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The papers in this issue provide an excellent example of how pertinent distinctions which emerge from analysis of significant data sets can be communicated to colleagues and used to make sense of observations. The distinctions are vividly described, illustrated and exemplified, and used to chart maturation in student use of examples from middle school, through high school and into university. Curiously, no corresponding maturation was detected in students' choice of examples to use for themselves. Contrast was detected between the way students used the same examples for comprehending a conjecture and testing its validity, and the way that some mathematicians used specifically constructed examples for locating underlying structure. What emerged for me from reading these papers is confirmation of the central role of attention, the productiveness of engaging students at the earliest ages and throughout their schooling with the detection and expression of generality, and the importance of being explicit about the scope of generality encompassed by a claim. Purposeful use of examples by students could be expected to develop as teachers explicitly use examples purposefully with and for students. A reasonable conjecture might be that getting students to be explicit about the scope of generality, of possible variation of which they are aware, might shed light on obstacles and barriers to reasoning which might otherwise lead to proof. [ABSTRACT FROM AUTHOR]

Excerpted from my book Generally Speaking, this paper introduces "concept‐driven sociology," a special way of theorizing designed to reveal abstract social patterns. As such, it examines the methodological process by which we can "distill" generic patterns from the culturally, historically, and situationally specific contexts in which we encounter them. It thus champions a "generic sociology" that is pronouncedly transcontextual (transcultural, transhistorical, transsituational, and translevel) in its scope. In order to uncover generic, transcontextual social patterns, we need to collect our data in a wide range of social contexts. Such contextual diversity is manifested multi‐culturally, multihistorically, multisituationally, as well as at multiple levels of social aggregation. True to its message, the book illustrates generic social patterns by drawing on numerous examples from diverse cultural contexts and historical periods and a wide range of diverse social domains, as well as by disregarding scale. Emphasizing cross‐contextual commonality, concept‐driven sociology tries to reveal formal "parallels" across seemingly disparate contexts. The paper features the four main types of cross‐contextual analogies concept‐driven sociologists tend to use—cross‐cultural, cross‐historical, cross‐domain, as well as cross‐level—disregarding conventionally noted substantive differences in order to note conventionally disregarded formal equivalences. [ABSTRACT FROM AUTHOR]

Copyright of Lexikos is the property of Bureau of the Woordeboek van die Afrikaanse Taal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this paper is to investigate the usefulness of examples that show typical learner errors in online pedagogical dictionaries of English for the accuracy of error correction as well as immediate and delayed retention of usage. The optimal positioning of examples of errors in entries is also researched. In an online experiment, participants did a sentence correction exercise with the help of purpose-built monolingual dictionary entries, where the provision and positioning of examples showing errors were controlled. Two test versions were created, which differed only in the presence of examples of errors in the entries. Usage retention was observed immediately after the test and two weeks later. The results indicate that it is worthwhile to include examples of errors in online learners' dictionaries because they contribute greatly to the retention of usage in the long run. They also help to rectify errors, though the effect is not statistically significant. The positioning of examples showing errors in entries has no influence on error correction accuracy or usage retention. The study reveals examples of errors to be a valuable induction-oriented stand-alone dictionary component placed outside warning boxes, which typically include explicit grammar rules and promote deduction. [ABSTRACT FROM AUTHOR]

This paper aims to illustrate examples of exercises that are used during the practical course of Romanian as a foreign language. The course is entitled Oral and Written Communication I and is taught during the first semester of the preparatory year of Romanian language for foreign citizens at the Technical University of Cluj-Napoca. The exercises address topics pertaining to the first concepts assimilated in any foreign language (family, personal space/home, the university context, daily activities in personal, social or special situations - at the doctor's, travel, etc.), both orally and in writing. For more clarity and accuracy, the paper relies on examples taken from the personal experience of teaching a group of 25 foreign students. [ABSTRACT FROM AUTHOR]

This study investigates middle school students' reasoning about parallelism and perpendicularity of two line segments. Data were collected from 83 middle school students through an identification task consisting of various examples and non-examples of the parallelism and perpendicularity of two line segments. One-to-one interviews were also conducted with fifteen students to support students' written reasons. The results indicated that middle school students identify parallel/perpendicular line segments by using three types of reasoning: visual reasoning, attribute reasoning, and language-based reasoning. With the influence of the concept images shaped by prototypical and intuitive examples and linguistic factors, some students either focused on non-critical attributes of the concepts as the critical ones or omitted critical attributes of the concepts. Hence, they either identified examples of parallel line segments and perpendicular line segments as non-examples or considered non-examples of the concepts as examples. [ABSTRACT FROM AUTHOR]

With due interpretative caution and trying not to fall into simplification or cliché, it could be stated that the “rational” mind learns with “pure concepts” based mainly on the understanding of the essence and attributes of their objects of knowledge. The “logical” mind, on the other hand, learns to unravel the theoretical consequences of a formula within an abstract language. On its side, the “creative” mind of the designer acquires and achieves the object of knowledge—creativity—through a deep understanding of already completed designs. This paper aims to delve into the process of analysis of design examples, a process that could somehow resemble Alchemy, in which the alembic could be the pencil. Drawing is the analytical tool that allows the designer to distil the essence of the studied references departing from the overflow of images that arrive to the eye. With the gathering of different successful design examples, the designers build up a repository stocked in their memory that enlarges their creative capacity when facing new challenges. [ABSTRACT FROM AUTHOR]

Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians' practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their craft in authentic settings. In this paper we critically analyze the rationality of using task-based interviews to investigate mathematical practice, focusing on how task-based interview studies have been used to inform our understanding of mathematicians' use of examples in mathematical practice. We discuss four specific generalizations about mathematical practice drawn from these studies, and suggest other types of studies that can be used to corroborate or challenge those generalizations. [ABSTRACT FROM AUTHOR]

The interpretation and reuse of previous design solutions, or precedents, is central to design. This paper describes qualitative research conducted over three years at two institutions, aimed at investigating the role of design knowledge re-use in project-based mechanical design courses. Research data were collected through participant observation, student interviews, anonymous questionnaires, and website analytics. The paper identifies challenges that must be addressed in order to support novice engineers in rehearsing the types of knowledge required to successfully reason about and engage with design precedents. Two categories of design precedents are identified: concept precedents and detail precedents. Providing students with access to the latter is identified as a particular challenge, as is providing students with access to engineering communities of practice. Approaches to addressing these challenges are discussed. [ABSTRACT FROM AUTHOR]

Copyright of Verba: Anuario Galego de Filoloxia is the property of Universidad de Santiago de Compostela, Servicio de Publicaciones and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

There is broad agreement that the choice of mathematical examples is central to the teaching of mathematics and that a teacher's choice of examples may either facilitate or impede learners' understanding. From this starting point it can be deduced that programmes of instruction for teachers should include the study of mathematical examples. However, there is much to learn about the kind of professional development that might support beginner teachers in the careful choice of examples. This paper presents a case study of a group of sixteen students on a one-year Primary PGCE (5-11) programme who met each month over the first six months of their course to consider example sets. The research events explored how student responses to examples presented in textbooks changed over time. The outcomes of this study suggest that over time students noticed more about opportunities for generalisation and progression in the mathematical constructs explored in the example sets. Students also noted many of the pedagogical concerns associated with textbook use. The outcomes of this study lead to the recommendation that programmes of instruction include explicit opportunities for beginner teachers to generate, explore and reflect upon examples for real or hypothetical classroom situations. [ABSTRACT FROM AUTHOR]

Abstract This paper argues that not only does history matter to legal epistemology, but also that understanding legal epistemology can yield a certain understanding of the past. The paper focuses on the common law practice of precedent and argues that there is no set of rules, principles, reasons or material facts that constitute the fixed or foundational content of past decisions (a 'timeless what' that determines its own relevance), but rather that what is taken by a judge resolving a particular dispute to be the content of past decisions depends on the active and creative construal of relevance engaged in by that judge. Precedents are better thought of as 'thick resources with dynamic content'. Such content is constrained by a variety of stabilising practices, but never so constrained as to determine how it can be construed to be relevant. This image of law's past may offer a general view of the past as something with which we can actively and creatively relate in the course of coping with the present. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a view of three central conceptual activities in the learning of mathematics: concept formation, conjecture formation and conjecture verification. These activities also take place in everyday thinking, in which the role of examples is crucial. Contrary to mathematics, in everyday thinking examples are, very often, the only tool by which we can form concepts and conjectures, and verify them. Thus, relying on examples in these activities in everyday thought processes becomes immediate and natural. In mathematics, however, we form concepts by means of definitions and verify conjectures by mathematical proofs. Thus, mathematics imposes on students certain ways of thinking, which are counterintuitive and not spontaneous. In other words, mathematical thinking requires a kind of inhibition from the learners. The question is to what extent this goal can be achieved. It is quite clear that some people can achieve it. It is also quite clear that many people cannot achieve it. The crucial question is what percentage of the population is interested in achieving it or, moreover, what percentage of the population really cares about it. [ABSTRACT FROM AUTHOR]

This paper summarizes a talk given by the author at the Indian Academy of Sciences, Bengaluru on December 12, 2019. It outlines the multiplicity of situations where measurements on directions in two, three, or more dimensions are observed, and form the basis for answering various scientific questions. After briefly outlining the novelty in dealing with such data and the need for an entirely different set of analytical tools, one of the basic questions that arises before any further inference viz. testing isotropy of circular data, is addressed. The author was initiated into this topic of directional statistics by Professor C R Rao during the 1960s and is pertinent to this occasion celebrating him. [ABSTRACT FROM AUTHOR]

In this paper we consider a very useful inequality that Murray Klamkin1) proved in 1975 (Uldmkin, 1975). The inequality has many applications, proving new inequalities included. A proof and some applications are proposed. [ABSTRACT FROM AUTHOR]

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating systematic lists of examples that they examined for patterns, an activity that we call “Comprehensive Example Generation”. We elaborate this construct, and we discuss ways in which it afforded productive conjecturing activity. The results suggest further research and pedagogical implications for explicitly targeting examples in conjecturing, and the study contributes to a body of literature that points to the benefits of exploring, identifying, and leveraging examples in proof-related activity. [ABSTRACT FROM AUTHOR]

This paper raises the possibility of enhancing prospective and practicing teachers' awareness of example use in classrooms by using theories to analyze an authentic case. The study was carried out in the context of a university course where participants analyzed an excerpt from a tenth-grade geometry class. A qualitative analysis of participants' comments related to example use in the case revealed that different participants related to different theories when discussing the same example. The most frequent aspect of example use noted was the psychological aspect, such as the use of intuitive and non-intuitive examples. In general, teachers felt that the case activity contributed to their understanding of example use in the classroom, although not necessarily to a great extent. One implication of the study is that analyzing an authentic case while focusing on certain theories, such as example use, may serve as a rehearsal for the teacher who wishes to reflect on and analyze example use in her or his classroom. Thus, theory is brought into the practice of teaching. [ABSTRACT FROM AUTHOR]

Nearly every known pair of isospectral but nonisometric manifolds — with as most famous members isospectral bounded ℝ-planar domains which makes one “not hear the shape of a drum” [M. Kac, Can one hear the shape of a drum? Amer. Math. Monthly 73(4 part 2) (1966) 1–23] — arise from the (group theoretical) Gassmann–Sunada method. Moreover, all the known ℝ-planar examples (so counter examples to Kac’s question) are constructed through a famous specialization of this method, called transplantation. We first describe a number of very general classes of length equivalent manifolds, with as particular cases isospectral manifolds, in each of the constructions starting from a given example that arises itself from the Gassmann–Sunada method. The constructions include the examples arising from the transplantation technique (and thus in particular the known planar examples). To that end, we introduce four properties — called FF, MAX, PAIR and INV — inspired by natural physical properties (which rule out trivial constructions), that are satisfied for each of the known planar examples. Vice versa, we show that length equivalent manifolds with FF, MAX, PAIR and INV which arise from the Gassmann–Sunada method, must fall under one of our prior constructions, thus describing a precise classification of these objects. Due to the nature of our constructions and properties, a deep connection with finite simple groups occurs which seems, perhaps, rather surprising in the context of this paper. On the other hand, our properties define in some sense physically irreducible pairs of length equivalent manifolds — “atoms” of general pairs of length equivalent manifolds, in that such a general pair of manifolds is patched up out of irreducible pairs — and that is precisely what simple groups are for general groups. [ABSTRACT FROM AUTHOR]

Automated source code documentation approaches often describe methods in abstract terms, using the words contained in the static source code or code excerpts from repositories. In this paper, we describe DynamiDoc: a simple automated documentation generator based on dynamic analysis. Our representation-based approach traces the program being executed and records string representations of concrete argument values, a return value and a target object state before and after each method execution. Then, for each method, it generates documentation sentences with examples, such as "When called on [3, 1.2] with element = 3, the object changed to [1.2]". Advantages and shortcomings of the approach are listed. We also found out that the generated sentences are substantially shorter than the methods they describe. According to our small-scale study, the majority of objects in the generated documentation have their string representations overridden, which further confirms the potential usefulness of our approach. Finally, we propose an alternative, variable-based approach that describes the values of individual member variables, rather than the state of an object as a whole. [ABSTRACT FROM AUTHOR]

Both international examination results and scientific evidence related to the teaching and learning of school algebra point to the necessity for analyzing mathematical practice in the classroom. In this context, we have formulated the research objective of characterizing the mathematical work that teachers favor based on the examples that they implement in the teaching of topics within the domain of secondary school algebra. To this end, this study is situated within the interpretive paradigm utilizing an instrumental collective case study approach. The study design entails the selection of two representative cases of mathematics teachers in Chilean schools, with the objective of understanding and describing their mathematical work in the secondary school classroom based on the examples they present. The results show that the first teacher utilizes varied examples that activate distinct forms of mathematical thinking, promoting the activation of both instrumental and discursive genesis. In contrast, the second teacher follows a more traditional approach, with the use of examples to illustrate and motivate, and a direct presentation of knowledge, activating primarily semiotic genesis, in which a transition between the numerical and the algebraic is lacking. Ultimately, the results highlight the importance of deeper consideration of the choice of examples in the teaching of algebra and how these examples can influence students' learning. Furthermore, additional ideas are put forward for future work in this line of research associated with the use of examples in the classroom. [ABSTRACT FROM AUTHOR]

The paper outlines some important concepts extracted from control systems theory and demonstrates their usefulness in thinking freshly about engineering practices. The concepts provide a universal, discipline-free framework, by which engineering practices can be approached, de-mystified and advances made. The mathematics is downplayed and the underlying concepts are promoted. Examples of advanced thinking using control systems theory are given in planning, management, risk management, work study, value management, constructability, general problem solving, investment and material and structure characterisation. [ABSTRACT FROM PUBLISHER]

In this paper I discuss a Kantian conception of cosmopolitan education. It suggests that we pursue the highest good - an object of morality - in the world together, and requires that we acknowledge the value of freedom, render ourselves both efficacious and autonomous in practice, cultivate our judgment, and unselfishly co-operate in the co-ordination and fulfilment of our morally permissible ends. Now, such an accomplishment is one of the most difficult challenges, and may not be achieved in our time, if ever. In the first part of the paper I show that we, according to Kant, have to interact with each other, and comply with the moral law in the quest of general happiness, not merely personal happiness. In the second part, I argue that a cosmopolitan design of teacher education in Kantian terms can establish moral character, even though good moral character is ultimately the outcome of free choice. Such a design can do so by optimizing the freedom of those concerned to set and pursue their morally permissible ends, and to cultivate their judgment through the use of examples. This requires, inter alia, that they be enabled, and take responsibility, to think for themselves, in the position of everyone else, and consistently; and to strengthen their virtue or self-mastery to comply, in practice, with the moral law. [ABSTRACT FROM AUTHOR]

In this paper we shall analyze multiple choice question tests for entrance examinations from probability point of view. Multiple choice question tests are used for example for entrance examinations at Prague University of Economics, we shall analyze these tests at the Faculty of Business Administration. We shall report on probability methods, which can be used for modelling of these tests. In this case model of binomial distribution can be used for answering the following questions (under assumption of random choice of answers): what is the probability, that the number of correct answers exceeds given number, what is expected number of correct answers, etc. Results of this analysis can be used for consideration of the appropriateness of these tests. [ABSTRACT FROM AUTHOR]

Copyright of Transformations in Business & Economics is the property of Vilnius University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this context, include mental acts of organisational reflection. [ABSTRACT FROM AUTHOR]

Building on the papers in this special issue as well as on our own experience and research, we try to shed light on the construct of example spaces and on how it can inform research and practice in the teaching and learning of mathematical concepts. Consistent with our way of working, we delay definition until after appropriate reader experience has been brought to the surface and several ‘examples’ have been discussed. Of special interest is the notion of accessibility of examples: an individual’s access to example spaces depends on conditions and is a valuable window on a deep, personal, situated structure. Through the notions of dimensions of possible variation and range of permissible change, we consider ways in which examples exemplify and how attention needs to be directed so as to emphasise examplehood (generality) rather than particularity of mathematical objects. The paper ends with some remarks about example spaces in mathematics education itself. [ABSTRACT FROM AUTHOR]

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness. [ABSTRACT FROM AUTHOR]

This paper aims to illustrate examples of exercises that are used during the practical course of Romanian as a foreign language. The course is entitled Oral and Written Communication I and is taught during the first semester of the preparatory year of Romanian language for foreign citizens at the Technical University of Cluj-Napoca. The exercises address topics pertaining to the first concepts assimilated in any foreign language (family, personal space/home, the university context, daily activities in personal, social or special situations – at the doctor’s, travel, etc.), both orally and in writing. For more clarity and accuracy, the paper relies on examples taken from the personal experience of teaching a group of 25 foreign students.

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematics with a reliance on the development of visual explanation while providing audio narration. In this paper, we report on a study undertaken at an Australian university, to investigate the perceived level of usefulness of captions and their automatic translations in a mathematics course. We discovered that students broadly agreed that captions are a useful learning feature: to allow flexibility of where and when a video is watched, but also to help understand speaker accents, and clarify explanations that are difficult to hear in the recording. Due to the high levels of use and perceived educational benefits of closed captions in online video but limited literature, there is a significant need for new research in this area. An urgent discussion is needed to explore how students engage with closed captions, how they may support learning, and to investigate implications on instructional design of mathematical videos. [ABSTRACT FROM AUTHOR]

This paper describes a study in which we investigated relationships between defining mathematical concepts - increasing and decreasing infinite sequences - explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and the effect of classifying on subsequent explaining and defining. We report that (1) student-generated definitions and explanations were highly variable in content and quality; (2) explicitly considering the meaning of the concept facilitated subsequent classification, and giving a personal definition or explanation had a greater effect than studying a given definition; (3) classifying before defining or explaining resulted in significantly poorer definitions and explanations. We discuss the implications of these results for the teaching of abstract pure mathematics, relating our discussion to existing work on the concept image/concept definition distinction and on working with examples. [ABSTRACT FROM AUTHOR]

This article explores the examples of the Quechua grammars composed between 1560 and 1753: a total of nine missionary arts. It analyses the marking of the examples, their topics, their function and their origin so that, on the one hand, it brings to light the links that exist between the grammars of this tradition and, on the other hand, it connects the examples used by the missionaries with the didactic and evangelizing purposes of these grammatical texts. To this end, this paper focuses on the analysis of the chapters related to nouns. [ABSTRACT FROM AUTHOR]

This paper develops a three-layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length ps of the soil movement. They are repeated for a series of linearly increasing ps (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free-head and capped piles. The solutions are presented in non-dimensional charts and elaborated through three examples. The study reveals the following: On-pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p-multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33-0.5 and 0.8-1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5-0.72 for moving clay under embankment loading., Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests., The normalised rotational stiffness is equal to 0.1-0.15 for the capped piles, which increases the pile displacement with depth., The three-layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Copyright of Forma y Funcion is the property of Universidad Nacional de Colombia, Facultad de Ciencias Humanas, Departamento de Linguistica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents an example-guided, anthro-pometry-based modeling method for creating 3D human body models from users' input of partial anthropometric measurements with a given example dataset. Rather than directly forming a mapping between the partial measurements and the body model, we first estimate a set of chosen 30 measurements from the input based on the example-oriented measurement analysis. We then create an initial 3D model using the example-oriented radial basis function model that maps the set of 30 measurements to the body shape space and is established based on the given examples. We finally refine the 3D model by constrained optimization to create the target body model. Our method has several advantages: (1) the created model is guaranteed to match the input measurements and reflects the shape characteristics of examples; (2) the input requirement is modest, which makes it useful in practice; and (3) the information of both the measurements and examples is fully utilized. We demonstrate the effectiveness, accuracy, flexibility and extensibility of the method by various experimental evaluations and a Kinect-based body customization application. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to provide some practical guidance to researchers on how statistical power analysis can be used to estimate sample size in empirical design. The paper describes the key assumptions underlying statistical power analysis and illustrates through several examples how to determine the appropriate sample size. The examples use hypotheses often tested in sport sciences and verified with popular statistical tests including the independent-samples t-test, one-way and two-way analysis of variance (ANOVA), correlation analysis, and regression analysis. Commonly used statistical packages allow researchers to determine appropriate sample size for hypothesis testing situations listed above. [ABSTRACT FROM AUTHOR]

Copyright of El Profesional de la Información is the property of EPI SCP and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Systematic research in the wide field of practical knowledge is a recent phenomenon. In this paper, the approaches which have been developed in the main centres of research into practical knowledge in Norway and Sweden are compared with an emphasis on their potential for revitalizing the study of ethics. The focus on narratives and reflection based on the researcher’s own professional experience which is the distinguishing feature of the centre for practical knowledge at the University of Nordland is seen as a very promising addition to the traditional repertory of ethical studies. [ABSTRACT FROM AUTHOR]

Copyright of Media4u Magazine is the property of Ing. Jan Chromy, Ph.D. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties concerning asymptotes. The paper describes 1 tutorial with 10 students and a follow-up revision session with 2 of the students the same day concerning the use of this theorem in which the tutor used the pedagogic strategy of learner-generated examples. The students' responses and the tutor's observations are analysed using constructs of example spaces, structure of attention and dimensions of possible variation. [ABSTRACT FROM AUTHOR]

Proof is central to mathematical practice, yet a perennial concern is that students of all ages struggle in learning to prove. Mathematics education scholars have suggested that overreliance on examples to justify the truth of statements is a contributing factor for students' difficulties. While example-based reasoning has typically been viewed as a stumbling block to learning to prove, we view example-based reasoning as an important object of study and posit that examples play both a foundational and an essential role in the development, exploration, and understanding of conjectures, as well as in subsequent attempts to develop proofs of those conjectures. In this paper, we provide an overview of our project whose goals were to (a) investigate the nature of middle school and high school students', undergraduate students', and mathematicians' thinking about the examples they use when developing, exploring, and proving conjectures; and (b) investigate ways in which thinking about and analyzing examples may facilitate the development of students' learning to prove. [ABSTRACT FROM AUTHOR]

• We compare the example use of 38 students and 6 mathematicians in the context of proving. • Both populations used similar criteria, affordances, purposes, and strategies with examples. • The mathematicians were more attuned to the purposes that their selected examples would fulfill. • They were also more attuned how their examples fit into the logical structures of the conjectures. Examples can play a productive role in the development of conjectures and proofs, but there is more to learn about what makes example use productive. The example use of mathematicians, who themselves are experts at developing conjectures and proofs, may provide insight into ways to support students in using examples productively. In this paper, we compare the example use of six mathematicians and 38 middle school, high school, undergraduate students as they reasoned about interviewer-provided conjectures and developed their own conjectures. We note broad similarities between the two groups in terms of the purposes for which they used examples and the strategies with which they selected and used examples. In the context of these similarities, we highlight two key areas in which the populations differed: (1) the coordination (or lack thereof) between purpose and strategy of examples, and (2) the role of the logical structure of conjectures in choosing and using examples. [ABSTRACT FROM AUTHOR]

The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples were considered. The nuclei of two of the examples were also obtained and these were used to establish the classification of these Osborn loops up to isomorphism. Moreover, the central properties of these examples were examined and were all found to be having a trivial center and no non-trivial normal subloop. Therefore, these examples of Osborn loops are simple Osborn loops. [ABSTRACT FROM AUTHOR]

In this paper, we theorise about the different kinds of relationship between examples and the classes of mathematical objects that they exemplify as they arise in mathematical activity and teaching. We ground our theorising in direct experience of creating a polynomial that fits certain constraints to develop our understanding of engagement with examples. We then relate insights about exemplification arising from this experience to a sequence of lessons. Through these cases, we indicate the variety of fluent uses of examples made by mathematicians and experienced teachers. Following Thompson's concept of 'didactic object' (Symbolizing, modeling, and tool use in mathematics education. Kluwer, Dordrecht, The Netherlands, pp 191-212, ), we talk about 'didacticising' an example and observe that the nature of students' engagement is important, as well as the teacher's intentions and actions (Thompson avoids using a verb with the root 'didact'. We use the verb 'didacticise' but without implying any connection to particular theoretical approaches which use the same verb.). The qualities of examples depend as much on human agency, such as pedagogical intent or mathematical curiosity or what is noticed, as on their mathematical relation to generalities. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of students' understanding and handling of examples in the framework of an example-based introductory mathematics undergraduate course. The plan of the course included a wide use of graphs in standard lectures, tutoring sessions as well as in examinations. This study deals with the notion of increasing function, which has been introduced by means of both the standard definition and a range of examples and non-examples, most often conveyed through graphs. We have analysed students' interpretations of the notion of increasing function as they applied them in a set of written examination tests. The data gathered have been completed by a number of interviews of students whose answers were difficult to interpret. The outcomes underline the importance of linguistic and semiotic competence and suggest that the design of innovative teaching paths should take care of the linguistic and semiotic skills needed to handle the representations involved. [ABSTRACT FROM AUTHOR]

video remix is generally created by arranging selected video clips and combining them with other media streams such as audio clips and video transition effects. This paper proposes a system for semi-automatically creating video remixes of good expressive quality. Given multiple original video clips, audio clips, and transition effects as the input, the proposed system generates a video remix by five processes: I) video clip sequence generation, II) audio clip selection, III) audio boundary extraction, IV) video segment extraction, and V) transition effect selection, based on the spatial and temporal structural patterns automatically learned from professionally created video remix examples. Experiments using movie trailers of action genre as video remix examples not only demonstrate that video remixing by professionals can be imitated based on examples but also reveal that the video clip sequence generation and audio clip selection are the most important processes to improve the perceived expressive quality of video remixes. [ABSTRACT FROM AUTHOR]