Empirical generalisation as an inadequate cognitive scaffold to theoretical generalisation of a more complex concept

The impact of prior learning on new learning is highlighted by the case of Dean, a Year 8 student who developed his own method to find the sum of the interior angles of a polygon without knowing why his method worked. Enriched transcripts and visual displays of the cognitive, social (Dreyfus, Hershkowitz, & Schwarz, 2001) and affective elements (Williams, 2002) of Dean's interrupted abstraction process informed the identification of factors that inhibited Dean's constructing process. It was found Dean possessed an empirical, not theoretical, generalization (Davydov, 1990) about sums of interior angles of triangles that was an inadequate cognitive artifact for constructing the new more complex theoretical generalization. The study suggests use of tasks designed with the opportunity develop assumed knowledge in conjunction with new concepts.

Hierarchical rule generalisation for speaker identification in fiction books

This paper presents a hierarchical pattern matching and generalisation technique which is applied to the problem of locating the correct speaker of quoted speech found in fiction books. Patterns from a training set are generalised to create a small number of rules, which can be used to identify items of interest within the text. The pattern matching technique is applied to finding the Speech-Verb, Actor and Speaker of quotes found in ction books. The technique performs well over the training data, resulting in rule-sets many times smaller than the training set, but providing very high accuracy. While the rule-set generalised from one book is less effective when applied to different books than an approach based on hand coded heuristics, performance is comparable when testing on data closely related to the training set.

Predicting the rolling force in hot steel rolling mill using an ensemble model

Accurate prediction of the roll separating force is critical to assuring the quality of the final product in steel manufacturing. This paper presents an ensemble model that addresses these concerns. A stacked generalisation approach to ensemble modeling is used with two sets of the ensemble model members, the first set being learnt from the current input-output data of the hot rolling finishing mill, while another uses the available information on the previous coil in addition to the current information. Both sets of ensemble members include linear regression, multilayer perceptron, and k-nearest neighbor algorithms. A competitive selection model (multilayer perceptron) is then used to select the output from one of the ensemble members to be the final output of the ensemble model. The ensemble model created by such a stacked generalization is able to achieve extremely high accuracy in predicting the roll separation force with the average relative accuracy being within 1% of the actual measured roll force.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

Broadcast anti-jamming systems

In a traditional anti-jamming system a transmitter who wants to send a signal to a single receiver spreads the signal power over a wide frequency spectrum with the aim of stopping a jammer from blocking the transmission. In this paper, we consider the case that there are multiple receivers and the transmitter wants to broadcast a message to all receivers such that colluding groups of receivers cannot jam the reception of any other receiver. We propose efficient coding methods that achieve this goal and link this problem to well-known problems in combinatorics. We also link a generalisation of this problem to the Key Distribution Pattern problem studied in combinatorial cryptography

Sir, can x equal x plus two?

Technology in classrooms has brought opportunities to develop new ways of teaching and learning, as well as new ways of thinking and communicating. The author describes a lesson which aimed to have the grade four children in the class construct on the computer screen images of rectangles. The lesson provided the opportunity to learn about some powerful generalisations about rectangles as well to learn about their geometric and algebraic understandings.

Diversities in the professional organization of accountants : a comparability study with insights from the Chinese experience

While spatial, historical and cultural variations across different countries have prevented any generalisation to be made of the professionalization process, various analytical themes can be said to have emerged in scholarly inquires relating to the professional organization of accountants. In highlighting these broad themes, this study argues that they have all revolved around one important relationship-that of the state and the accounting profession. The dynamics and the fluid nature of this intriguing relationship is further captured and contrasted in this study through an investigation of an episode of intra-professional conflict during the professionalization experience of the Chinese accountants.

Nonribosomal peptide synthetases as technological platforms for the synthesis of highly modified peptied bioeffectors - cyclosporin synthetase as a complex example

Many microbial peptide secondary metabolites possess important medicinal properties, of which the immunosuppressant cyclosporin A is an example. The enormous structural and functional diversity of these low-molecular weight peptides is attributable to their mode of biosynthesis. Peptide secondary metabolites are assembled non-ribosomally by multi-functional enzymes, termed non-ribosomal peptide synthetases. These systems consist of a multi-modular arrangement of the functional domains responsible for the catalysis of the partial reactions of peptide assembly. The extensive homology shared among NRPS systems allows for the generalisation of the knowledge garnered from studies of systems of diverse origins. In this review we shall focus the contemporary knowledge of non-ribosomal peptide biosynthesis on the structure and function of the cyclosporin biosynthetic system, with some emphasis on the re-direction of the biosynthetic potential of this system by combinatorial approaches.

Lessons from arts experiences for service-dominant logic

Purpose – The purpose of this paper is to consider whether art experiences can inform service-dominant logic (SDL) discourse through an exploration of the co-production and co-creation processes of art experiences.

Design/methodology/approach – Empirical knowledge gained about art experiences is analysed to identify emergent themes about co-production and co-creation. Four modes of qualitative data collection are employed: research participant diaries, photo elicitation, in depth interviews and focus groups.

Findings – Key findings are there are three stakeholders involved in the co-creation of art experiences, which all have critical and different roles; co-creation and co-production are both temporally based and evolving and there are points where they interact and intersect; and high levels of engagement in co-production enhance individuals' contribution to the co-creation of positive value and make their participation in future co-production opportunities more likely.

Research limitations/implications – The paper is exploratory and not a general population study. The methodology and sample of participants employed do not allow for the generalisation of the findings to the broader population.

Practical implications – Organisations may benefit from devising strategies to encourage greater dialogue and connection between all stakeholders involved in co-production and co-creation. The higher the level of individuals' co-production of art experiences the greater likelihood of positive value being co-created. Furthermore, the greater the possibility of individuals engaging in other co-production experiences in the future. While individuals are attracted to co-production possibilities, there are factors that are external to an experience that can act as either barriers to or facilitators of co-production, and that consequently impact on co-creation.

Originality/value – There is little extant research that explores the applicability of art experiences to SDL. This paper is significant in that it employs empirical research methods to develop knowledge on the topic. Furthermore, this paper is innovative in that it seeks to see whether the art experiences can inform generic marketing models, rather than whether generic marketing models can inform arts marketing.

Metamemory training for memory disorders in adults with a closed head injury

The purpose of the present study was to investigate the efficacy of a memory and metamemory training program on memory performance and metamemory judgement accuracy in adults with a closed head injury. A multiple baseline across subjects design was used with six subjects. All subjects were seen at least two years post-injury. Training included general metamemory information about the nature of memory, use of a specific memory strategy to assist verbal recall (to Preview, Question, Read, State and Test- PQRST), specific metamemory information about the strategy, and a self instruction procedure (WTSC- What is the task, Select a strategy to use, Try out strategy, Check to evaluate strategy effectiveness). During the training period all subjects recalled greater than fifty percent of paragraph ideas while using PQRST. Follow-up tests showed that five of the six subjects maintained recall levels but a gradual decrease in slope was observed over eight weeks post-training. Tests of recall, recognition and metamemory judgements on Sentence and Action Tasks were used to evaluate generalisation of training. Two subjects showed improved recall and two subjects showed improved recognition performance. In addition, four subjects demonstrated greater metamemory judgement accuracy about recognition performance following training. Improved performance post-training was also observed for three subjects on the Rivermead Behavioral Memory Test and the Logical Memory subtest of the Wechsler Memory Scale-Revised, greater than that expected for repeated testing. Several factors were identified as having a role in subjects’ ability to benefit from training.

Convex hulls in concept induction

Classification learning is dominated by systems which induce large numbers of small axis-orthogonal decision surfaces. This strongly biases such systems towards particular hypothesis types but there is reason believe that many domains have underlying concepts which do not involve axis orthogonal surfaces. Further, the multiplicity of small decision regions mitigates against any holistic appreciation of the theories produced by these systems, notwithstanding the fact that many of the small regions are individually comprehensible. This thesis investigates modeling concepts as large geometric structures in n-dimensional space. Convex hulls are a superset of the set of axis orthogonal hyperrectangles into which axis orthogonal systems partition the instance space. In consequence, there is reason to believe that convex hulls might provide a more flexible and general learning bias than axis orthogonal regions. The formation of convex hulls around a group of points of the same class is shown to be a usable generalisation and is more general than generalisations produced by axis-orthogonal based classifiers, without constructive induction, like decision trees, decision lists and rules. The use of a small number of large hulls as a concept representation is shown to provide classification performance which can be better than that of classifiers which use a large number of small fragmentary regions for each concept. A convex hull based classifier, CH1, has been implemented and tested. CH1 can handle categorical and continuous data. Algorithms for two basic generalisation operations on hulls, inflation and facet deletion, are presented. The two operations are shown to improve the accuracy of the classifier and provide moderate classification accuracy over a representative selection of typical, largely or wholly continuous valued machine learning tasks. The classifier exhibits superior performance to well-known axis-orthogonal-based classifiers when presented with domains where the underlying decision surfaces are not axis parallel. The strengths and weaknesses of the system are identified. One particular advantage is the ability of the system to model domains with approximately the same number of structures as there are underlying concepts. This leads to the possibility of extraction of higher level mathematical descriptions of the induced concepts, using the techniques of computational geometry, which is not possible from a multiplicity of small regions.

Computing in a social context : gender difference in participation

The thesis reviews the literature relating to girls and computing within a framework which is structured around three specific questions. First, are there differences between girls and boys in their participation in class computing activities and/or in non-class computing activities? Second, do these differences in participation in computing activities have broader implications which justify the growing concern about the under-representation of girls? Third, wahy are girls under-represented in these activities? Although the available literature is predominantly descriptive, the underlying implicit theoretical model is essentially a social learning model. Girl's differential participation is attributed to learned attitudes towards computing rathan to differences between girls and boys in general ability. These attitudes, which stress the masculine, mathematical, technological aspects of computing are developed through modelling, direct experience, intrinsic and extrinsic reinforcement and generalisation from pre-existing, attitudes to related curriculum areas. In the literature it is implicitly assumed that these attitudes underlie girl's decisions to self-select out of computing activities. In this thesis predictions from a social learning model are complemented by predictions derived from expectancy-value, cognitive dissonance and self-perception theories. These are tested in three separate studies. Study one provides data from a pretest-posttest study of 24 children in a year four class learning BASIC. It examines pre- and posttest differences between girls and boys in computing experience, knowledge and achievement as well as the factors relating to computing achievement. Study two uses a pretest-posttest control group design to study the gender differences in the impact of the introduction of Logo into years 1, 3, 5 and 7 in both a coeducational and single-sex setting using a sample of 222 children from three schools. Study three utilises a larger sample of 1176 students, drawn from three secondary schools and five primary schools, enabling an evaluation of gender differences in relation to a wide range of class computing experiences and in a broader range of school contexts. The overall results are consistent across the three studies, supporting the contention that social factors, rather than ability differences influence girls' participation and achievement in computing. The more global theoretical framework, drawing on social learning, expectancy-value, cognitive dissonance and self-perception theories, provides a more adequate explanation of gender differences in participation than does any one of these models.

Second person : a point of view? The function of the second person pronoun in narrative prose fiction

This thesis looks at the functions and effects of the ‘second-person’ pronoun in narrative prose fiction, with particular focus on the fluidity and ambiguity of the mode that I will call Protean-'you.' It is a mode in which it is unclear whether the ‘you’ is a character, the narrator, a reader/narratee, or no-one in particular—or a combination of these—so that readers find ‘second-person’ utterances at once familiar and deeply strange. I regard the ‘second person’ as a special case of narrative ‘person’ that, at its most fluid, can produce an experience of reading quite unlike that of reading traditional ‘first-‘ and ‘third-person’ narrative. Essentially, this unique experience comes about because Protean-‘you’ neglects to constitute the stable modes of subjectivity that readers expect to find within narrative textuality. These stable modes of subjectivity, modelled on what I will refer to as Cartesianism’s hegemonic notion of the self, have been thoroughly formalised and naturalised within the practices of ‘first-‘ and ‘third-person’ narrative. The Protean-‘you’ form of ‘second-person’ narrative, conversely, is a mode of narrative discourse that puts readers in a place of doubt and uncertainty, its unsettling equivocations forcefully disrupting accustomed, mimetic explanations of narrative and denying us access to the foundational, authorising subject of classical Cartesian thought. Rather than founding a notion of ‘second-person’ narrative and narrative ‘person’ generally on Cartesianism's ‘self-ish’ logic of unified, privatised identity, I turn to C.S, Peirce's notion of the semiotic self and to developments in post-structuralist thought. Essentially, the conception of subjectivity underpinning my arguments is Peirce's proposition that the self is to be conceived of not as a cogito, but as a sign by which the conscious entity knows itself. It is a sign, moreover, that is constantly being re-read, reinterpreted, so that identity is never self-complete. This reconception of subjectivity is necessary because 1 will argue that the effects of Protean-‘you’ arise in some part from a tension between Cartesianism's hegemony and what philosophical pragmatism and post-structuralism glimpse as the actual condition of the human subject—the subject as dispersed and contingent rather than unified and authoritative. Most discussions of ‘second-person’ narrative conceive of the mode in terms of implicit communicative relations, in some measure instituting Cartesianism's notion of the intentionalist self at the centre of literary meaning. I contrast the paradigmatic address model that arises from this conception against a model that approaches the analysis of ‘second-person’ narrative modality in terms of a referential function, that is, in terms of the object or objects referred to deictically by the ‘second-person’ pronoun. Two principal functions of ‘second-person’ textuality are identified and discussed at length. The first is generalisation, which is rarely dissipated altogether, a situation that contributes to the ambiguities of the pronoun's reference in much ‘second-person’ fiction. The second principal function is that of address, that is, the allocutionary function. Clearly, although stories that continually refer to a ‘you’ can seem quite baffling and unnatural, not all ‘second-person’ narratives unsettle the reader. In order to make the ‘second person's’ outlandish narratives knowable and stable, we bring to bear on them in our habits of reading whatever hermeneutic frames, whatever interpretive keys, come to hand, including a large number of unexceptional forms of literary and ‘natural’ discourse that employ the ‘second-person’ pronoun. These forms include letter writing and internal dialogue (i.e., talking to one's self), the language of the courtroom, the travelogue, the maxim, and so on. In looking at the ways in which the radicalising potentials of ‘second-person’ discourse are contained or recuperated, I focus on issues of vraisemblance and mimesis. Vraisemblance can be described as the ‘system of conventions and expectations which rests on/reinforces that more general system of ‘mutual knowledge’ produced within a community for the realisation and maintenance of a whole social world’. All of the forms of the vraisemblable are already instituted within social, cultural relations, so that what vraisemblance describes is the way we fit the inscriptions we read-that is, the way in which we naturalise what we read-into those given cultural and social forms. I also look at the conventionalising and naturalising work done by notions of mimesis in explaining relations between the world, our being in it, and texts, proposing that mimesis provides a principle buttress by which the good standing of the metaphor of ‘person’ is preserved in traditional and pre-critical modes of analysis. Indeed, the critic’s recourse to ‘person’ is in some measure always an engagement with mimesis. Any discussion that maintains that mimesis is in some way productive of meaning-which this thesis in fact does-must identify mimesis as a merely conventional category within practices of reading and semiosis more generally, and at the very least remove that term from its traditional position of transparent primacy and authority. Some of the most interesting and insightful arguments about ‘second-person’ narrative propose that the ‘second person’s’ most striking effects derive from the constitution of an ‘intersubjective’ experience of reading in which the subject positions of the ‘you’-protagonist, reader-narratee and narrator are combined into a fluid and indeterminate multiple subjectivity. Notions of intersubjectivity frequently position themselves as liberating the reader from Cartesianism's fixed, authoritative modes of subjectivity, Frequently, however, they tend implicitly to reinstate Cartesianism's notion of the self at the centre of textual practice and subjectivity. I look at Daniel Gunn's novel ‘Almost You’, at length in this context, illustrating the constant overdetermination of the ‘you’ and the novel's narrating voice, and demonstrating that this overdetermination leaves the origin of the narrative discourse, the identity of the narrator, and the ontological nature of both principal protagonists utterly ambiguous. The fluidity and ambiguity of Protean-‘you’ in ‘Almost You’ is discussed in terms of ‘second-person’ intersubjectivity, but with a view to demonstrating the indebtedness by the notion of intersubjectivity to Cartesianism's hegemony of ‘person’. I then turn to a discussion of what might be a more ‘old fashioned’ if perhaps ultimately more far-reaching approach to the ‘second person’s’ often startling ambiguities. This is Keats's notion of negative capability, a capacity or quality in which a person ‘is capable of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact and reason.’ I suggest that Protean-‘you’ texts will license all of the readings of ambiguity and fluidity proposed in my discussion of ‘Almost You’, but conclude that the instances of indeterminacy illustrate no more than that: the fluidity and deep ambiguity, and thus, finally, the lack of coherence, of Protean-‘you’ discourse. This has particular implications for how we are to consider readers’ experiences of narrative texts. More fundamentally, it has implications for how we are to consider readers as subjects. I suggest that unstable, ambiguous instances of ‘second-person’ narrative can tear the complex and systematic embroidery of ideological suture that unifies Cretinism’s experience or sense of subjectivity, leaving the reader in a condition of epistemological and ontological havoc. I go on to argue that much of the deeply unsettling effect of Protean-‘you’ discourse anises because its utterances explicitly gesture towards Cretinism’s notion of self. Protean-‘you’ involves a sense of address that is much more pronounced than we are accustomed to facing when reading literary narrative, alerting us to the presence of inscribed anthropomorphic subjects. At the very same time, protean-‘you’ leaves its inscribed subjects indeterminate, ambiguous. This conflict generates a tension between the anticipation of the emergence of speaking and listening selves and our inability to find them. I go on to propose that Protean-‘you’ narrative's lack of coherence is also to be understood as the condition of narrative actuality generally, but a condition that is vigorously mediated against by dominant practices of reading and writing, hocusing my discussion in this respect on the issue of narrative ‘person,’ I argue that narrative ‘person’ is constituted within texts as an apparent unity, but that it is in fact, produced as unitary solely within the practice of making sense, that is, Within our habits of reading, and so is never finally unified. I propose that this is the case for ‘first-‘ and ‘third-person’ modes no less than for the ‘second.’ Where ‘second-person’ narrative at its most radical and Protean differs from conventional ‘first-‘ and ‘third-person’ narratives is the degree to which each has been circumscribed by practices of tantalization, containment and limit, and, in particular, Cretinism’s hegemony of ‘person.’ It may be that the most significant insights ‘second-person’ narrative has to offer are to be found within its capacity to reveal to the engaged reader the underlying condition of narrative discourse, and more generally, its capacity to reveal the actual condition of the human subject-a condition in which, exactly like its textual corollary of narrative ‘person,’ the self is glimpsed as thoroughly dispersed and contingent.

Understanding and developing structure - its importance for mathematics learning

This issue comes at a time when mathematics education research is becoming more intently focused on the development of "structure" as salient to generalised mathematics learning. Not surprisingly the attention on structure creates particular synergies with the increasingly rich field of research on algebraic thinking and arithmetic processes, particularly in the early years. In many ways, this special issue is concerned with describing the process of "structuring" that enables abstraction and generalisation. A recent MERJ special issue, Abstraction in Mathematics Education (Mitchelmore & White, 2007), illustrated theories of abstraction aligning these to notions of underlying structure. The importance of structure in the transition from school to university was also highlighted by Godfrey and Thomas (2008), and Novotna and Hoch (2008) in the previous special issue of MERJ (Thomas, 2008). In this special issue we present six papers that provide evidence of developing structure as critical for all learners of mathematics throughout schooling.