Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

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 (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Spiritual wisdom of Taoism in business : through the lens of interpretation realism in a Cisco end-to-end case study

This paper explores how the amalgamated wisdom of East and West can instigate a wisdombased renaissance of humanistic epistemology (Rooney & McKenna, 2005) to provide a platform of harmony in managing knowledge-worker productivity, one of the biggest management challenges of the 21st century (Drucker, 1999). The paper invites further discussions from the social and business research communities on the significance of "interpretation realism" technique in comprehending philosophies of Lao Tzu Confucius and Sun Tzu (Lao/Confucius/Sun] written in "Classical Chinese." This paper concludes with a call to build prudent, responsible practices in management which affects the daily lives of many (Rooney & McKenna, 2005) in today's knowledgebased economy. Interpretation Realism will be applied to an analysis of three Chinese classics of Lao/Confucius/Sun which have been embodied in the Chinese culture for over 2,500 years. Comprehending Lao/Confucius/Sun's philosophies is the first step towards understanding Classical Chinese culture. However, interpreting Chinese subtlety in language and the yin and yang circular synthesis in their mode of thinking is very different to understanding Western thought with its open communication and its linear, analytical pattern of Aristotelian/Platonic wisdom (Zuo, 2012). Furthermore, Eastern ways of communication are relatively indirect and mediatory in culture. Western ways of communication are relatively direct and litigious in culture (Goh, 2002). Furthermore, Lao/Confucius/Sun's philosophies are difficult to comprehend as there are four written Chinese formats and over 250 dialects: Pre-classical Chinese Classical Chinese Literary Chinese and modern Vernacular Chinese Because Classical Chinese is poetic, comprehension requires a mixed approach of interpretation realism combining logical reasoning behind "word splitting word occurrences", "empathetic metaphor" and "poetic appreciation of word.

Reluctantly virtual : modelling copyright industry dynamics

During the evolution of the music industry, developments in the media environment have required music firms to adapt in order to survive. Changes in broadcast radio programming during the 1950s; the Compact Cassette during the 1970s; and the deregulation of media ownership during the 1990s are all examples of changes which have heavily affected the music industry. This study explores similar contemporary dynamics, examines how decision makers in the music industry perceive and make sense of the developments, and reveals how they revise their business strategies, based on their mental models of the media environment. A qualitative system dynamics model is developed in order to support the reasoning brought forward by the study. The model is empirically grounded, but is also based on previous music industry research and a theoretical platform constituted by concepts from evolutionary economics and sociology of culture. The empirical data primarily consist of 36 personal interviews with decision makers in the American, British and Swedish music industrial ecosystems. The study argues that the model which is proposed, more effectively explains contemporary music industry dynamics than music industry models presented by previous research initiatives. Supported by the model, the study is able to show how “new” media outlets make old music business models obsolete and challenge the industry’s traditional power structures. It is no longer possible to expose music at one outlet (usually broadcast radio) in the hope that it will lead to sales of the same music at another (e.g. a compact disc). The study shows that many music industry decision makers still have not embraced the new logic, and have not yet challenged their traditional mental models of the media environment. Rather, they remain focused on preserving the pivotal role held by the CD and other physical distribution technologies. Further, the study shows that while many music firms remain attached to the old models, other firms, primarily music publishers, have accepted the transformation, and have reluctantly recognised the realities of a virtualised environment.

'Explain in plain English' questions revisited : data structures problems

Recent studies have linked the ability of novice (CS1) programmers to read and explain code with their ability to write code. This study extends earlier work by asking CS2 students to explain object-oriented data structures problems that involve recursion. Results show a strong correlation between ability to explain code at an abstract level and performance on code writing and code reading test problems for these object-oriented data structures problems. The authors postulate that there is a common set of skills concerned with reasoning about programs that explains the correlation between writing code and explaining code. The authors suggest that an overly exclusive emphasis on code writing may be detrimental to learning to program. Non-code writing learning activities (e.g., reading and explaining code) are likely to improve student ability to reason about code and, by extension, improve student ability to write code. A judicious mix of code-writing and code-reading activities is recommended.

Classification of pathology reports for cancer registry notifications

Objective: To develop a system for the automatic classification of pathology reports for Cancer Registry notifications. Method: A two pass approach is proposed to classify whether pathology reports are cancer notifiable or not. The first pass queries pathology HL7 messages for known report types that are received by the Queensland Cancer Registry (QCR), while the second pass aims to analyse the free text reports and identify those that are cancer notifiable. Cancer Registry business rules, natural language processing and symbolic reasoning using the SNOMED CT ontology were adopted in the system. Results: The system was developed on a corpus of 500 histology and cytology reports (with 47% notifiable reports) and evaluated on an independent set of 479 reports (with 52% notifiable reports). Results show that the system can reliably classify cancer notifiable reports with a sensitivity, specificity, and positive predicted value (PPV) of 0.99, 0.95, and 0.95, respectively for the development set, and 0.98, 0.96, and 0.96 for the evaluation set. High sensitivity can be achieved at a slight expense in specificity and PPV. Conclusion: The system demonstrates how medical free-text processing enables the classification of cancer notifiable pathology reports with high reliability for potential use by Cancer Registries and pathology laboratories.

A threshold concepts focus to curriculum design: supporting student learning through application of variation theory

This project develops and evaluates a model of curriculum design that aims to assist student learning of foundational disciplinary ‘Threshold Concepts’. The project uses phenomenographic action research, cross-institutional peer collaboration and the Variation Theory of Learning to develop and trial the model. Two contrasting disciplines (Physics and Law) and four institutions (two research-intensive and two universities of technology) were involved in the project, to ensure broad applicability of the model across different disciplines and contexts. The Threshold Concepts that were selected for curriculum design attention were measurement uncertainty in Physics and legal reasoning in Law. Threshold Concepts are key disciplinary concepts that are inherently troublesome, transformative and integrative in nature. Once understood, such concepts transform students’ views of the discipline because they enable students to coherently integrate what were previously seen as unrelated aspects of the subject, providing new ways of thinking about it (Meyer & Land 2003, 2005, 2006; Land et al. 2008). However, the integrative and transformative nature of such threshold concepts make them inherently difficult for students to learn, with resulting misunderstandings of concepts being prevalent...

Promoting Statistical Literacy Through Data Modelling in the Early School Years

This chapter addresses data modelling as a means of promoting statistical literacy in the early grades. Consideration is first given to the importance of increasing young children’s exposure to statistical reasoning experiences and how data modelling can be a rich means of doing so. Selected components of data modelling are then reviewed, followed by a report on some findings from the third-year of a three-year longitudinal study across grades one through three.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.

Automated classification of limb fractures from free-text radiology reports using a clinician-informed gazetteer methodology

Background Timely diagnosis and reporting of patient symptoms in hospital emergency departments (ED) is a critical component of health services delivery. However, due to dispersed information resources and a vast amount of manual processing of unstructured information, accurate point-of-care diagnosis is often difficult. Aims The aim of this research is to report initial experimental evaluation of a clinician-informed automated method for the issue of initial misdiagnoses associated with delayed receipt of unstructured radiology reports. Method A method was developed that resembles clinical reasoning for identifying limb abnormalities. The method consists of a gazetteer of keywords related to radiological findings; the method classifies an X-ray report as abnormal if it contains evidence contained in the gazetteer. A set of 99 narrative reports of radiological findings was sourced from a tertiary hospital. Reports were manually assessed by two clinicians and discrepancies were validated by a third expert ED clinician; the final manual classification generated by the expert ED clinician was used as ground truth to empirically evaluate the approach. Results The automated method that attempts to individuate limb abnormalities by searching for keywords expressed by clinicians achieved an F-measure of 0.80 and an accuracy of 0.80. Conclusion While the automated clinician-driven method achieved promising performances, a number of avenues for improvement were identified using advanced natural language processing (NLP) and machine learning techniques.

The Language : Rationale and Fundamentals

The Business Process Management domain has evolved at a dramatic pace over the past two decades and the notion of the business process has become a ubiquitous part of the modern business enterprise. Most organizations now view their operations in terms of business processes and manage these business processes in the same way as other corporate assets. In recent years, an increasingly broad range of generic technology has become available for automating business processes. This is part of a growing trend in the software engineering field throughout the past 40 years, where aspects of functionality that are potentially reusable on a widespread basis have coalesced into generic software components. Figure 2.1 illustrates this trend and shows how software systems have evolved from the monolithic applications of the 1960s developed in their entirety often by a single development team to today’s offerings that are based on the integration of a range of generic technologies with only a small component of the application actually being developed from scratch. In the 1990s, generic functionality for the automation of business processes first became commercially available in the form of workflow technology and subsequently evolved in the broader field of business process management systems (BPMS). This technology alleviated the necessity to develop process support within applications from scratch and provided a variety of off-the-shelf options on which these requirements could be based. The demand for this technology was significant and it is estimated that by 2000 there were well over 200 distinct workflow offerings in the market, each with a distinct conceptual foundation. Anticipating the difficulties that would be experienced by organizations seeking to utilize and integrate distinct workflow offerings, the Workflow Management Coalition (WfMC), an industry group formed to advance technology in this area, proposed a standard reference model for workflow technology with an express desire to seek a common platform for achieving workflow interoperation.

Disclosures of social value creation : a case study of three global social enterprises

This study seeks to fill in gap in the existing literature by looking at how and whether disclosure of social value creation becomes a part of legitimation strategies of social enterprises. By using legitimacy reasoning, this study informs that three global social organizations, Grameen Bank, Charity Water, and the Bill and Melinda Gates Foundation provide evidence of the use of disclosures of social value creation in order to conform with the expectations of the broader community—the community that wants to see poverty and injustice free world.

Connectivity of workflow nets : the foundations of stepwise verification

Behavioral models capture operational principles of real-world or designed systems. Formally, each behavioral model defines the state space of a system, i.e., its states and the principles of state transitions. Such a model is the basis for analysis of the system’s properties. In practice, state spaces of systems are immense, which results in huge computational complexity for their analysis. Behavioral models are typically described as executable graphs, whose execution semantics encodes a state space. The structure theory of behavioral models studies the relations between the structure of a model and the properties of its state space. In this article, we use the connectivity property of graphs to achieve an efficient and extensive discovery of the compositional structure of behavioral models; behavioral models get stepwise decomposed into components with clear structural characteristics and inter-component relations. At each decomposition step, the discovered compositional structure of a model is used for reasoning on properties of the whole state space of the system. The approach is exemplified by means of a concrete behavioral model and verification criterion. That is, we analyze workflow nets, a well-established tool for modeling behavior of distributed systems, with respect to the soundness property, a basic correctness property of workflow nets. Stepwise verification allows the detection of violations of the soundness property by inspecting small portions of a model, thereby considerably reducing the amount of work to be done to perform soundness checks. Besides formal results, we also report on findings from applying our approach to an industry model collection.

Developing Co-operating Legal Knowledge Based Systems

In attempting to build intelligent litigation support tools, we have moved beyond first generation, production rule legal expert systems. Our work supplements rule-based reasoning with case based reasoning and intelligent information retrieval. This research, specifies an approach to the case based retrieval problem which relies heavily on an extended object-oriented / rule-based system architecture that is supplemented with causal background information. Machine learning techniques and a distributed agent architecture are used to help simulate the reasoning process of lawyers. In this paper, we outline our implementation of the hybrid IKBALS II Rule Based Reasoning / Case Based Reasoning system. It makes extensive use of an automated case representation editor and background information.

Teaching and using analogy in law

Analogy plays a central role in legal reasoning, yet how to analogize is poorly taught and poorly practiced. We all recognize when legal analogies are being made: when a law professor suggests a difficult hypothetical in class and a student tentatively guesses at the answer based on the cases she read the night before, when an attorney advises a client to settle because a previous case goes against him, or when a judge adopts one precedent over another on the basis that it better fits the present case. However, when it comes to explaining why certain analogies are compelling, persuasive, or better than the alternative, lawyers usually draw a blank. The purpose of this article is to provide a simple model that can be used to teach and to learn how analogy actually works, and what makes one analogy superior to a competing analogy. The model is drawn from a number of theories of analogy making in cognitive science. Cognitive science is the “long-term enterprise to understand the mind scientifically.” The field studies the mechanisms that are involved in cognitive processes like thinking, memory, learning, and recall; and one of its main foci has been on how people construct analogies. The lessons from cognitive science theories of analogy can be applied to legal analogies to give students and lawyers a better understanding of this fundamental process in legal reasoning.