Centripetal and centrifugal language forces in one elementary school second language mathematics classroom

Research on the learning and teaching of mathematics in contexts of language diversity has highlighted a number of common tensions that arise in a variety of contexts. These tensions can be explained by Bakhtin’s characterization of two sets of forces that are present in any utterance: centripetal forces represent the drive for unitary language, standardisation and linguistic hegemony; centrifugal forces represent the presence of heteroglossia, stratification and decentralisation. In this paper, I use this theoretical perspective to examine ethnographic data from a study of a second language mathematics classroom in Canada, in which the students are almost all speakers of Cree, one of the original languages of Canada. My analysis highlights three situations in which the tension between centripetal and centrifugal forces is particularly salient: the students’ use of Cree; working on mathematical word problems; and producing mathematical explanations.     

Programming Languages,Microcomputers and O.R.

The relationship between O.R. and computer programming is considered. The programming languages involved, and their respective roles, are reviewed. Criteria for assessing a programming language for O.R. are discussed, particularly in view of the increasing use of microcomputers within O.R.     

Infinitesimal Perturbation Analysis: A Tool for Simulation

Perturbation analysis is a technique that expedites the process of performing experiments on discrete-event simulation models. This makes it possible to derive sensitivity estimates from one computer execution of a simulation model. Infinitesimal perturbation analysis (IPA) is one class of algorithms used in perturbation analysis. In this paper, the techniques and algorithms used in simulation to perform infinitesimal perturbation analysis are examined. Each algorithm is discussed in detail, with comments concerning implementation problems and examples with experimental results for serial transfer lines. The results of this paper show that for simple systems, IPA can be easily implemented in a general-purpose simulation language such as SIMAN. Unfortunately, for any given system, parameter or performance measure, the algorithm used to generate the gradient may vary. Additionally, algorithms for more complex classes of problems do not yet exist. This problem hampers the current possibility of incorporating IPA into general-purpose simulation languages.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

Review of Simulation Languages

The rapid acceptance of the need for special programming languages to aid in computer simulation has led to a large number of such languages in recent years. The purpose of this paper is to review the principal of these languages and to make a comparison of their characteristics. The first characteristic discussed is the method of dealing with time advance and the organization. This is followed by a discussion on the naming and structure of entities.An important aspect of simulation is the comprehensiveness of the test facilities which then receive discussion. The facilities provided by the various programs for introducing procedures or subroutines is described, with special emphasis on sampling, statistic-collecting and output procedures.Lastly, the facilities provided for development are discussed and the paper ends with a brief summary of each of the languages covered.     

Mathematics textbook development for primary grades and its teachers in Mozambique

This is an analysis of the author’s involvement since 1970 in textbook development for primary schools and adult education in Mozambique, focusing on integrating local cultural traditions, covering the period up to 2013. As main example, addition of the type 8?+?5?=?13 is used around the question of whether textbooks (and curricula) advocate counting strategies and/or computation strategies. Different visualisations of these strategies in textbooks and corresponding manipulatives are analysed. During the 1990s, local languages started to be used in adult education, apart from Portuguese, Mozambique’s official language. Unschooled adults showed the importance of verbal computation in Mozambican languages—Bantu languages—most of which use also the auxiliary base five, apart from the base-ten numerals. The 2003 curriculum for primary education introduced the possibility of using local languages, and NGO’s started translating textbooks into 16 Mozambican languages. The paper includes an analysis of some of these textbooks and concludes with the author’s ideas in his teacher’s guides on teaching mathematics in Mozambican languages, showing the opportunities of verbal computation, exploring base-five numerals supported by finger gestures, instead of finger counting.     

Regular Component Splittable Languages

Every infinite regular language contains a regular subset of the formuv+w for some words u, v, w, where v is not the empty word. The regularsubsets of the above form are called regular components. Some well-knowncontext-free languages, such as the Dyck language and the balanced language(over an alphabet X with |X| = 2), are decomposed as disjointunions of disjunctive languages. In this paper, we investigate thedecompositions of some of the regular languages and the context-freelanguages as disjoint unions of regular components. An infinite language iscalled regular component splittable if it can be expressed as a disjointunion of regular components and a finite set. We show that the Dycklanguage, the balanced language and some disjunctive context-free splittablelanguages are regular component splittable. We also present an example toshow that there is a disjunctive context-free language which is not regularcomponent splittable.     

Languages for Statistics and Data Analysis

Abstract

Languages for data analysis and statistics must be able to cover the entire spectrum from improvisation and fast prototyping to the implementation of streamlined, specialized systems for routine analyses. Such languages must not only be interactive but also programmable, and the distinctions between language, operating system, and user interface get blurred. The issues are discussed in the context of natural and computer languages, and of the different types of user interfaces (menu, command language, batch). It is argued that while such languages must have a completely general computing language kernel, they will contain surprisingly few items specific to data analysis—the latter items more properly belong to the “literature” (i.e., the programs) written in the language.     

On the process of gaining language as a resource in mathematics education

In this paper, we expand our prior work on mathematics education in contexts of language diversity by elaborating on the three perspectives on language described by Ruiz (NABE J 8(2):15–34, 1984): language-as-right, language-as-resource, and language-as-problem. We illustrate our arguments with data taken from research contexts in Catalonia-Spain and South Africa. In these two parts of the world, the language policy in education has long been an issue, with a monolingual orientation that values one language (i.e., Catalan in Catalonia and English in South Africa) over others. Throughout the introduction of specific examples of policy documents, classroom practices, and participants’ reports, our main point is that the right of using the students’ languages makes sense because it is itself more than an intrinsic human right; it is an option that potentially benefits the creation of mathematics learning opportunities. Especially for the instances of classroom practices, our examples can be considered as representative in that they point to a common situation in our data: despite the fact of the language of learning and teaching being fixed, there is room for the learners and the teacher to take or react to a decision on what language to use, with whom, and how in concrete moments of the interaction. However, on the basis of our studies and drawing on the literature in mathematics education and language diversity, we argue that language rights are not sufficiently connected to language as a pedagogical resource. The enactment of these rights is still contributing in many ways to the social and political construction of problems concerning the role of certain languages in classroom interaction. We conclude the paper by discussing some possibilities for framing language as a resource that provide effective support to all students’ learning of mathematics.     

MAGIC: The Design and Use of an Interactive Modelling Language for Mathematical Programming

The desirability of computer aids for the building as well asthe solving of Mathematical Programming models is argued. Ashort survey is given of some of the distinct approaches possiblein designing matrix generators/languages for such a role. Itis then suggested that the approach most suited to general modelsis to design a language close to widely used mathematical notation.The facilities needed in such a language are discussed and theimplementation using the MAGIC (MAtrix Generator InstructionConvertor) language described.     

On-line identification of language measure parameters for discrete-event supervisory control

The discrete-event dynamic behavior of physical plants is often represented by regular languages that can be realized as deterministic finite state automata (DFSA). The concept and construction of signed real measures of regular languages have been recently reported in literature. Major applications of the language measure are: quantitative evaluation of the discrete-event dynamic behavior of unsupervised and supervised plants; and analysis and synthesis of optimal supervisory control algorithms in the discrete-event setting. This paper formulates and experimentally validates an on-line procedure for identification of the language measure parameters based on a DFSA model of the physical plant. The recursive algorithm of this identification procedure relies on observed simulation and/or experimental data. Efficacy of the parameter identification procedure is demonstrated on the test bed of a mobile robotic system, whose dynamic behavior is modelled as a DFSA for discrete-event supervisory control.     

Simulation in Microcomputers Revisited

This note discusses experiences in running discrete-events simulation models on an Apple II microcomputer. The use of PASCAL as a simulation language is commented on. To give an indication of the type of simulations that can be run on a micro, a fairly complex model relating to icebreaking operations is discussed. Run times for this model are mentioned. It is indicated how those run times can be reduced by programming part of the random number generation in assembly language. The conclusion is that significant simulation work can be done on a small micro like the Apple II.     

Parallel simulation of large scale multibody systems

Virtual prototyping plays an ever increasing role in the engineering disciplines. Nowadays, engineers can rely on powerful tools like object oriented modeling languages, e.g., Modelica. Models written in this language can be simulated by open source software as well as commercial tools. The advantage of this approach is that the engineers can concentrate themselves on modeling, whereas the numerical intricacies of the simulation are handled by the software. On the other hand the simulations are usually slower than implementations which are parallelized and optimized manually. This can lead to computation times which are infeasible in practice, e.g., when a real time simulation is necessary for a hardware-in-the-loop simulation. In this contribution we are concerned with speeding up such automated simulations by parallelization (on desktop hardware as well as HPC systems). We examine the parallelism across the system approaches. Additionally, the influence of the problem formulation on the simulation time is discussed. The implemented methods are demonstrated on engineering examples. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Disjunctive splittability of languages

Decompositions of languages over a finite alphabetX are investigated. Let T be a class of languages overX satisfying the following condition: (#) T contains at least one dense language, and every dense subset of an element in T is again in T. A language is said to be DT-splittable if it is a disjoint union of infinitely many discrete disjunctive languages in T which are locally finite of rank 1. It is shown that a language is DT-splittable if and only if it is a union of dense languages in T. The class P of all prefix codes satisfies the condition (#). DP-splittability of languages is investigated in detail. A language A is said to besemi-DT-splittable if A\F is DT-splittable for some finite languageF. Semi-DP-splittability is investigated. Semi-DP-splittability of catenations of languages is also studied.     

Combinatorial properties of boundary NLC graph languages

Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs)which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Boundary NLC (BNLC) grammars are NLC grammars with the property that whenever - in a graph already generated - two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages.In this paper we investigate the behaviour of graph invariants within BNLC languages. First we demonstrate that there is a dependency between the chromatic number and the clique number of graphs in BNLC languages (while this is wellknown not to be true for arbitrary graph languages). Secondly, we introduce a new graph invariant, the so-called index of a graph which seems to be very suitable for describing the adjacency structure of a graph. Then we prove that every BNLC language is of bounded index (which is shown not to be true for arbitrary graph languages). Thus we exhibit properties (concerning graph invariants) of BNLC languages which are intrinsic to this class. We use them to demonstrate that certain graph languages are not BNLC languages.     

Program control of operating systems

The traditional job control language becomes superfluous if the existing programming languages are extended slightly. Such extensions also allow drivers and operating systems to be programmed entirely in high level languages. Ultimately, we may see machine independent operating systems. A framework is presented for an extendable operating system which allows a simple, uniform implementation of these language extensions.     

The Dynamic Geometrisation of Computer Programming

The goal of this paper is to explore dynamic geometry environments (DGE) as a type of computer programming language. Using projects created by secondary students in one particular DGE, we analyse the extent to which the various aspects of computational thinking—including both ways of doing things and particular concepts—were evident in their work, drawing specifically on frameworks for computational thinking that are designed for the purpose of mathematics education. We show how many of the practices associated with the use of propositional programming languages also feature in the more spatial and temporal register of the geometric ‘language’ of DGEs.     

A statistical approach to crosslingual natural language tasks

The existence of huge volumes of documents written in multiple languages on Internet leads to investigate novel algorithmic approaches to deal with information of this kind. However, most crosslingual natural language processing (NLP) tasks consider a decoupled approach in which monolingual NLP techniques are applied along with an independent translation process. This two-step approach is too sensitive to translation errors, and in general to the accumulative effect of errors. To solve this problem, we propose to use a direct probabilistic crosslingual NLP system which integrates both steps, translation and the specific NLP task, into a single one. In order to perform this integrated approach to crosslingual tasks, we propose to use the statistical IBM 1 word alignment model (M1). The M1 model may show a non-monotonic behaviour when aligning words from a sentence in a source language to words from another sentence in a different, target language. This is the case of languages with different word order. In English, for instance, adjectives appear before nouns, whereas in Spanish it is exactly the opposite. The successful experimental results reported in three different tasks - text classification, information retrieval and plagiarism analysis - highlight the benefits of the statistical integrated approach proposed in this work.