Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

Theoretical critique of the work of art : co-producers in research

The ways in which the "traditional" tension between words and artwork can be perceived has huge implications for understanding the relationship between critical or theoretical interpretation, art and practice, and research. Within the practice-led PhD this can generate a strange sense of disjuncture for the artist-researcher particularly when engaged in writing the exegesis. This paper aims to explore this tension through an introductory investigation of the work of the philosopher Andrew Benjamin. For Benjamin criticism completes the work of art. Criticism is, with the artwork, at the centre of our experience and theoretical understanding of art – in this way the work of art and criticism are co-productive. The reality of this co-productivity can be seen in three related articles on the work of American painter Marcia Hafif. In each of these articles there are critical negotiations of just how the work of art operates as art and theoretically, within the field of art. This focus has important ramifications for the writing and reading of the exegesis within the practice-led research higher degree. By including art as a significant part of the research reporting process the artist-researcher is also staking a claim as to the critical value of their work. Rather than resisting the tension between word and artwork the practice-led artist-researcher need to embrace the co-productive nature of critical word and creative work to more completely articulate their practice and its significance as research. The ideal venue and opportunity for this is the exegesis.

Thermal analysis of synthetic reevesite and cobalt substituted reevesite (Ni,Co)6Fe2(OH)16(CO3)•4H2O

The mineral reevesite and the cobalt substituted reevesite have been synthesised. The d(003) spacings of the minerals ranged from 7.54 to 7.95 Å. The maximum d(003) value occurred at around Ni:Co 0.4:0.6. This maximum in interlayer distance is proposed to be due to a greater number of carbonate anions and water molecules intercalated into the structure. The stability of the reevesite and cobalt doped reevesite was determined by thermogravimetric analysis. The maximum temperature of the reevesite occurs for the unsubstituted reevesite and is around 220°C. The effect of cobalt substitution results in a decrease in thermal stability of the reevesites. Four thermal decomposition steps are observed and are attributed to dehydration, dehydroxylation and decarbonation, decomposition of the formed carbonate and oxygen loss at ~807 °C. A mechanism for the thermal decomposition of the reevesite and the cobalt substituted reevesite is proposed.

The return of a forgotten polymer : Polycaprolactone in the 21st century

During the resorbable-polymer-boom of the 1970s and 1980s, polycaprolactone (PCL) was used in the biomaterials field and a number of drug-delivery devices. Its popularity was soon superseded by faster resorbable polymers which had fewer perceived disadvantages associated with long term degradation (up to 3-4 years) and intracellular resorption pathways; consequently, PCL was almost forgotten for most of two decades. Recently, a resurgence of interest has propelled PCL back into the biomaterials-arena. The superior rheological and viscoelastic properties over many of its aliphatic polyester counterparts renders PCL easy to manufacture and manipulate into a large range of implants and devices. Coupled with relatively inexpensive production routes and FDA approval, this provides a promising platform for the production of longer-term degradable implants which may be manipulated physically, chemically and biologically to possess tailorable degradation kinetics to suit a specific anatomical site. This review will discuss the application of PCL as a biomaterial over the last two decades focusing on the advantages which have propagated its return into the spotlight with a particular focus on medical devices, drug delivery and tissue engineering.

Dating and intimacy in the 21st century : the use of online dating sites in Australia

This article examines the growing phenomenon of online dating and intimacy in the 21st century. The exponential rise of communications technologies, which is both reflective and constitutive of an increasingly networked and globalized society, has the potential to significantly influence the nature of intimacy in everyday life. Yet, to date, there has been a minimal response by sociologists to seek, describe and understand this influence. In this article, we present some of the key findings of our research on online dating in Australia, in order to foster a debate about the sociological impacts on intimacy in the postmodern world. Based on a web audit of more than 60 online dating sites and in-depth interviews with 23 users of online dating services, we argue that recent global trends are influencing the uptake of online technologies for the purposes of forming intimate relations. Further, some of the mediating effects of these technologies – in particular, the hypercommunication – may have specific implications for the nature of intimacy in the global era.

Practising public relations in the global community of the 21st century : a comparison of business practices and culture in three world regions

Non-Western practitioners across the globe instinctively attempt to implement Western-based public relations models and theories, often unsuccessfully, regardless of their surrounding environment. This paper reviews business practices and reveals that in Europe, company interests are a main priority, while in Asia, the line between business and personal relationships is extremely blurred. Cultural dimensions and topois were even more varied between the three regions. Implications for the adoption of Western models of public relations practice are discussed.

Artful determination : "state of the art" and PCME Ltd v. Goyen COntrols Co. UK Ltd

In a recent decision by Mr Justice Laddie, a patent was held anticipated by, inter alia, prior use of a device which fell within the claims of the patent in suit, even though its circuitry was enclosed in resin. The anticipating invention had been "made available to the public" within the terms of section 2 (2) of the Patents Act 1977 because its essential integers would have been revealed by an interesting character, the "skilled forensic engineer".

An ESR study of irradiated poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA)

Poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA) with 2 mol% perfluoropropyl vinyl ether (PPVE) was exposed to γ-irradiation in vacuum at both 77 K and room temperature and the ESR spectra recorded. Both the main chain, CF2–C.F–CF2, and end chain, CF2C.F2 radicals were identified at both temperatures and their thermal stabilities measured. No radicals unique to the radiolytic cleavage at the PPVE units were observed at room temperature, either due to the low concentration of the comonomer or β-scission to form a chain end radical and a non-radical species. G-values for radical formation at room temperature and 77 K were found to be 0.93 and 0.16, respectively.

Management of co-occurring substance use disorders

Reviewing the breadth of current knowledge on schizophrenia, this handbook provides clear, practical guidelines for effective assessment and treatment in diverse contexts. Leading authorities have contributed 61 concise chapters on all aspects of the disorder and its clinical management. In lieu of exhaustive literature reviews, each chapter summarizes the current state of the science; highlights key points the busy practitioner needs to know; and lists recommended resources, including seminal research studies, invaluable clinical tools, and more. Comprehensive, authoritative, and timely, the volume will enable professionals in any setting to better understand and help their patients or clients with severe mental illness.

Trends in Australian contact lens prescribing during the first decade of the 21st Century (2000–2009)

Purpose: The aim was to document contact lens prescribing trends in Australia between 2000 and 2009. ---------- Methods: A survey of contact lens prescribing trends was conducted each year between 2000 and 2009. Australian optometrists were asked to provide information relating to 10 consecutive contact lens fittings between January and March each year. ---------- Results: Over the 10-year survey period, 1,462 practitioners returned survey forms representing a total of 13,721 contact lens fittings. The mean age (± SD) of lens wearers was 33.2 ± 13.6 years and 65 per cent were female. Between 2006 and 2009, rigid lens new fittings decreased from 18 to one per cent. Low water content lenses reduced from 11.5 to 3.2 per cent of soft lens fittings between 2000 and 2008. Between 2005 and 2009, toric lenses and multifocal lenses represented 26 and eight per cent, respectively, of all soft lenses fitted. Daily disposable, one- to two-week replacement and monthly replacement lenses accounted for 11.6, 30.0 and 46.5 per cent of all soft lens fittings over the survey period, respectively. The proportion of new soft fittings and refittings prescribed as extended wear has generally declined throughout the past decade. Multi-purpose lens care solutions dominate the market. Rigid lenses and monthly replacement soft lenses are predominantly worn on a full-time basis, whereas daily disposable soft lenses are mainly worn part-time.---------- Conclusions: This survey indicates that technological advances, such as the development of new lens materials, manufacturing methods and lens designs, and the availability of various lens replacement options, have had a significant impact on the contact lens market during the first decade of the 21st Century.