Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Interdisciplinarity vs disciplinarity : developing knowledge for problem solving in middle years of schooling

Interdisciplinary studies are fundamental to the signature practices for the middle years of schooling. Middle years researchers claim that interdisciplinarity in teaching appropriately meets the needs of early adolescents by tying concepts together, providing frameworks for the relevance of knowledge, and demonstrating the linking of disparate information for solution of novel problems. Cognitive research is not wholeheartedly supportive of this position. Learning theorists assert that application of knowledge in novel situations for the solution of problems is actually dependent on deep discipline based understandings. The present research contrasts the capabilities of early adolescent students from discipline based and interdisciplinary based curriculum schooling contexts to successfully solve multifaceted real world problems. This will inform the development of effective management of middle years of schooling curriculum.

Potency in professional development for teachers

There has been significant research into the impact of professional development (PD) on professional organisation and behaviour. PD has emerged in a diversity of forms in schools. Programs range form one hit seminars provided by an external consultant, through to a broad range of programmed development plans that integrate seminars; school based planning groups, action research, collaborative projects across schools, clusters and with critical friends, and mentoring. PD has been delivered to prompt school and teacher professional transformation or to support an ongoing development plan. PD is not uni-lateral and exists to support a very wide range of school and teacher development needs. The relevance and effectiveness of PD design and delivery is tied to the nature of the PD need and the context of provision. This paper reports an investigation into efficacy of various approaches to PD in Queensland schools. The research drew on responses to an online survey tool, focus groups and semi-structured interviews with PD coordinators, teachers, and school and district administrators to develop a model for effective PD planning that considers strategies for addressing current and future PD need and amelioration of barriers to PD effectiveness.

Bioactive mesopore-glass microspheres with controllable protein-delivery properties by biomimetic surface modification

Microsphere systems with the ideal properties for bone regeneration need to be bioactive, and at the same time possess the capacity for controlled protein/drug-delivery; however, the current crop of microsphere system fails to fulfill these properties. The aim of this study was to develop a novel protein-delivery system of bioactive mesoporous glass (MBG) microspheres by a biomimetic method through controlling the density of apatite on the surface of microspheres, for potential bone tissue regeneration. MBG microspheres were prepared by using the method of alginate cross-linking with Ca2+ ions. The cellular bioactivity of MBG microspheres was evaluated by investigating the proliferation and attachment of bone marrow stromal cell (BMSC). The loading efficiency and release kinetics of bovine serum albumin (BSA) on MBG microspheres were investigated after coprecipitating with biomimetic apatite in simulated body fluids (SBF). The results showed that MBG microspheres supported BMSC attachment and the Si containing ionic products from MBG microspheres stimulated BMSCs proliferation. The density of apatite on MBG microspheres increased with the length of soaking time in SBF. BSA-loading efficiency of MBG was significantly enhanced by co-precipitating with apatite. Furthermore, the loading efficiency and release kinetics of BSA could be controlled by controlling the density of apatite formed on MBG microspheres. Our results suggest that MBG microspheres are a promising protein-delivery system as a filling material for bone defect healing and regeneration.

Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

Student perceptions of the impact of online discussion forum participation on learning outcomes

Choosing the “right” type of technology, either synchronous or asynchronous, to facilitate learning outcomes is a new challenge as the pace of emerging technologies increases and diversifies. Teachers are encouraged to design courses that require collaboration in online learning communities to facilitate the development of higher order thinking skills for life long learning. It is therefore important to gather evidence of the kinds of opportunities afforded to students and whether the students themselves endorse collaborative online tools as a legitimate method of assisting in their learning. This paper outlines the way in which one secondary school has used an online discussion forum to support students in the International Baccalaureate (IB) Diploma Program in enhancing research skills and skills for lifelong learning. The paper considers whether online collaborative tools are perceived by students as a positive way to improve learning outcomes.

The mechanical response of the ovine lumbar anulus fibrosus to uniaxial, biaxial and shear loads

Analytical and computational models of the intervertebral disc (IVD) are commonly employed to enhance understanding of the biomechanics of the human spine and spinal motion segments. The accuracy of these models in predicting physiological behaviour of the spine is intrinsically reliant on the accuracy of the material constitutive representations employed to represent the spinal tissues. There is a paucity of detailed mechanical data describing the material response of the reinforced­ground matrix in the anulus fibrosus of the IVD. In the present study, the ‘reinforced­ground matrix’ was defined as the matrix with the collagen fibres embedded but not actively bearing axial load, thus incorporating the contribution of the fibre-fibre and fibre-matrix interactions. To determine mechanical parameters for the anulus ground matrix, mechanical tests were carried out on specimens of ovine anulus, under unconfined uniaxial compression, simple shear and biaxial compression. Test specimens of ovine anulus fibrosus were obtained with an adjacent layer of vertebral bone/cartilage on the superior and inferior specimen surface. Specimen geometry was such that there were no continuous collagen fibres coupling the two endplates. Samples were subdivided according to disc region - anterior, lateral and posterior - to determine the regional inhomogeneity in the anulus mechanical response. Specimens were loaded at a strain rate sufficient to avoid fluid outflow from the tissue and typical stress-strain responses under the initial load application and under repeated loading were determined for each of the three loading types. The response of the anulus tissue to the initial and repeated load cycles was significantly different for all load types, except biaxial compression in the anterior anulus. Since the maximum applied strain exceeded the damage strain for the tissue, experimental results for repeated loading reflected the mechanical ability of the tissue to carry load, subsequent to the initiation of damage. To our knowledge, this is the first study to provide experimental data describing the response of the ‘reinforced­ground matrix’ to biaxial compression. Additionally, it is novel in defining a study objective to determine the regionally inhomogeneous response of the ‘reinforced­ground matrix’ under an extensive range of loading conditions suitable for mechanical characterisation of the tissue. The results presented facilitate the development of more detailed and comprehensive constitutive descriptions for the large strain nonlinear elastic or hyperelastic response of the anulus ground matrix.

The relationship between implied and realized volatility : evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Gifted young adolescents and email : developing a personal language of self

This paper reports on the use of email as a means to access the self-constructions of gifted young adolescents. Australian research shows that gifted young adolescents may feel more lonely and misunderstood than their same-age counterparts, yet they are seldom asked about their lives. Emerging use of online methods as a means of access to individual lives and perceptions has demonstrated the potential offered by the creation of digital texts as narrative data. Details are given of a qualitative study that engaged twelve children aged between 10 and 14 years, who were screened for giftedness, in a project involving the generation of emailed journal entries sent over a period of 6 months. With emphasis on participatory principles, individual young adolescents produced self-managed journal entries that were written and sent to the researcher from personal computers outside the school setting. Drawing from a theoretical understanding of self as constructed within dialogic relationships, the digital setting of email is proposed as a narrative space that fosters healthy self-disclosure. This paper outlines the benefits of using email as a means to explore emotions, promote reflective accounts of self and support the development of a personal language for self-expression. Individual excerpts will be presented to show that the harnessing of personal narratives within an email context has potential to yield valuable insights into the emotions, personal realities and experiences of gifted young adolescents. Findings will be presented to show that the co-construction of self-expressive and explanatory narratives supported by a facilitative adult listener promoted healthy self-awareness amongst participants. This paper contributes to appreciative conversations about using online methods as a flexible and practical avenue for conducting educational research. Furthermore, digital writing in email form will be presented as having distinct advantages over face-to-face methods when utilised with gifted young adolescents who may be unwilling to disclose information within school-based settings.

Driving performance on monotonous roads

Driving on motorways has largely been reduced to a lane-keeping task with cruise control. Rapidly, drivers are likely to get bored with such a task and take their attention away from the road. This is of concern in terms of road safety – particularly for professional drivers - since inattention has been identified as one of the main contributing factors to road crashes and is estimated to be involved in 20 to 30% of these crashes. Furthermore, drivers are not aware that their vigilance level has decreased and that their driving performance is impaired. Intelligent Transportation System (ITS) intervention can be used as a countermeasure against vigilance decrement. This paper aims to identify a variety of metrics impacted during monotonous driving - ranging from vehicle data to physiological variables - and relate them to two monotonous factors namely the monotony of the road design (straightness) and the monotony of the environment (landscape, signage, traffic). Data are collected in a driving simulator instrumented with an eye tracking system, a heart rate monitor and an electrodermal activity device (N=25 participants). The two monotonous factors are varied (high and low) leading to the use of four different driving scenarios (40 minutes each). We show with Generalised Linear Mixed Models that driver performance decreases faster when the road is monotonous. We also highlight that road monotony impairs a variety of driving performance and vigilance measures, ranging from speed, lateral position of the vehicle to physiological measurements such as heart rate variability, blink frequency and electrodermal activity. This study informs road designers of the importance of having a varied road environment. It also provides a range of metrics that can be used to detect in real-time the impairment of driving performance on monotonous roads. Such knowledge could result in the development of an in-vehicle device warning drivers at early signs of driving performance impairment on monotonous roads.

Shared leadership in Queensland schools : a collective case study

Shared leadership has been identified as a key governance base for the future of government and Catholic schools in Queensland, the state’s two largest providers of school education. Shared leadership values the contributions that many individuals can make through collaboration and teamwork. It claims to improve organisational performance and reduce the increasing pressures faced by principals. However despite these positive features, shared leadership is generally not well understood, not well accepted and not valued by those who practice or study leadership. A collective case study method was chosen, incorporating a series of semi-structured interviews with principals and the use of official school documents. The study has explored the current understanding and practice of shared leadership in four Queensland schools and investigated its potential for use.