Designing an intelligent teaching simulator for learning to teach by practicing

Learning to teach is difficult for prospective teachers because of the complex nature of the work of teaching. Practicing (Lampert in J Teach Educ 61(1–2):21–34, 2010), interacting with the practice of teaching from a first-person perspective, may give them a unique experience in learning to teach. Computer-based simulators in which the apprentice teacher can interact with virtual students may be used to create that kind of experience. In this paper, we show how to apply techniques in artificial intelligence to design an intelligent learning environment. We show how to model the apprentice’s decision making and resources that can help him or her improve the practice of teaching.     

On the evolution of an intelligent maintenance optimization system

In this paper the author reviews the development of an intelligent maintenance optimization system over the past 16 years. The paper starts with discussion of the initial motivation behind developing the system and the designs of the early versions of a computer program to access maintenance history data and provide an analysis. The concept behind this system was gradually developed to incorporate a rule base for the selection of a suitable model for preventive maintenance (PM) scheduling and then to a fully developed knowledge-based system for decision support. The need to incorporate case-based reasoning thus creating a hybrid system that can learn with use in addition to using elicited knowledge from experts is discussed. The experience with system validation with two versions of the system is analysed. The paper also reviews the extensive fundamental work on developing appropriate PM models that can deal with real data patterns. Finally, the scope for future development is presented.     

MARKEX: An intelligent decision support system for product development decisions

A new methodology for the development of new products and an intelligent DSS, named MARKEX, which is an implementation of this methodology, are presented in this paper. The system acts as a consultant for marketers, providing visual support to enhance understanding and to overcome lack of expertise. The databases of the system are the results of consumer surveys, as well as financial information of the enterprises involved in the decision making process. The system's model base encompasses statistical analysis, preference analysis, and consumer choice models. MARKEX incorporates partial knowledge bases to support decision makers in different stages of the product development process.     

Prototyping an intelligent decision support system for improving urban infrastructures management

This paper describes an intelligent decision support system (IDSS) dedicated to coordinated management of urban infrastructures (SIGIU). This system identifies the data and related treatments common to several municipal activities and defines the requirements and functionalities of the computer tools developed to improve the delivery, performance and coordination of municipal services to the population. The resulting cooperative system called SIGIU is composed of a global planning and coordination system (SYGEC) and a set of integrated operating systems (SYDEX), each of them being associated with a specific urban system (sewerage, waterworks, etc.). In order to support the decision-making process, an IDSS was developed as a knowledge-based system provided with inference mechanisms that enables SYGEC and SYDEX to make strategic choices in terms of technical interventions on municipal infrastructures. The knowledge-based system stores experts' knowledge as well as solutions to past problems. Preliminary implementation results show that SIGIU effectively and efficiently supports the decision-making process related to managing urban infrastructures.     

Modeling the learning process in an automated instruction system

Organization and operation of an automated instruction system (AIS) are discussed. For evaluation and retention of learning material, mathematical modeling methods are employed. A regression model is constructed of the process of learning of a fragment of a course in computers and programming.Translated from Dinamicheskie Sistemy, No. 4, pp. 116–120, 1985.     

Uniqueness in an integral geometry problem and an inverse problem for the kinetic equation

In this paper, we discuss the uniqueness in an integral geometry problem along the straight lines in a strongly convex domain. Our problem is related with the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation and then the uniqueness theorem is proved using the tools of Fourier analysis.     

A changing trajectory of proof learning in the geometry inquiry classroom

The purpose of this study is to explore how students changes through learning to construct mathematical proofs in an inquiry-based middle school geometry class in Korea. Although proof has long been considered as one of the most important aspects of mathematics education, it is well-known that it is one of the most difficult areas of school mathematics for students. The geometry inquiry classroom (GIC) is an experimental class designed to teach geometry, especially focusing on teaching proof, based on students’ own inquiry. Based on a 2-year participant observation in the GIC, this study was conducted to address the following research question: how has students’ practice of mathematical proof been changed through their participation in the GIC? The in-depth analysis of the classroom discourse identified three stages through which the students’ practice of mathematical proof was transformed in the GIC: ‘emergent understanding of proof’, ‘proof learning as a goal-oriented activity’, ‘experiencing proof as the practice of mathematics’. The study found that as learning evolved through these stages, so the mathematics teacher’s role shifted from being an instructor to a mediator of communication. Most importantly, this research showed that the GIC has created a learning environment where students develop their competence in constructing meaningful mathematical proof and grow to be ‘a human who proves’, ultimately ‘a person who playfully engages with mathematics’.     

The development of a hybrid intelligent maintenance optimisation system (HIMOS)

This paper reports on the development of a hybrid intelligent maintenance optimisation system (HIMOS) for decision support. It is a follow-up to an earlier paper published in the Journal of the Operational Research Society in 1995. Both papers refer to systems where there are very many components which may break down independently. When a component breaks down, corrective action (CO) is required. The problem is to determine the optimal maintenance policy, essentially the frequency of preventive maintenance (PM) which minimises the sum of down time due to PM and CO.HIMOS, like its predecessor IMOS, uses an ‘intelligent’ decision support system to carry out an automated analysis of the maintenance history data. Maintenance data are presented to the system and the most suitable mathematical model from a model-base is identified utilising a hybrid knowledge/case based system (KBS/CBR). Thus initially a rule base is applied to select a model, as in the case of IMOS. If no model is matched, the system reverts to its historical case-base to match the current case with a similar case that has been previously modelled. This double reasoning adds to the system's true learning capabilities (intelligence) and increases the rate of success of model selection. A prototype system is written in Visual Basic® for an IBM compatible PC. The study results include optimal PM intervals for a sample of industrial data sets. The results of the validation exercise of HIMOS against expert advice has shown that the system functions satisfactorily.     

Modelling and system identification of an experimental apparatus for anomaly detection in mechanical systems

This paper presents design, modelling and system identification of a laboratory test apparatus that has been constructed to experimentally validate the concepts of anomaly detection in complex mechanical systems. The test apparatus is designed to be complex in itself due to partially correlated interactions amongst its individual components and functional modules. The experiments are conducted on the test apparatus to represent operations of mechanical systems where both dynamic performance and structural durability are critical.     

On the geometry of the Calogero-Moser system

We discuss a special eigenstate of the quantized periodic Calogero—Moser system associated to a root system. This state has the property that its eigenfunctions, when regarded as multivalued functions on the space of regular conjugacy classes in the corresponding semisimple complex Lie group, transform under monodromy according to the complex reflection representation of the affine Hecke algebra. We show that this endows the space of conjugacy classes in question with a projective structure. For a certain parameter range this projective structure underlies a complex hyperbolic structure. If in addition a Schwarz type of integrality condition is satisfied, then it even has the structure of a ball quotient minus a Heegner divisor. For example, the case of the root system E₈ with the triflection monodromy representation describes a special eigenstate for the system of 12 unordered points on the projective line under a particular constraint.     

Measuring striving for understanding and learning value of geometry: a validity study

The current study aimed to construct a questionnaire that measures students’ personality traits related to striving for understanding and learning value of geometry and then examine its psychometric properties. Through the use of multiple methods on two independent samples of 402 and 521 middle school students, two studies were performed to address this issue to provide support for its validity. In Study 1, exploratory factor analysis indicated the two-factor model. In Study 2, confirmatory factor analysis indicated the better fit of two-factor model compared to one or three-factor model. Convergent and discriminant validity evidence provided insight into the distinctiveness of the two factors. Subgroup validity evidence revealed gender differences for striving for understanding geometry trait favouring girls and grade level differences for learning value of geometry trait favouring the sixth- and seventh-grade students. Predictive validity evidence demonstrated that the striving for understanding geometry trait but not learning value of geometry trait was significantly correlated with prior mathematics achievement. In both studies, each factor and the entire questionnaire showed satisfactory reliability. In conclusion, the questionnaire was psychometrically sound.     

Numerical and experimental study of the flow in an eccentric Couette-Taylor system with small gap

Various papers were dedicated to the technical and industrial aspects of the Taylor–Couette flow, by analyzing the flow structure in dependence of characteristic parameters. Also some studies concerning the influence of an eccentrical position of the rotating inner cylinder relatively to the fixed outer cylinder exist in the case of a large gap width. The principal technical application of such studies is the flow in journal bearings where the gap width is very small, of the order 0.1\% relative to the inner cylinder radius. Analytical and numerical investigations of the flow in journal bearings are generally based on the two–dimensional Reynolds approximation. This investigation in aiming at a validation of the range where the Reynolds equation is applicable in relation to the characteristical parameters: gap width, eccentricity and Reynolds number. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry

We show that there is a close relation between standing-wave solutions for the FitzHugh-Nagumo system where 0<a<1/2 and δ γ=β ² ∈ (0,a), and the following combinatorial problem: (*) Given K points Q ₁ , . . . , Q _K ∈R ^N with minimum distance 1, find out the maximum number of times that the minimum distance 1 can occur. More precisely, we show that for any given positive integer K, there is a δ _K >0 such that for 0<δ<δ _K , there exists a standing-wave solution (u _δ ,ν _δ ) to the FitzHugh-Nagumo system with the property that u _δ has K spikes Q ^δ ₁,. . .,Q ^δ _K and approaches an optimal configuration in (*), where .     

Generalizations of the centroid with an application in stochastic geometry

The centroid of a subset of with positive volume is a well‐known characteristic. An interesting task is to generalize its definition to at least some sets of zero volume. In the presented paper we propose two possible ways how to do that. The first is based on the Hausdorff measure of an appropriate dimension. The second is given by the limit of centroids of ε‐neighbourhoods of the particular set when ε goes to 0. For both generalizations we discuss their existence and basic properties. Then we focus on sufficient conditions of existence of the second generalization and on conditions when both generalizations coincide. It turns out that they can be formulated with the help of the Minkowski content, rectifiability, and self‐similarity. Since the centroid is often used in stochastic geometry as a centre function for certain particle processes, we present properties that are needed for both generalizations to be valid centre functions. Finally, we also show their continuity on compact convex m‐sets with respect to the Hausdorff metric topology.     

Designing and using professional development resources for inquiry-based learning

This paper describes an attempt to design, analyse and refine professional development (PD) resources that encourage the implementation of inquiry-based learning (IBL). We describe the iterative development of the resources in England with over 100 mathematics teachers from secondary, tertiary and adult education and then analyse the impact these resources had on teachers’ beliefs and practices and the issues arising. This evaluation revealed that teachers had moved away from transmission-based orientations, encouraged by the use of less structured tasks and sample lesson plans, but some found it difficult to adopt IBL pedagogies. The most significant issues for teachers may be summarised as: confusing IBL with ‘discovery’ learning; developing and managing collaborative cultures within the classroom; and planning lessons that adapt to the emerging needs of learners.     

Continuous dependence of heat flux on spatial geometry for the generalized Maxwell-Cattaneo system

In the Generalized Maxwell-Cattaneo equations the temperature and heat flux are separate variables that are related through a system of partial differential equations. In a previous paper [5] the authors established continuous dependence of the temperature on spatial geometry. In this paper inequalities are derived which imply continuous dependence of the heat flux on spatial geometry. The arguments employed here are quite different and more complicated than those of the previous paper.     

Principles of development of an interactive computing system for analyzing the stability and inflatibility of a parachute

This article describes the structure of a software package developed to study the stationary modes of motion of parachute systems and analyze their stability. A brief discussion of optimality criteria for such packages is given. A classification of the instabilities in the mechanics of a parachute is presented.Translated fromDinamicheskie Sistemy, No. 6, pp. 3–10, 1987.     

The indicator of contact boundaries for an integral geometry problem

We pose and study a rather particular integral geometry problem. In the two-dimensional space we consider all possible straight lines that cross some domain. The known data consist of the integrals over every line of this kind of an unknown piecewise smooth function that depends on both points of the domain and the variables characterizing the lines. The object we seek is the discontinuity curve of the integrand. This problem arose in the author’s previous research in X-ray tomography. In essence, it is a generalization of one mathematical aspect of flaw detection theory, but seems of interest in its own right. The main result of this article is the construction of a special function that can be unbounded only near the required curve. Precisely for this reason we call the function the indicator of contact boundaries. A uniqueness theorem for the solution follows rather easily from the property of indicators.