Search results for: counterexamples

Authors: Nodelman V.

Abstract:

Despite serious difficulties in the assimilation of the conceptual system of Calculus, software in the educational process is used only occasionally, and even then, mainly for illustration purposes. The following are a few reasons: The non-trivial nature of the studied material, Lack of skills in working with software, Fear of losing time working with software, The variety of the software itself, the corresponding interface, syntax, and the methods of working with the software, The need to find suitable models, and familiarize yourself with working with them, Incomplete compatibility of the found models with the content and teaching methods of the studied material. This paper proposes an active use of the developed non-commercial software VusuMatica, which allows removing these restrictions through Broad support for the studied mathematical material (and not only Calculus). As a result - no need to select the right software, Emphasizing the unity of mathematics, its intrasubject and interdisciplinary relations, User-friendly interface, Absence of special syntax in defining mathematical objects, Ease of building models of the studied material and manipulating them, Unlimited flexibility of models thanks to the ability to redefine objects, which allows exploring objects characteristics, and considering examples and counterexamples of the concepts under study. The construction of models is based on an original approach to the analysis of the structure of the studied concepts. Thanks to the ease of construction, students are able not only to use ready-made models but also to create them on their own and explore the material studied with their help. The presentation includes examples of using VusuMatica in studying the concepts of limit and continuity of a function, its derivative, and integral.

Keywords: counterexamples, limitations and requirements, software, teaching and learning calculus, user-friendly interface and syntax

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Authors: Anne Mette Nyvad, Ken Ramshøj Christensen

Abstract:

In the syntax literature, it has standardly been assumed that relative clauses and complement wh-clauses are islands for extraction in English, and that constraints on extraction from syntactic islands are universal. However, the Mainland Scandinavian languages has been known to provide counterexamples. Previous research on Danish has shown that neither relative clauses nor embedded questions are strong islands in Danish. Instead, extraction from this type of syntactic environment is degraded due to structural complexity and it interacts with nonstructural factors such as the frequency of occurrence of the matrix verb, the possibility of temporary misanalysis leading to semantic incongruity and exposure over time. We argue that these facts can be accounted for with parametric variation in the availability of CP-recursion, resulting in the patterns observed, as Danish would then “suspend” the ban on movement out of relative clauses and embedded questions. Given that Danish does not seem to adhere to allegedly universal syntactic constraints, such as the Complex NP Constraint and the Wh-Island Constraint, what happens in L2 English? We present results from a study investigating how native Danish speakers judge extractions from island structures in L2 English. Our findings suggest that Danes transfer their native language parameter setting when asked to judge island constructions in English. This is compatible with the Full Transfer Full Access Hypothesis, as the latter predicts that Danish would have difficulties resetting their [+/- CP-recursion] parameter in English because they are not exposed to negative evidence.

Keywords: syntax, islands, second language acquisition, danish

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Authors: Fayssal Tayalati

Abstract:

Although languages use very divergent constructional strategies, all existential constructions appear to invariably involve an implicit or explicit locative constituent. This locative constituent either surface as a true locative phrase or are realized as a possessor noun phrase. However, while much research focuses on the supposed underlying syntactic relation of locative and possessive existential constructions, not much is known about possible semantic factors that could govern the choice between these constructions. The main question that we address in this talk concerns the choice between the two related constructions in Modern Standard Arabic (MAS). Although both are used to express the existence of something somewhere, we can distinguish three contexts: First, for some types of entities, only the EL construction is possible (e.g. (1a) ṯammata raǧulun fī l-ḥadīqati vs. (1b) *(kāna) ladā l-ḥadīqati raǧulun). Second, for other types of entities, only the possessive construction is possible (e.g. (2a) ladā ṭ-ṭawilati aklun dāʾiriyyun vs. (2b) *ṯammata šaklun dāʾiriyyun ladā/fī ṭ-ṭawilati). Finally, for still other entities, both constructions can be found (e.g. (3a) ṯammata ḥubbun lā yūṣafu ladā ǧārī li-zawǧati-hi and (3b) ladā ǧārī ḥubbun lā yūṣafu li-zawǧati-hi). The data covering a range of ontologically different entities (concrete objects, events, body parts, dimensions, essential qualities, feelings, etc.) shows that the choice between the existential locative and the possessive constructions is closely linked to the conceptual autonomy of the existential theme with respect to its location or to the whole that it is a part of. The construction with ṯammata is the only possible one to express the existence of a fully autonomous (i.e. nondependent) entity (concrete objects (e.g.1) and abstract objects such as events, especially the ones that Grimshaw called ‘simple events’). The possessive construction with (kāna) ladā is the only one used to express the existence of fully non-autonomous (i.e. fully dependent on a whole) entities (body parts, dimensions (e.g. 2), essential qualities). The two constructions alternate when the existential theme is conceptually dependent but separable of the whole, either because it has an autonomous (independent) existence of the given whole (spare parts of an object), or because it receives a relative autonomy in the speech through a modifier (accidental qualities, feelings (e.g. 3a, 3b), psychological states, among some other kinds of themes). In this case, the modifier expresses an approximate boundary on a scale, and provides relative autonomy to the entity. Finally, we will show that kinship terms (e.g. son), which at first sight may seem to constitute counterexamples to our hypothesis, are nonetheless supported by it. The ontological (non-)autonomy of located or possessed entities is also reflected by morpho-syntactic properties, among them the use and the choice of determiners, pluralisation and the behavior of entities in the context of associative anaphora.

Keywords: existence, possession, autonomous entities, non-autonomous entities

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