Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

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.

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.

A comparison of two business cycle dating methods

We study the suggestion that Markov switching (MS) models should be used to determine cyclical turning points. A Kalman filter approximation is used to derive the dating rules implicit in such models. We compare these with dating rules in an algorithm that provides a good approximation to the chronology determined by the NBER. We find that there is very little that is attractive in the MS approach when compared with this algorithm. The most important difference relates to robustness. The MS approach depends on the validity of that statistical model. Our approach is valid in a wider range of circumstances.

Efficient and accurate retrieval of business process models through indexing

Recent years have seen an increased uptake of business process management technology in industries. This has resulted in organizations trying to manage large collections of business process models. One of the challenges facing these organizations concerns the retrieval of models from large business process model repositories. For example, in some cases new process models may be derived from existing models, thus finding these models and adapting them may be more effective than developing them from scratch. As process model repositories may be large, query evaluation may be time consuming. Hence, we investigate the use of indexes to speed up this evaluation process. Experiments are conducted to demonstrate that our proposal achieves a significant reduction in query evaluation time.

Doing business : knowledges in the internationalised business lecture

This paper investigates the oracy (listening/speaking) genres enacted in an undergraduate entry point unit in the internationalised university of the 21st century, and the kind of knowledges these genres elicit and perform. This paper focuses on a series of lectures in the business studies unit and how anecdotal knowledge from both the lecturer’s and the students’ lived experiences was elicited as grist for the curriculum. The analysis of lecture talk suggests that the lecture today is no longer a monologic display of expert disciplinary knowledge bestowed upon the learner. Rather, it is increasingly a multimedia performance with an underlying ethic of engagement and interactivity. Of particular interest is the way international students’ knowledges were elicited to resource the internationalised curriculum with authenticity and insight. The knowledges thus assembled are analysed through Bernstein’s conceptual distinction between vertical and horizontal knowledge structures. The paper offers suggestions on how to maximise the potential and minimize the risks of this more interactive genre of lecture, with particular regard to enabling the participation of the international student.

Ties that blind? How strong ties affect small business owner-managers’ perceived trustworthiness of their advisors

This research investigates how a strong personal relationship (strong tie) between a small business owner-manager and his professional or informal advisor affects the relationship between the advisor's recent performance and the owner-manager's perceptions of the advisor's trustworthiness in terms of ability, benevolence and integrity. A negative moderating effect could point to a 'tie that blinds': the owner-manager may be less critical in evaluating the advisor's perceived trustworthiness in light of their recent performance, because of the existing personal relationship. A conceptual model is constructed and examined with survey data comprising 153 young Finnish businesses. The results show that strong ties increase the owner-manager's perception of the advisor's integrity, disregarding their recent performance. For professional advisors, strong ties reduce the impact of recent performance in the owner-manager's evaluation of their ability. For informal advisors, a strong tie makes it more likely that their benevolence will be evaluated highly in light of their recent performance. While the results show that 'ties can blind' under certain circumstances, the limitations of the study raise the need for further research to specify these contextual factors and examine the causal link between the choice of advisor and business performance.

Micro-family-owned business : transitory survival mechanism or long term wealth creator?

Principal Topic: Entrepreneurship is key to employment, innovation and growth (Acs & Mueller, 2008), and as such, has been the subject of tremendous research in both the economic and management literatures since Solow (1957), Schumpeter (1934, 1943), and Penrose (1959). The presence of entrepreneurs in the economy is a key factor in the success or failure of countries to grow (Audretsch and Thurik, 2001; Dejardin, 2001). Further studies focus on the conditions of existence of entrepreneurship, influential factors invoked are historical, cultural, social, institutional, or purely economic (North, 1997; Thurik 1996 & 1999). Of particular interest, beyond the reasons behind the existence of entrepreneurship, are entrepreneurial survival and good ''performance'' factors. Using cross-country firm data analysis, La Porta & Schleifer (2008) confirm that informal micro-businesses provide on average half of all economic activity in developing countries. They find that these are utterly unproductive compared to formal firms, and conclude that the informal sector serves as a social security net ''keep[ing] millions of people alive, but disappearing over time'' (abstract). Robison (1986), Hill (1996, 1997) posit that the Indonesian government under Suharto always pointed to the lack of indigenous entrepreneurship , thereby motivating the nationalisation of all industries. Furthermore, the same literature also points to the fact that small businesses were mostly left out of development programmes because they were supposed less productive and having less productivity potential than larger ones. Vial (2008) challenges this view and shows that small firms represent about 70% of firms, 12% of total output, but contribute to 25% of total factor productivity growth on average over the period 1975-94 in the industrial sector (Table 10, p.316). ---------- Methodology/Key Propositions: A review of the empirical literature points at several under-researched questions. Firstly, we assess whether there is, evidence of small family-business entrepreneurship in Indonesia. Secondly, we examine and present the characteristics of these enterprises, along with the size of the sector, and its dynamics. Thirdly, we study whether these enterprises underperform compared to the larger scale industrial sector, as it is suggested in the literature. We reconsider performance measurements for micro-family owned businesses. We suggest that, beside productivity measures, performance could be appraised by both the survival probability of the firm, and by the amount of household assets formation. We compare micro-family-owned and larger industrial firms' survival probabilities after the 1997 crisis, their capital productivity, then compare household assets of families involved in business with those who do not. Finally, we examine human and social capital as moderators of enterprises' performance. In particular, we assess whether a higher level of education and community participation have an effect on the likelihood of running a family business, and whether it has an impact on households' assets level. We use the IFLS database compiled and published by RAND Corporation. The data is a rich community, households, and individuals panel dataset in four waves: 1993, 1997, 2000, 2007. We now focus on the waves 1997 and 2000 in order to investigate entrepreneurship behaviours in turbulent times, i.e. the 1997 Asian crisis. We use aggregate individual data, and focus on households data in order to study micro-family-owned businesses. IFLS data covers roughly 7,600 households in 1997 and over 10,000 households in 2000, with about 95% of 1997 households re-interviewed in 2000. Households were interviewed in 13 of the 27 provinces as defined before 2001. Those 13 provinces were targeted because accounting for 83% of the population. A full description of the data is provided in Frankenberg and Thomas (2000), and Strauss et alii (2004). We deflate all monetary values in Rupiah with the World Development Indicators Consumer Price Index base 100 in 2000. ---------- Results and Implications: We find that in Indonesia, entrepreneurship is widespread and two thirds of households hold one or several family businesses. In rural areas, in 2000, 75% of households run one or several businesses. The proportion of households holding both a farm and a non farm business is higher in rural areas, underlining the reliance of rural households on self-employment, especially after the crisis. Those businesses come in various sizes from very small to larger ones. The median business production value represents less than the annual national minimum wage. Figures show that at least 75% of farm businesses produce less than the annual minimum wage, with non farm businesses being more numerous to produce the minimum wage. However, this is only one part of the story, as production is not the only ''output'' or effect of the business. We show that the survival rate of those businesses ranks between 70 and 82% after the 1997 crisis, which contrasts with the 67% survival rate for the formal industrial sector (Ter Wengel & Rodriguez, 2006). Micro Family Owned Businesses might be relatively small in terms of production, they also provide stability in times of crisis. For those businesses that provide business assets figures, we show that capital productivity is fairly high, with rates that are ten times higher for non farm businesses. Results show that households running a business have larger family assets, and households are better off in urban areas. We run a panel logit model in order to test the effect of human and social capital on the existence of businesses among households. We find that non farm businesses are more likely to appear in households with higher human and social capital situated in urban areas. Farm businesses are more likely to appear in lower human capital and rural contexts, while still being supported by community participation. The estimation of our panel data model confirm that households are more likely to have higher family assets if situated in urban area, the higher the education level, the larger the assets, and running a business increase the likelihood of having larger assets. This is especially true for non farm businesses that have a clearly larger and more significant effect on assets than farm businesses. Finally, social capital in the form of community participation also has a positive effect on assets. Those results confirm the existence of a strong entrepreneurship culture among Indonesian households. Investigating survival rates also shows that those businesses are quite stable, even in the face of a violent crisis such as the 1997 one, and as a result, can provide a safety net. Finally, considering household assets - the returns of business to the household, rather than profit or productivity - the returns of business to itself, shows that households running a business are better off. While we demonstrate that uman and social capital are key to business existence, survival and performance, those results open avenues for further research regarding the factors that could hamper growth of those businesses in terms of output and employment.

Virtual Environment Visualisation of Executable Business Process Models

Business Process Modelling is a fast growing field in business and information technology, which uses visual grammars to model and execute the processes within an organisation. However, many analysts present such models in a 2D static and iconic manner that is difficult to understand by many stakeholders. Difficulties in understanding such grammars can impede the improvement of processes within an enterprise due to communication problems. In this chapter we present a novel framework for intuitively visualising animated business process models in interactive Virtual Environments. We also show that virtual environment visualisations can be performed with present 2D business process modelling technology, thus providing a low barrier to entry for business process practitioners. Two case studies are presented from film production and healthcare domains that illustrate the ease with which these visualisations can be created. This approach can be generalised to other executable workflow systems, for any application domain being modelled.

Collaborative business process modeling using 3D virtual environments

Process modeling is a complex organizational task that requires many iterations and communication between the business analysts and the domain specialists involved in the process modeling. The challenge of process modeling is exacerbated, when the process of modeling has to be performed in a cross-organizational, distributed environment. Some systems have been developed to support collaborative process modeling, all of which use traditional 2D interfaces. We present an environment for collaborative process modeling, using 3D virtual environment technology. We make use of avatar instantiations of user ego centres, to allow for the spatial embodiment of the user with reference to the process model. We describe an innovative prototype collaborative process modeling approach, implemented as a modeling environment in Second Life. This approach leverages the use of virtual environments to provide user context for editing and collaborative exercises. We present a positive preliminary report on a case study, in which a test group modelled a business process using the system in Second Life.

Enablers and barriers to the organizational adoption of sustainable business practices

Individuals, organizations, and governments are increasingly becoming aware of the necessity of sustainability in living, organizing, performing, and managing work. In this context, “green IS” has become an established colloquial term, acknowledging that information technology, corporate information systems, and the surrounding practices are both a contributor to the sustainability challenge and a potential enabler for green and sustainable practices. To date, however, there are few reported studies on the role of information systems for the challenge, and solution, of sustainability. This paper presents results from a case study of a world-wide operating IT software solution provider that is engaged in the development and adoption of sustainable practices. Our study suggests that the adoption of sustainable practices comes along with a number of particularities. We found information technology to be a key enabler of transparency about the progress of sustainability operations. We further found personal, motivator factors as well as organizational factors such as business inclusion, strategy definition, and a dialectic top-management and bottom-up support, to play a role in enabling a company to manage their sustainability. We describe a set of conjectures forthcoming from our case analysis, and detail some implications for further research in this area.

On the usage of labels and icons in business process modeling

The value of business process models is dependent not only on the choice of graphical elements in the model, but also on their annotation with additional textual and graphical information. This research discusses the use of text and icons for labeling the graphical constructs in a process model. We use two established verb classification schemes to examine the choice of activity labels in process modeling practice. Based on our findings, we synthesize a set of twenty-five activity label categories. We propose a systematic approach for graphically representing these label categories through the use of graphical icons, such that the resulting process models are easier and more readily understandable by end users. Our findings contribute to an ongoing stream of research investigating the practice of process modeling and thereby contribute to the body of knowledge about conceptual modeling quality overall.

The ability of economic thinking : the “nature” versus “nurture” debate

In their studies, Eley and Meyer (2004) and Meyer and Cleary (1998) found that there are sources of variation in the affective and process dimensions of learning in mathematics and clinical diagnosis specific to each of these disciplines. Meyer and Shanahan (2002) argue that: General purpose models of student learning that are transportable across different discipline contexts cannot, by definition, be sensitive to sources of variation that may be subject-specific (2002. p. 204). In other words, to explain the differences in learning approaches and outcomes in a particular discipline, there are discipline-specific factors, which cannot be uncovered in general educational research. Meyer and Shanahan (2002) argue for a need to "seek additional sources of variation that are perhaps conceptually unique ... within the discourse of particular disciplines" (p. 204). In this paper, the development of an economics-specific construct (called economic thinking ability) is reported. The construct aims to measure discipline-sited ability of students that has important influence on learning in economics. Using this construct, economic thinking abilities of introductory and intermediate level economics students were measured prior to the commencement, and at the end, of their study over one semester. This enabled factors associated with students' pre-course economic thinking ability and their development in economic thinking ability to be investigated. The empirical findings will address the 'nature' versus 'nurture' debate in economics education (Frank, et aI., 1993; Frey et al., 1993; Haucap and Tobias 2003). The implications for future research in economics education will also be discussed.

Teaching the economic way of thinking : a new approach to teaching introductory economics in a business degree

In teaching introductory economics there has been a tendency to put a lot of emphasis on imparting abstract models and technical skills to students (Stilwell, 2005; Voss, Blais, Greens, & Ahwesh, 1986). This model building approach has the merit of preparing the grounding for students 10 pursue further studies in economics. However, in a business degree with only a small proportion of students majoring in economics, such an approach tend to alienate the majority of students transiting from high school in to university. Surveys in Europe and Australia found that students complained about the lack of relevance of economics courses to the real world and the over-reliance of abstract mathematical modelling (Kirman, 2001; Lewis and Norris, 1997; Siegfried & Round, 2000). BSB112 Economics 1 is one of the eight faculty core units in the Faculty of Business at QUT, with over 1000 students in each semester. In semester I 2008, a new approach to teaching this unit was designed aiming to achieve three inter-related objectives: (1) to provide business students with a first insight into economic thinking and language, (2) to integrate economic analysis with current Australian social, environmental and political issues, and (3) to cater for students with a wide range of academic needs. Strategies used to achieve these objectives included writing up a new text which departs from traditional economics textbooks in important ways, integrating students' cultures in teaching and learning activities, and devising a new assessment format to encourage development of research skills and applications rather than reproduction of factual knowledge. This paper will document the strategies used in this teaching innovation, present quantitative and qualitative evidence to evaluate this new approach and suggest ways of further improvement.

The mobile Internet and small business : an exploratory study of needs, uses and adoption with full-adopters of technology

The technological environment in which contemporary small and medium-sized enterprises (SMEs) operate can only be described as dynamic. The exponential rate of technological change, characterised by perceived increases in the benefits associated with various technologies, shortening product life cycles and changing standards, provides for the SME a complex and challenging operational context. The primary aim of this research was to concentrate on those SMEs that had already adopted technology in order to identify their needs for the new mobile data technologies (MDT), the mobile Internet. The research design utilised a mixed approach whereby both qualitative and quantitative data was collected to address the question. Overall, the needs of these SMEs for MDT can be conceptualised into three areas where the technology will assist business practices; communication, eCommerce and security.