Role Of Notation Research Articles

(Re-)Assembling Notations in the Performance of Early Music

This article draws on fieldwork observations of a vocal ensemble specialised in early music, describing the role of historical manuscripts in their creative process. It pursues two closely related questions: that of the status of the musical work as an agent of historical authenticity, and the type of creativity involved in this process of research, rehearsal, and performance. As such, it provides critical reflection on the use of concepts of material agency in the study of musical performance practices, and contributes to a reconsideration of the role of notation in musical creativity. It argues that historically informed performance may be considered as a form of experimental musical practice, in that it aims to cultivate new approaches to musical performance and in that its process may be described in terms of the testing of musical materials.

Counting with Alice

There are many mathematical references in Lewis Carroll’s two tales for children: Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass (1872). Many critics suggested that Carroll inserted hidden meanings in those passages. We rather consider them as part of the story’s setting and narrative. Yet, those passages may be interpreted and used as convenient to illustrate mathematical ideas. In this paper, we consider two passages from the Alice tales that relate to arithmetic, and we discuss them in relation to issues of personal identity, mathematical certainty, the role of notations and the processes of composition and decomposition in mental calculation. Hence, we show how literary texts can be used to convey ideas related to mathematics, mathematical culture and mathematical education. We conclude on the importance of mathematical writings as literary texts.

The Role of Notations in Mathematics

The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, notations may play a crucial role in mathematical discovery in different ways. Some examples are given to illustrate these ways.

Notation as material culture

One of the warmest April days on record greeted the start of the interdisciplinary conference ‘Material cultures of music notation’, held from 20 to 22 April 2018 at Utrecht University. The historical importance of the Academiegebouw (where the Union of Utrecht was signed in 1579, unifying several of the northern provinces of the Netherlands), as well as its convenient location on Dom Square in the heart of the city made it an ideal setting for the conference. Funded through a Veni postdoctoral grant by the NWO (Netherlands Organization for Scientific Research), ‘Material cultures of music notation’ aimed to approach the notation of music—in the broadest sense—‘not just as a vessel of music-theoretical knowledge, but as an object of social interaction and cultural exchange’ (see http://notationcultures.com). The wide-reaching theme attracted interest from musicologists from numerous subdisciplines as well as scholars from other fields from all over the world. Forty-four papers were presented in two parallel sessions, most of which were mixed sessions with varied content and research perspectives, covering topics ranging from piano rolls and the role of notation in improvisation to notation in South Indian music and modern digital techniques. The subdiscipline of early music was well represented, with almost a quarter of all papers dealing with medieval or early modern topics.

The Role of Number Notation: Sign-Value Notation Number Processing is Easier than Place-Value.

Number notations can influence the way numbers are handled in computations; however, the role of notation itself in mental processing has not been examined directly. From a mathematical point of view, it is believed that place-value number notation systems, such as the Indo-Arabic numbers, are superior to sign-value systems, such as the Roman numbers. However, sign-value notation might have sufficient efficiency; for example, sign-value notations were common in flourishing cultures, such as in ancient Egypt. Herein we compared artificial sign-value and place-value notations in simple numerical tasks. We found that, contrary to the dominant view, sign-value notation can be applied more easily than place-value notation for multi-power comparison and addition tasks. Our results are consistent with the popularity of sign-value notations that prevailed for centuries. To explain the notation effect, we propose a natural multi-power number representation based on the numerical representation of objects.

Phonological Theory: The Essential Readings (review)

Reviewed by: Phonological theory: The essential readings ed. by John A. Goldsmith Marc Pierce Phonological theory: The essential readings. Ed. by John A. Goldsmith. Oxford & Malden, MA: Blackwell Publishers, 1999. Pp. viii, 438. This volume reprints 22 influential phonology papers (in some cases, abridged versions thereof), originally published between 1947 and 1996. The papers include among others: ‘On the role of notation in generative phonology’ (22–33) by James D. McCawley, ‘From cyclic phonology to lexical phonology’ (34–62) by Paul Kiparsky, ‘Phonology with tiers’ (303–12) by Alan S. Prince, ‘The syllable’ (328–50) by Elisabeth O. Selkirk, and ‘Immediate constituents of Mazateco syllables’ (313–27) by Kenneth L. Pike and Eunice Victoria Pike. There is also a useful ‘Introduction’ (1–16) by the editor and a detailed index. All but one of the papers are couched in some version of generative phonology, the single exception being the paper by Kenneth and Eunice Pike. Most of the advances in generative phonology are discussed here, including metrical phonology, auto-segmental phonology, syllable theory, prosodic morphology, and optimality theory. This is an extremely valuable book. It reprints classic articles in a convenient format, thus rendering repeated trips to the library and extensive use of the photocopier unnecessary. I wish that none of the articles had been abridged, and one could of course quibble about the choice of articles. These are minor objections, however, and do not detract from the general usefulness of the volume. Marc Pierce University of Michigan Copyright © 2001 Linguistic Society of America

Notation and nature of task in comprehending design rationale

This paper provides the elements of a ground theory on how design rationale can be effectively re-used across design generations. In particular, we explore the role of notation, argumentative structure and task conditions under which comprehension in that context can be facilitated. An experiment is set up in order to investigate whether and under which task requirements visual formalisms outperform text and whether Vessey's 'cognitive fit' argument stands true in decision-making activities related to the design of interactive systems. Results confirm that visual formalisms enhance the comprehension of design argumentation, and in particular, tables facilitate quicker access to meaningful information. There are also indications that complex argumentation schemata that are depicted graphically are acquired quicker by novices. We then lay out a framework of the notational and task conditions under which comprehension of design rationale by novices is optimised.

The role of notation and knowledge representation in the determination of programming strategy: A framework for integrating models of programming behavior

A number of accounts of expert programming behavior have been advanced. These models of the programming activity have served to highlight the range of factors that are thought to underpin programming strategy. However, such accounts have tended to emphasize either the effects of the organization of the programmer's knowledge representation or the role played by features of the notation of the task language on the emergence, development, and support of particular forms of strategy. Such work has neglected to (a) provide an account of the way in which these factors might interact to determine programming strategy, and (b) shed light upon the nature of the development of particular strategies as programming skill increases. This article presents the results of an empirical analysis of the strategies employed by programmers of varying skill levels using different programming languages. The development of particular forms of strategy is hypothesized to be related both to the development of systematic asymmetries in programmers' generic plan-based representations of programming knowledge and to the way in which features of the notation of particular programming languages might differentially support particular strategies. However, the results of the study reported here suggest that these effects must be interpreted within a broad developmental context. Hence, as programming skill develops, it appears that the notation of the task language tends to take precedence as a determinant of strategy, but has less relevance at beginning stages of skill development and within the context of expert performance. This finding would not be predicted by current models of the programming activity because such models suggest that any notational effects will tend to be consistent regardless of the skill level attained by the programmer. This article endeavors to extend current models of programming by emphasizing the need to consider in detail not only the development of programming strategy, but also the way in which knowledge representation and features of the task langauge interact to give rise to particular forms of programming behavior.

The Role of Notation and Knowledge Representation in the Determination of Programming Strategy: A Framework for Integrating Models of Programming Behavior

A number of accounts of expert programming behavior have been advanced. These models of the programming activity have served to highlight the range of factors that are thought to underpin programming strategy. However, such accounts have tended to emphasize either the effects of the organization of the programmer's knowledge representation or the role played by features of the notation of the task language on the emergence, development, and support of particular forms of strategy. Such work has neglected to (a) provide an account of the way in which these factors might interact to determine programming strategy, and (b) shed light upon the nature of the development of particular strategies as programming skill increases.This article presents the results of an empirical analysis of the strategies employed by programmers of varying skill levels using different programming languages. The development of particular forms of strategy is hypothesized to be related both to the development of systematic asymmetries in programmers' generic plan‐based representations of programming knowledge and to the way in which features of the notation of particular programming languages might differentially support particular strategies. However, the results of the study reported here suggest that these effects must be interpreted within a broad developmental context. Hence, as programming skill develops, it appears that the notation of the task language tends to take precedence as a determinant of strategy, but has less relevance at beginning stages of skill development and within the context of expert performance. This finding would not be predicted by current models of the programming activity because such models suggest that any notational effects will tend to be consistent regardless of the skill level attained by the programmer. This article endeavors to extend current models of programming by emphasizing the need to consider in detail not only the development of programming strategy, but also the way in which knowledge representation and features of the task langauge interact to give rise to particular forms of programming behavior.

On the role of notation in the formulation of mathematical models

Models (in the sense of paradigms or archetypes) of the processes involved in mathematical modelling have been proposed by a number of authors. Many of these models have common features and a consensus is emerging. One stage of the modelling process is the formulation of a mathematical model from the original real problem situation. This paper concentrates on the role of the particular symbolic representation chosen for the mathematical model and points out the far‐reaching effects that notation may have for the complete modelling process.

I. Objectives of Applied Mathematics Education

Previous article Next article I. Objectives of Applied Mathematics EducationC. C. LinC. C. Linhttps://doi.org/10.1137/1009062PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails The Process of Applied Mathematics Cross Ref On the role of notation in the formulation of mathematical models9 July 2006 | International Journal of Mathematical Education in Science and Technology, Vol. 13, No. 5 Cross Ref Mathematics in Biomedicine11 April 2018 | The American Mathematical Monthly, Vol. 86, No. 6 Cross Ref Volume 9, Issue 2| 1967SIAM Review History Published online:18 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1009062Article page range:pp. 293-311ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

On The Role of Notation in Mathematics

When Ahmes the Egyptian, author of the oldest mathematical treatise now extant—written nearly two thousand years before Christ, i. e., about the time of Joseph—was presented to Pharaoh, his king, as a learned mathematician, Pharaoh remarked: “Professor, I assure you that I entertain a profound respect for one skilled in the higher mathematics for of all the subjects with which my tutor sought vainly to acquaint me, this was the one to which I could discover neither head, tail nor middle.” This little piece of unwritten history I am able to announce to you for the first time, having inferred it by a process of generalization. For this is the substance of the first remark ventured by Augustus Mutt when introduced to Mathematicus ever since. That Ahmes, too, was a genuine mathematician is attested by his behavior—likewise here reported for the first time—for he assumed a look of superior wisdom and reserve, mingled wits satisfaction, but deprecated the royal humility and presented Pharaoh with a copy of payrus, which bore the modest title: “Directions for obtaining the knowledge of all dark things.”