A global survey of international perspectives on modelling in mathematics education

In this article we survey the current debate on modelling and, describe different perspectives on this debate. We relate these perspectives with earlier perspectives and show similarities and differences between these different approaches.     

Assumptions and methodologies in OR

This paper argues that the subject of methodology is importnat for OR practitioners and academics. It isolates four common assumptions about OR from the normal literature of OR, and shows how they lead to identifiable methodological positions. It is argued that the future of OR depends, in part at least, on methodological debate. If it is to be successful, this debate requires some understanding of the assumptions of other people.     

THE POSSIBILITY OF CONTINUOUS GROWTH WITH EXHAUSTIBLE RESOURCES: UNKNOWINGLY AN AGREEMENT HAS BEEN REACHED,BUT IT MAY NOT BE CORRECT

ABSTRACT. It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that, unnoticed by pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarizes some preliminary work by the author that indicates that this common position may not be correct.     

Rejoinder on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

This note replies to comments made on our contribution to the Low Quality Data debate.     

Flip or flop? Students’ perspectives of a flipped lecture in mathematics

This paper describes students’ perspectives of a one-off flipped lecture in a large undergraduate mathematics service course. The focus was on calculating matrix determinants and was designed specifically to introduce debate and argumentation into a mathematics lecture. The intention was to promote a deeper learning and understanding through engagement with the added hope of instilling some passion for the subject. During the lecture, students were asked to vote with their feet, literally moving around the lecture theatre to form groups according to their shared favourite technique for calculating matrix determinants. Group discussions were then followed by a whole class debate facilitated by the lecturers, before they wrapped up the lecture by resolving the professional disagreements that had come to light during the debate. Following the lecture, data on student perspectives was gathered using both surveys and focus groups. Within this paper, we share the data and reveal the interesting results that emerged from our analysis. Despite remaining unconvinced as to whether flipped lectures are better for learning, students reported greater engagement and increased understanding of the material covered.     

Sociology and Social Theory in Agent Based Social Simulation: A Symposium

A lengthy and intensive debate about the role of sociology in agent based social simulation dominated the email list simsoc@jiscmail.ac.uk during the autumn of 2000. The debate turned on the importance of models being devised to capture the properties of whole social systems and whether those properties should determine agent behaviour or, conversely, whether the properties of social systems should emerge from the behaviour and interaction of the agents and, if so, how that emergence should be represented. The positions of four of the main protagonists concerned specifically with the modelling issues are reprised and extended in this symposium.     

A Kuhnian Crisis in Management Science?

A survey of the Journal of the O.R. Society in 1978 shows that Ackoff's papers were part of a quite widespread and often pessimistic debate about the practical success of O.R. A similar survey for 1968 shows, on the other hand, a widespread mood of optimism. It is suggested that O.R. is now in a period of crisis analogous to that described by Kuhn in the Natural Sciences, when the dominant framework of assumptions appears to fail in relation to important problems. When such failures persist, alternative frameworks are proposed challenging the hitherto accepted view, and an increasingly wide-ranging debate develops. Many of the features of such debates, as outlined by Kuhn, seem to be present in the current controversy within O.R. More specifically, it seems possible in O.R. and related fields to identify three rival sets of proposals, which may be labelled official, reformist (e.g. Ackoffian) and revolutionary. However, the debate in O.R. differs from that in the Natural Sciences because it is not just about the best means of understanding the empirical world. It is also about the type of social world to be constructed through the framework of assumptions adopted. Our view is that in the current debate, proponents of the reformist stance will probably win. However, this may be very much an interim solution.     

Towards theoretical foundations of mathematics education

Although research in mathematics education developed in the last decades as a vivid scientific field, the nature and the place of theories in the field are still under discussion. H.-G. Steiner contributed to this debate in several ways. He not only intervened in the scientific debate but also played an active role in organizing the discipline and the scientific discussion at the international level. This paper attempts to give a synthetic view of the evolution of mathematics education with respect to theory by focusing on the French situation of research in mathematics education and paying a particular attention to the role and contribution of H.-G. Steiner.     

Useful Monte Carlo optimization

This contribution to the debate on Monte Carlo optimization methods shows that there exist techniques that may be useful in many technical applications.     

Transitivity revisited

A survey is given of research on transitivity.The debate about the assumption of transitivity turns upon the interpretation of certain real world experiences     

From Standardized Tests To: Alternative Methods: Some Current Resources on Methods to Assess Learning in Gerneral Education

In late 1968 Change Magazine asked four men to debate the impact and meaning of campus violence and confrontation politics. The participants were Michael Rossman, who helped lead the Free Speech Movement on the Berkeley campus in 1964; Morris Abram, the new president of Brandeis University, who soon thereafter faced a major student crisis on his own campus; Seymour M. Lipset, the Harvard sociologist and a respected scholar of student movements; and Michael Vozick, a founder of San Francisco State's Experimental College who is now associated with the National Student Association. Their debate reflects many of the dilemmas, tragedies and semantic fissures that are now increasingly common to the American campus.     

Experimental evidence on robustness of data envelopment analysis

There is an on-going debate about variable selection in data envelopment analysis (DEA) as there are no diagnostic checks for model misspecification. This paper contributes to this debate by investigating the sensitivity of DEA efficiency estimates to including inappropriate and/or omitting several important variables in a large-sample DEA model. Data are simulated from constant, increasing and decreasing returns-to-scale (RS) Cobb–Douglas production processes. For constant and decreasing RS processes with irrelevant inputs, DEA tends to overestimate efficiency in almost all production units. When relevant variables are omitted, variable RS appears to be a safer option. The correct RS specification is vital when the DEA model includes irrelevant variables. The effect of omission of relevant inputs on individual production unit efficiency is more adverse compared to the inclusion of irrelevant ones.     

A Consultant's Reflections on Client Management

To further the debate on the practice of operational research, an external consultant's viewpoints are considered about client management before, in the midst and towards the conclusion of an assignment. Relationships and communications are particularly emphasised.     

Internalism empowered: how to bolster a theory of justification with a direct realist theory of awareness

The debate in the philosophy of perception between direct realists and representationalists should influence the debate in epistemology between internalists and externalists about justification. If direct realists are correct, there are more consciously accessible justifiers for internalists to exploit than externalists think. Internalists can retain their distinctive internalist identity while accepting this widened conception of internalistic justification: even if they welcome the possibility of cognitive access to external facts, their position is still quite distinct from the typical externalist position. To demonstrate this, Alvin Goldman??s critique of internalism is shown to ignore important lessons from the case for direct realism about perception. In particular, it unjustifiably assumes that internalism entails that only facts simultaneous with the justification of a belief can justify the belief. Goldman??s definition of a ??justifier?? is also inconsistent with the overall guidance conception of epistemology he takes for granted in his critique of internalism.     

O.R. and the Systems Movement: Mappings and Conflicts

The ‘crisis’ debate in O.R. expresses concern at the divergence between textbook O.R. and what practitioners actually do. The debate is examined by comparing O.R., systems analysis and systems engineering. They are all wedded to logic in situations in which logic may not be paramount. The science in O.R. applies only to aggregate results, but the practitioner must deal with a specific situation. The tradition of systems thinking which emerged from organismic biology is described. It leads to a way out of the O.R. ‘crisis’, by providing a formal structuring of a paradigm of learning rather than optimization. O.R. can aspire to match natural science, and pass the problems by; or it can close the textbook/practitioner gap by changing its concept of ‘being scientific’.     

Policies for biodefense revisited: The prioritized vaccination process for smallpox

Handling bioterror events that involve contagious agents is a major concern for authorities and a cause for debate among policymakers about the best response policy. At the core of this debate stands the question which of the two post-event policies to adopt: mass vaccination or trace (also called ring or targeted) vaccination. We present a new dynamic epidemic-intervention model that captures key features of the situation and generalizes some previous assumptions regarding the probability distributions of inter-temporal parameters. It is shown that a mixture of mass and trace vaccination policies—the prioritized vaccination policy—is more effective than either of the two aforementioned policies.     

A Critical Comment on Integer Goal Programming

This note is a contribution to the on-going debate about the merits and demerits of goal programming. We concentrate on the special case of integer goal programming. Examples show that the approach is questionable, especially if used in connection with a standard branch-and-bound-based solution technique.     

Shadow pricing of undesirable outputs in nonparametric analysis

For three decades a growing interest in the modeling of desirable and undesirable outputs has led to a theoretical and methodological debate in the nonparametric literature on production technology and efficiency. The first main discussion is about the way of modeling ‘bad/undesirables’ as inputs or outputs, or by transformation functions. The second debate concerns the implications of the weak disposability assumption in the modeling of bad outputs, in particular the possibility of assigning unexpected signs to shadow prices of bad outputs. In addition, we point out a current error in the modeling of weak disposability under a variable returns to scale technology. In this paper we introduce a hybrid model to ensure the economically meaningful jointness of good and bad outputs while constraining shadow prices of bad outputs to their expected sign. We argue that it is a sound compromise to model undesirable outputs with a meaningful primal/dual economic interpretation. Finally we propose an extension to define shadow prices for undesirable outputs following the Law of One Price (LoOP) rule.     

Experience and Time

In this discussion, I claim that the debate over ‘the bias towards the present’ turns on an axiological question. Is the value of a present experience greater than its value when past? I argue not and hold that our bias towards the present, understood as a pure time preference, is irrational.     

Hospital Waiting List Management Models

This paper describes work carried out with hospital consultants in Lancaster District Health Authority to develop and use computerized waiting list management models. The ‘what if?’ models produced have been found to be a very useful tool in the constructive debate about problems faced by consultants and managers, and of the options available to them.