgrounds, who spend less time on campus and less face-to-face time in class, many law academics feel ill-equipped to respond to the challenge of engaging law students in time and cost efficient ways. Intentionally learning and using student names has potential to humanise the law school experience, build community, and positively impact upon the wellbeing of students and staff.

First full-scale trials of pebble matrix filtration

Protecting slow sand filters from high turbidity waters by pre-treatment using Pebble Matrix Filtration (PMF) has been studied in the laboratory at University College London followed by pilot field trials in Papua New Guinea and Serbia. Subsequently, the construction of two full-scale PMF units, one out of concrete (4.8m x4.8m x 3.0m high) and the other using pre-cast Ferro-cement panels (900mm x 1600mm x 20mm thick) with an effective diameter of 4.7m and 3m height, and the combined effective plan area of 40 m2 was completed to protect an existing Slow Sand Filter system at the National Water Supply Drainage Board (NWSDB) in Sri Lanka. Although the plant was completed in April 2008 due to some major repairs to address some leaks and other construction defects in both filters, monitoring was intermittent until November 2008. The results on the plant performance are presented here along with some of the construction problems encountered during the project.

Comparing different approach and avoidance models of learning and personality in the prediction of work, university, and leadership outcomes

Jackson (2005) developed a hybrid model of personality and learning, known as the learning styles profiler (LSP) which was designed to span biological, socio-cognitive, and experiential research foci of personality and learning research. The hybrid model argues that functional and dysfunctional learning outcomes can be best understood in terms of how cognitions and experiences control, discipline, and re-express the biologically based scale of sensation-seeking. In two studies with part-time workers undertaking tertiary education (N equals 137 and 58), established models of approach and avoidance from each of the three different research foci were compared with Jackson's hybrid model in their predictiveness of leadership, work, and university outcomes using self-report and supervisor ratings. Results showed that the hybrid model was generally optimal and, as hypothesized, that goal orientation was a mediator of sensation-seeking on outcomes (work performance, university performance, leader behaviours, and counterproductive work behaviour). Our studies suggest that the hybrid model has considerable promise as a predictor of work and educational outcomes as well as dysfunctional outcomes.

The influence of extracellular matrix on the generation of vascularized, engineered, transplantable tissue

In a recently described model for tissue engineering, an arteriovenous loop comprising the femoral artery and vein with interposed vein graft is fabricated in the groin of an adult male rat, placed inside a polycarbonate chamber, and incubated subcutaneously. New vascularized granulation tissue will generate on this loop for up to 12 weeks. In the study described in this paper three different extracellular matrices were investigated for their ability to accelerate the amount of tissue generated compared with a no-matrix control. Poly-D,L-lactic-co-glycolic acid (PLGA) produced the maximal weight of new tissue and vascularization and this peaked at two weeks, but regressed by four weeks. Matrigel was next best. It peaked at four weeks but by eight weeks it also had regressed. Fibrin (20 and 80 mg/ml), by contrast, did not integrate with the generating vascularized tissue and produced less weight and volume of tissue than controls without matrix. The limiting factors to growth appear to be the chamber size and the capacity of the neotissue to integrate with the matrix. Once the sides of the chamber are reached or tissue fails to integrate, encapsulation and regression follow. The intrinsic position of the blood supply within the neotissue has many advantages for tissue and organ engineering, such as ability to seed the construct with stem cells and microsurgically transfer new tissue to another site within the individual. In conclusion, this study has found that PLGA and Matrigel are the best matrices for the rapid growth of new vascularized tissue suitable for replantation or transplantation.