Can Indirect Causation be Real?

Causal realists maintain that the causal relation consists in “something more” than its relata. Specifying this relation in nonreductive terms is however notoriously difficult. Michael Tooley has advanced a plausible account avoiding some of the relation’s most obvious difficulties, particularly where these concern the notion of a cross-temporal “connection.” His account distinguishes discrete from nondiscrete causation, where the latter is suitable to the continuity of cross-temporal causation. I argue, however, that such accounts face conceptual difficulties dating from Zeno’s time. A Bergsonian resolution of these difficulties appears to entail that, for the causal realist, there can be no indirect causal relations of the sort envisioned by Tooley. A consequence of this discussion is that the causal realist must conceive all causal relations as ultimately direct.     

Inductive and Deductive Justification of Knowledge: Flexible Judgments Underneath Stable Beliefs in Teacher Education

Personal epistemological beliefs are considered to play an important role for processes of learning and teaching. However, research on personal epistemology is confronted with theoretical issues as there is conflicting evidence regarding the structure, stability, and context-dependence of epistemological beliefs. We give evidence how theoretical and methodological issues can partly be resolved by distinguishing between relatively stable “epistemological beliefs” and situation-specific “epistemological judgments.” A qualitative content analysis of a series of semistructured interviews (study 1) with pre-service teachers, teachers, and teacher educators as well as a statistical analysis of pre-service teachers’ extensive answers in questionnaires (study 2), both on the topic of “mathematical discovery,” reveal not only beliefs of the participants but also different qualities of judgments. Therefore, in further research both aspects of beliefs should be considered in a more differentiated manner when categorizing belief structures.     

Benefits analysis—a robust assessment approach

Benefits Analysis has been evolving over the past decade from roots in multi-criteria analysis, causal mapping and multi-methodology. It has now reached a level of maturity such that it deserves to be treated as a method in its own right, and this paper seeks to document the method and provide guidance on its use. Benefits Analysis is a systematic method for formulating complex, multi-factor investment appraisal problems where decision-makers seek to realize non-financial benefits. Such decision problems abound in military OR, particularly the management of equipment capability and research. Benefits Analysis connects qualitative and quantitative OR methods and facilitates robust assessment, including multi-methodology. This paper describes the principles of Benefits Analysis and discusses its application to a variety of real problems, including research management, capability management, balance of investment, business case development and benefit quantification strategies.     

Constrained derivative-free optimization on thin domains

Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.     

Understanding kindergarten teachers’ perspectives of teaching basic geometric shapes: a phenomenographic research

Geometry is one of the disciplines children involve within early years of their lives. However, there is not much information about geometry education in Turkish kindergarten classes. The current study aims to examine teachers’ perspectives on teaching geometry in kindergarten classes. The researchers inquired about teachers’ in-class experiences in geometry and asked a series of questions such as “what are the benchmarks in your kindergarten class?”; “what kind of tools and materials you use to teach geometry in your class?”; “what shape do you teach first in your kindergarten class?”; “what do you expect to hear when you asked your students ‘what is square’?”; “how do you teach rectangular?”. The study utilized one of the qualitative research methods, namely phenomenography, to collect the data and analyze the data. The study involved with eight kindergarten teachers who work in different schools in central Kutahya, Turkey. The researchers collected data by conducting face-to-face half-structured interviews. The findings of this phenomenographic research showed that kindergarten teachers have some difficulties in teaching geometry and have lack of knowledge and skills in teaching geometry in kindergarten classes.     

组合优化算法中摆脱局部极小值的几种策略

局部搜索算法是一种非常有效的求解组合优化问题的算法 ,它具有通用、灵活等特点 .但是 ,由于搜索空间和目标函数的复杂性 ,目标函数在搜索空间中有许多局部极小值点 ,使算法在这些局部极小值点处被“卡住”,大大影响算法的效果 .对于此问题 ,笔者查阅了大量文献资料 ,结合自己的研究实践 ,总结出几种跳出局部极小“陷井”的策略 .使用这些策略 ,有望使算法更加完善 ,在求解组合优化问题过程中更能发挥其作用 .     

Reconstructing basic ideas in geometry—an empirical approach

“Basic ideas” (or “fundamental ideas” etc.) have been discussed in mathematical curriculum theory for about forty years. This paper will centre on the hypothesis that this concept can only be applied successfully by using it as a category for the analysis of concrete mathematical problems. This hypothesis will be illustrated by means of a sample problem from the Austrian Standards for Mathematics Education (“Bildungsstandards”). In this example, basic ideas are used in a content matter analysis which takes students' solutions to the problem as a starting point for the creation of a potentially substantial learning environment in trigonometry.     

A critical comment on Braun's “restricted access in exchange systems"*

In general this comment tackles the problems and difficulties potentially combined with an application of formal economic models and constructs, such as the Walras equilibrium and microeconmic demand theory, to pure sociological contexts. In particular, this is done by analyzing a further attempt, as recently suggested by Braun (1993 and 1994), to extend the well‐known Coleman Model by incorporating the embeddedness of social transactions in incomplete social network structures. “Pars pro toto” it is proved that Braun's conceptualization contains some weaknesses which imply that fundamental conclusions drawn in his article have to be revised.     

Computerunterstützung offener Aufgabenstellungen im Geometrieunterricht

The conventional and traditional way of mathematics teaching for the most part relies on practising and performance of algorithms and solutions of certain kinds of problems. The exclusive objective of the required activities for solving the convergent problems that are generally used in this connection is to achieve methodological competence. This approach reduces mathematics teaching to the purpose of achieving calculational competence and ignores an essential inherent component, namely the chance to stimulate the creativity and create incentives to generate something completely new. Lack of appropriate tools may be one reason explaining the fact that this creative aspect has been left almost unconsidered in teaching practice so far, because solving “open problems” requires specific tools and means. The following article is intended to demonstrate, with a concrete example from geometry teaching at lower secondary level, the opportunities opened up by the computer when used as a tool for introducing in class the typical problems and mathematical problem solving strategies required for mathematics beyond methods and calculational competence.     

Prospective teachers anticipate challenges fostering the mathematical practice of making sense

Problem solving has long been a priority in mathematics education, and the first Common Core mathematical practice (SMP1) focuses on this priority through the language of “Make sense of problems and persevere in solving them.” We present findings from a survey about how prospective elementary teachers' (PTs) make sense of potential difficulties with fostering SMP1. Findings suggested that PTs' common anticipated difficulties relate to planning a solution pathway and self monitoring whether the solution makes sense. Moreover, a third of PTs disclosed that their anticipated difficulties are linked to their own personal struggles with aspects of SMP1. An alternative interpretation of SMP1 surfaced in which a small number of PTs described SMP1 as necessitating that a teacher teach multiple solution methods to students, instead of engaging students in productive struggle to develop their own strategies. We present a framework illustrating the connections between SMP 1 and Pólya's problem solving phases, and we discuss how these findings connect to and build on previous research of PTs' experiences with problem solving. We offer implications for the targeted support needed in teacher preparation programs to address these struggles, to prevent them from being replicated in their students.     

A model of concept formation

At first we model the way an intelligence “I” constructs statements from phrases, and then how “I” interlocks these statements to form a string of statements to attain a concept. These strings of statements are called progressions. That is, starting with an initial stimulating relation between two phrases, we study how “I” forms the first statement of the progression and continues from this first statement to form the remaining statements in these progressions to construct a concept. We assume that “I” retains the progressions that it has constructed. Then we show how these retained progressions provide “I” with a platform to incrementally constructs more and more sophisticated conceptual structures. The reason for the construction of these conceptual structures is to achieve additional concepts. Choice plays a very important role in the progression and concept formation. We show that as “I” forms new concepts, it enriches its conceptual structure and makes further concepts attainable. This incremental attainment of concepts is a way in which we humans learn, and this paper studies the attainability of concepts from previously attained concepts. We also study the ability of “I” to apply its progressions and also the ability of “I” to electively manipulate its conceptual structure to achieve new concepts. Application and elective manipulation requires of “I” ingenuity and insight. We also show that as “I” attains new concepts, the conceptual structures change and circumstances arise where unanticipated conceptual discoveries are attainable. As the conceptual structure of “I” is developed, the logical and structural relationships between concepts embedded in this structure also develop. These relationships help “I” understand concepts in the context of other concepts and help “I₁” communicate to another “I₂” information and concept structures. The conceptual structures formed by “I” give rise to a directed web of statement paths which is called a convolution web. The convolution web provides “I” with the paths along which it can reason and obtain new concepts and alternative ways to attain a given concept.This paper is an extension of the ideas introduced in [1]. It is written to be self-contained and the required background is supplied as needed.     

Network companies and competitiveness: A framework for analysis

Business networking for the purpose of becoming globally more competitive seems to form the very basis of strategic decisions in many companies today. The concept of “network company” has recently been the subject of many studies in the literature, perhaps mostly due to its world wide practice among more successful companies. Yet, there is no model-based formal treatment of the concept per se leading to the development of frameworks that are instrumental in formulating networking strategies. This paper addresses itself to formalizing the concept of “network company” within the context of global competition. For this purpose, “network company” is positioned in the value chain of pertinent product–market chain systems and then its functioning is decomposed into a set of minimal and basic components, which are termed “elementary resources, methods, products, and activities”. The set thus defined at that detail level is used to analyze and evaluate “network companies” at any desired condensed level reflecting the needs of a project or a function for the purpose of competitive strategy formulation. The formal analytical framework developed is then discussed in association with three basic approaches to competitive strategy formulation: resource-based strategy, activity-based strategy, and strategy based on the economic theory of the firm. The usefulness of the proposed framework in connection with these approaches is expressed in terms of formal propositions.     

The multipliers‐free domain decomposition methods

This article concludes the development and summarizes a new approach to dual‐primal domain decomposition methods (DDM), generally referred to as “the multipliers‐free dual‐primal method.” Contrary to standard approaches, these new dual‐primal methods are formulated without recourse to Lagrange‐multipliers. In this manner, simple and unified matrix‐expressions, which include the most important dual‐primal methods that exist at present are obtained, which can be effectively applied to floating subdomains, as well. The derivation of such general matrix‐formulas is independent of the partial differential equations that originate them and of the number of dimensions of the problem. This yields robust and easy‐to‐construct computer codes. In particular, 2D codes can be easily transformed into 3D codes. The systematic use of the average and jump matrices, which are introduced in this approach as generalizations of the “average” and “jump” of a function, can be effectively applied not only at internal‐boundary‐nodes but also at edges and corners. Their use yields significant advantages because of their superior algebraic and computational properties. Furthermore, it is shown that some well‐known difficulties that occur when primal nodes are introduced are efficiently handled by the multipliers‐free dual‐primal method. The concept of the Steklov–Poincaré operator for matrices is revised by our theory and a new version of it, which has clear advantages over standard definitions, is given. Extensive numerical experiments that confirm the efficiency of the multipliers‐free dual‐primal methods are also reported here. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

The effect of human agent in project management

The article deals with the effect of a human agent on the activity realization in a project. It does so from the perspective of the Theory of Constraints where the weakest point is the deadline of partial activity. Every existing activity in any project is, to a higher or lower extent, determined by the effect of the human agent. The inefficiency of a number of projects in practice is largely caused by an unsuccessful realization of partial activities. The effect of the human agent is in this respect fundamental. The human agent, as an allocated resource in the activity, is liable to a number of non-specified impacts and stimuli, and as such s/he is rather versatile in his/her behaviour. The versatility of the human agent in projects can be described by the “Student Syndrome” phenomenon and by the first “Parkinson’s law”. Both these qualitative phenomena create a starting point for the introduced theoretical and quantitative research. The findings in this article are based on the set of real data of work effort of the students of daily study programme on one university in the Czech Republic. The article presents, as the authors’ own theoretical contribution, a mathematical model for the “Student Syndrome” phenomenon with a practical use in quantitative methods of project management. This model was derived analytically from a performed data analysis and we can assume that it will be useful for further theoretical development of quantitative methods in project management. In the article we deduce the theoretical differentiation of the “Student Syndrome” phenomenon in work effort into three terminable phases during three different types of resource work allocation. We can regard this original viewpoint as suggestive for the area of human resources management in projects. Its contribution lies in delimitation of time-targeted resource stimulation, which may lead to lower project costs, besides higher work efficiency and compliance with time-targeted deadlines of activity termination. The article brings the quantification of qualitative features of the human agent in project management.     

Criteria for Capital Investment: An Approach Through Decision Theory

The arbitrary character of such concepts as “Discounted Present Worth”, which are often advocated as methods of assessing and comparing investment opportunities, is discussed in Part 1 of this paper. It is also pointed out that, by their nature, these concepts are not particularly well adapted to situations in which “risk” is an important factor. In order to develop a method in which a logical approach to risk can be adopted, an understanding of the basic problem of Decision Making under Uncertainty is required. An introduction to this subject forms Part 2 of this paper. In Part 3 the problem of Plant Investment under Risk is considered, and a rational approach to this is developed. The importance of the “portfolio” concept in such problems is particularly demonstrated.     

Hereditary stress as a cultural force in mathematics

Among the forces affecting the course of mathematical evolution is what the author has called “hereditary stress.” The term designates a cultural, not a psychological force, and it is internal to mathematics, not environmental. It appears to be synonymous with what A. L. Kroeber called “potentialities” and G. Sarton termed “growth pressure.” Neither of these scholars gave any analysis of it. The present article attempts to do this in the restricted context of mathematics.Its chief components seem to be: (A) Capacity. The quantity and intrinsic interest of the results that the basic theory and methodology of a field are capable of yielding. (B) Significance. The field's promise of yielding results significant for the advancement of mathematics or related fields. (C) Challenge. The emergence of problems whose solutions require an ingenuity and/or methodology which distinguish them from those problems whose solutions are of a more routine character. (D) Status. The esteem in which the field is held. (E) Conceptual Stress. The stresses created by the need for new conceptual materials to furnish a logical basis for explaining phenomena; outstanding among these is symbolic stress. (F) Paradox. Emergence of paradoxes or inconsistencies.These are discussed individually. Analysis of Component (E), for example, shows that it evidently stems from several sources; e.g., the necessity for a new concept which will afford means of solving problems previously inaccessible; stresses created by the need for introducing order into a chaos of materials recognizably related; and the need for new attitudes toward mathematical existence and mathematical “reality.”     

Schülerprobleme beim Lösen von geometrischen Beweisaufgaben —eine Interviewstudie—

In this article we report on an interview study involving ten grade 8 students. These interviews served as a qualitative supplement for a large-scale quantitative study on proof and argumentation (N=659). During videotaped interviews the students were asked to solve geometrical proof problems. The results indicate that students’ difficulties with proof and logical argumentation may be explained by insufficient knowledge of facts, deficits in their methodological knoledge about mathematical proofs, and a lack of knowledge with respect to developing and implementing a proof strategy. Low-achieving students show difficulties with respect to all these three aspects, whereas high-achieving students’ difficulties are mainly based on deficits of developing an adequate and correct proof strategy.     

Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom

This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant’s class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as “I,” “we,” “they,” and “should/shouldn’t” elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.     

Perspectives of approximate dynamic programming

Approximate dynamic programming has evolved, initially independently, within operations research, computer science and the engineering controls community, all searching for practical tools for solving sequential stochastic optimization problems. More so than other communities, operations research continued to develop the theory behind the basic model introduced by Bellman with discrete states and actions, even while authors as early as Bellman himself recognized its limits due to the “curse of dimensionality” inherent in discrete state spaces. In response to these limitations, subcommunities in computer science, control theory and operations research have developed a variety of methods for solving different classes of stochastic, dynamic optimization problems, creating the appearance of a jungle of competing approaches. In this article, we show that there is actually a common theme to these strategies, and underpinning the entire field remains the fundamental algorithmic strategies of value and policy iteration that were first introduced in the 1950’s and 60’s.