What is on his mind?

We survey 19 questions and conjectures of Carsten Thomassen, most of which remain open.     

Virtual Teams: What are their Characteristics, and Impact on Team Performance?

To date, efforts to understand virtual teaming have been largely anecdotal and atheoretical. Therefore, drawing from the extant research in the groups domain, we attempt to ground the definition of a virtual team in well-established group-level constructs, and design a simulation study to investigate the impact of different virtual team characteristics on team performance. Essentially, we argue that the virtual team is defined by three key characteristics—the virtual team context, the virtual team composition, and the virtual team structure. Using the VDT computational discrete event simulation model as our experimental platform, we simulated different virtual team models, and examined their impact on various team performance dimensions. We found that virtual team characteristics have different effects on different aspects of team performance. The virtual context team had a lower rework volume but higher coordination volume and longer project duration than the virtual composition team. Interestingly, we also found that the virtual structure team performed better than the software development team baseline model in all aspects of team performance. Based on these results, we proposed strategies to improve performance in different types of virtual team. Specifically, we propose (1) increasing the ease of communication and availability of routines in the virtual context team; (2) clarifying role expectations and fostering a team culture in the virtual composition team; and (3) implementing a lateral structure in the virtual team. Our results also suggest that firms should consider situational demands, specifically tolerance for errors and coordination volume, when considering the design of virtual teams.     

A false belief about fractions – What is its source?

This paper presents the results of interviews with 174 participants solving a problem of elementary mathematics, connected with the part–whole approach to fractions. The motive for the investigation was a specific kind of difficulty observed during a case study conducted to verify the elementary school student's understanding of the concept of fractions. The authors decided to examine the problem in a broader population of mathematics learners at different levels of education: from elementary school to university students and graduates of science majors. Approximately 65% of respondents reported the wrong answer immediately after reading the fraction problem taken from the fourth grade of elementary school. Detailed analysis of the respondents’ performance showed that the source of many wrong answers was a false belief about fractions: The only way to get 1/n of a given whole is to divide this whole into n equal parts, not yet described in educational literature.     

Dirichlet and Neumann boundary conditions: What is in between?

Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C ₀ -semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions. RID="h1" ID="h1"Dédié à Philippe Bénilan RID="*" ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme".     

What Makes a Thing What It Is? Aristotle and Hegel on Identity

The notion of identity is investigated through Aristotle and Hegel as supporters of two different ontological conceptions: pluralism of substances and relational holism. Through Aristotle, I examine both the thesis according to which the identity of an object is constituted by its properties and the difficulties which this thesis encounters (e.g., those raised by Max Black). Aristotle easily defines the identity in species, in genus, and in number; some problems arise regarding the identity of individuals: for these, it is not enough to indicate the definition and the proper qualities, but matter is needed. Matter cannot, however, be a criterion for identifying duplicate objects: in this case, it plays at most the role of a “weak individuator.” A weak individuator involves relations with other entities. The use of relations in determining the identity of an entity is extensively treated by Hegel, according to whom, in order to define the identity of an object a multiplicity of particular objects is required and, therefore, relations among entities. I conclude by proposing a notion of the object understood not as an independent, separate, and autonomous item, but as a portion of the world, which is given in a phenomenological context and identifies a dialectical context.     

Do efficiency scores depend on input mix? A statistical test and empirical illustration

In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.     

What is a polar function and how to find derivative of it?

1. What are polar coordinates? I went from Chongqing to Beijing by air in 1992. When I came to the airport and watched big jetliners lumber into position on the runway for takeoff at the first time in my life, I asked questions to partner about how big jetliners got off at that position exactly. He made sure that people     

Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?

This paper develops a computational framework for inverting Gompertz–Makeham mortality hazard rates, consistent with compensation laws of mortality for heterogeneous populations, to define a longevity-risk-adjusted global (L-RaG) age. To illustrate its salience and possible applications, the paper calibrates and presents L-RaG values using country data from the Human Mortality Database (HMD). Among other things, the author demonstrates that when properly benchmarked, the longevity-risk-adjusted global age of a 55-year-old Swedish male is 48, whereas a 55-year-old Russian male is closer in age to 67. The paper also discusses the connection between the proposed L-RaG age and the related concept of Biological age, from the medical and gerontology literature. Practically speaking, in a world of growing mortality heterogeneity, the L-RaG age could be used for pension and retirement policy. In the language of behavioral finance and economics, a salient metric that adjusts chronological age for longevity risk might help capture the public’s attention, educate them about lifetime uncertainty and induce many of them to take action — such as working longer and/or retiring later.     

What do teachers need? Math and special education teacher educators’ perceptions of essential teacher knowledge and experience

Special education and mathematics education are becoming increasingly intertwined in inclusive classrooms. However, research and practice in these two fields are not always aligned. We discuss, in the context of extant research on pedagogical theory, concepts of access, and the findings of an exploratory study, how these two education sub-fields view teacher expertise. Teacher educators (from math and special education) were asked to rank the importance of different types of expertise for effectively posing purposeful mathematical questions. The groups differed significantly in their rankings of the importance of knowing individual students and general teaching experience. There were also notable differences between the groups’ rankings of the importance of knowing the needs of students with disabilities and mathematical content knowledge. The possible reasons for this are discussed, along with suggestions for improving professional collaboration.     

Re-sourcing teachers’ work and interactions: a collective perspective on resources, their use and transformation

This paper reviews the literature on the theme of mathematics teachers’ work and interactions with resources, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of research; (2) teachers’ interactions with resources in terms of their design and use; and (3) teachers’ interactions with resources in terms of teacher learning and professional development. From the literature, and the collection of papers in this issue, we argue that the collective dimensions play an important role in mathematics teachers’ work with resources and in their professional learning/development. Further empirical investigations are likely to be needed on: how teachers may work in collectives and with resources, and in which ways ‘productive’ collectives may form and work together; which roles particular resources can play in these delicate constellations and how particular resources may support teachers in their work and learning; and which kinds of resources offer opportunities for community building.     

Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics

While the general notion of ‘metaphor’ may offer a thoughtful analysis of the nature of mathematical thinking, this paper suggests that it is even more important to take into account the particular mental structures available to the individual that have been built from experience that the individual has ‘met-before.’ The notion of ‘met-before’ offers not only a principle to analyse the changing meanings in mathematics and the difficulties faced by the learner—which we illustrate by the problematic case of the minus sign—it can also be used to analyse the met-befores of mathematicians, mathematics educators and those who develop theories of learning to reveal implicit assumptions that support our thinking in some ways and act as impediments in others.     

Teachers’ metacognitive and heuristic approaches to word problem solving: analysis and impact on students’ beliefs and performance

We conducted a 7-month video-based study in two sixth-grade classrooms focusing on teachers’ metacognitive and heuristic approaches to problem solving. All problem-solving lessons were analysed regarding the extent to which teachers implemented a metacognitive model and addressed a set of eight heuristics. We observed clear differences between both teachers’ instructional approaches. Besides, we examined teachers’ and students’ beliefs about the degree to which metacognitive and heuristic skills were addressed in their classrooms and observed that participants’ beliefs were overall in line with our observations of teachers’ instructional approaches. In addition, we investigated how students’ problem-solving skills developed as a result of teachers’ instructional approaches. A positive relationship between students’ spontaneous application of heuristics to solve non-routine word problems and teachers’ references to these skills in their problem-solving lessons was found. However, this increase in the application of heuristics did not result in students’ better performance on these non-routine word problems.     

What is different across an ocean? How Singapore and US elementary mathematics curricula introduce and develop length measurement

This article compares the opportunity to learn length measurement in the USA and Singapore as revealed in the close analysis of some of their written elementary curriculum materials. Written curricula strongly influence students’ learning of mathematics, without completely determining it. The Trends in Third International Mathematics and Science study 2007 showed the relatively low performance of the US and Singapore fourth graders in measurement, which was attributed in part to the learning opportunities provided to the students. We examined and coded all instances of length measurement in three different US curricula and one Singapore curriculum through Grade 3, using a very detailed scheme that identified particular elements of conceptual, procedural and conventional knowledge and the textual forms that present this knowledge. Results show strong emphasis on measurement procedures, across all grades and curricula, in both countries. However, in numerous ways, the Singapore curriculum is more focused, organizationally, procedurally and conceptually. US curricula provide more diverse access to conceptual knowledge where Singapore materials focus on independent work involving procedures, within and across grade levels. Limitations of the curricula in both countries are discussed.     

Computer‐enhanced algebra resources: their effects on achievement and attitudes [1]

Findings from this study indicate that the use of computer-enhanced resources throughout an entire algebra course had no significant effect on algebra achievement, attitudes toward mathematics, and attitudes toward the instructional setting. Differences in ability did have a significant effect upon algebra achievement but did not significantly affect attitudes toward mathematics and the instructional setting. During the study, high- and average-ability students had a significant improvement in their attitudes toward computers. High-ability students were more reluctant to accept computers in the algebra course than average-ability students. An important finding of this study is that computer-related assignments can be given weekly throughout an entire course in second-year algebra without taking time and topics from the algebra content.