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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]

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]

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.)

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]

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]

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]

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.)

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]

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]

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 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]

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]

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]

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 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]

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]

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]

The post-pandemic recovery of the travel and tourism industry has continued into 2023. Overtourism is a factor limiting the development of famous and successful destinations and causing negative attitudes toward tourism among the local population. Effective regulation and management of overtourism involve proactive planning, stakeholder engagement, and the implementation of sustainable tourism practices. Recently destinations have implemented strict rules for visitors to preserve their environment, resources, cultural heritage, and traditions. The article reveals how famous destinations and European cities deal with the challenges of overtourism. The author examines some 'good practices' and measures taken by stakeholders in handling mass tourism. [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, the existence of absolutely continuous solutions and some properties will be studied for a nonlocal boundary value problem of a state-dependent differential equation. The infinite-point boundary condition and the Riemann–Stieltjes integral condition will also be considered. Some examples will be provided to illustrate our results. [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.)

This short paper compiles the main concepts behind some philosophical views, definitions, and examples of causality. This collection spans the realms of the four commonly adopted approaches to causality: Hume’s regularity, counterfactual, manipulation, and mechanisms. This short review is motivated by presenting simplified views and definitions and then supplements them with examples from various fields, including economics, education, medicine, politics, physics, and engineering. I hope this short review is helpful to new and interested readers with little knowledge of causality and causal inference.

In the prologue to the Rhetorica ad Herennium Book 4, the author boldly departs from tradition and explains that he will create his own examples, rather than drawing from poets and orators. This methodological discussion portrays itself as an exemplum and hence carries a meta-literary and mimetic dimension. In particular, this prologue anticipates and illustrates the precept propounded in Book 4; its fine style and rhythm amount to a defense of rhetoric itself; and this defense must be considered in the political and cultural context of the time. [ABSTRACT FROM AUTHOR]

This paper deals with the relation between words and hands in popular language, having culture and religiosity as backgrounds. It begins by pointing out the importance of the hand for the human being, which goes beyond anatomy and becomes an instrument of transformation and production of culture in its various aspects. Then it points out that the popular language expresses an eminently manual culture, even in its religious expressions. Finally it shows some examples of popular expressions that include a manual culture. These examples include terms that people most greet and express manual labor, like using verbal present instead of future and the mutilation of syntax. They also include expressions that involve a hidden longing of resisting and the will of overcoming a discriminating and exploring people society. [ABSTRACT FROM AUTHOR]

In this paper we consider proving to be the activity in search for a proof, whereby proof is the final product of this activity that meets certain criteria. Although there has been considerable research attention on the functions of proof (e.g., explanation), there has been less explicit attention in the literature on those same functions arising in the proving process. Our aim is to identify conditions for proving by mathematical induction to be explanatory for the prover. To identify such conditions, we analyze videos of undergraduate mathematics students working on specially designed problems. Specifically, we examine the role played by: the problem formulation, students’ experience with the utility of examples in proving, and students’ ability to recognize and apply mathematical induction as an appropriate method in their explorations. We conclude that particular combinations of these aspects make it more likely that proving by induction will be explanatory for the prover. [ABSTRACT FROM AUTHOR]

Successful language acquisition has long been a moot point for EFL linguists, teachers and ESOL students. As a consequence, ELT resources have been undergoing various shifts in language focus and methodology to the point where new approaches break away from tradition by empowering students in their effort to take charge of their own learning in a highly developed technological age, where access to a whole array of resources has become commonplace - the Internet, smartphone / tablet apps, multimedia support etc. This paper looks at these shifts from the point of view of the learner as the end-user of existing facilities but also based on a new role assigned to the language teacher: that of a 'manager' whose purpose is to equip students with the skills necessary towards their independence in language acquisition techniques. Namely, by taking account of the main precepts of the Lexical Approach, I will attempt to make a case for the presence, manipulation and putting to good use of language usage examples to be found in present ELT resources, with a focus on learner's dictionaries and self-study books. [ABSTRACT FROM AUTHOR]

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with uncertainties, which can be represented by a Takagi-Sugeno (T-S) model. There exist the parameter uncertainties in both state and input matrices, as well as the matched external disturbance. The key feature of this work is the great ability of the controller to deal with systems without assuming that the control matrices of each local T-S model to be same and knowing the priori information of the upper norm-bounds of uncertainties. A sufficient condition for the existence of the desired fuzzy SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. A numerical example is illustrated in order to show the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

A topical research question is how pre-service teachers develop professional competencies with regard to game-centered approaches such as 'Teaching Games for Understanding' (TGfU). In this context, research on teacher education assumes reflection on teaching examples – including real-life classroom practices – to have positive effects on teachers' professional development. The role of media used in such examples is unclear, however. While text-based teaching examples might be more favorable for novice learners due to a step-by-step presentation of information, video-based examples that capture the complexity and reality of teaching situations might better foster the learning of advanced pre-service teachers. In a field experiment, we taught principles of TGfU to 136 undergraduate physical education (PE) pre-service teachers and randomly assigned them to three conditions: they either reflected by themselves on a video-based or on a text-based teaching example or completed an open-ended planning-task. For the video-based example, a PE teacher and his class staged different scenes of a teaching unit following a script that focused on 'badminton-like' games considering steps and pedagogical principles of TGfU. The video-based example was transcribed and converted into a text-based example. Before the intervention, we assessed the pre-service teachers' knowledge of game-centered approaches. After the intervention, we measured their knowledge of TGfU and affective-motivational variables (interest, challenge, enjoyment, annoyance). The participants had a (rather low) comparable knowledge before the intervention. After the intervention, we found that reflecting on the video-based example had increased the knowledge of TGfU more than reflecting on the text-based example or completing an open-ended planning-task (medium effect). We found no interaction effect of prior knowledge and condition on the knowledge of TGfU at posttest. Participants with a video-based example reported higher interest and enjoyment after the intervention (medium effect). All other affective-motivational variables did not show significant differences. Other studies concentrating on teaching in classrooms found that text-based examples fostered pre-service teachers' competencies better than video-based examples if they had rather low prior knowledge. One explanation for the present finding could refer to the specific field of study: For novice PE pre-service teachers the supposed benefit of text-based teaching examples does not advance the learning process more than the supposed benefit of video-based examples (realistic display of constitutional aspects of PE). Since interest is closely related to (intrinsic) motivation, and the learners' motivation is fostered by realistic and authentic context, our finding regarding the condition effect on interest and enjoyment is consistent with assumptions of situated learning theory. Higher motivation, in turn, could lead to a more elaborate analysis of the video-based example, which may ultimately explain the higher level of knowledge, too. The current findings indicate that video-based examples are a very promising means for PE teacher education. This refers in particular to autonomous work in teacher education because in the present study the pre-service teachers reflected on the teaching examples by themselves. [ABSTRACT FROM AUTHOR]