The Importance of Teaching Students How to Read to Comprehend Mathematical Language

In this action research study of my classroom of 8th and 9th grade Algebra I students, I investigated if there are any benefits for the students in my class to learn how to read, translate, use, and understand the mathematical language found daily in their math lessons. I discovered that daily use and practice of the mathematical language in both written and verbal form, by not only me but by my students as well, improved their understanding of the textbook instructions, increased their vocabulary and also increased their understanding of their math lessons. I also found that my students remembered the mathematical material better with constant use of mathematical language and terms. As a result of this research, I plan to continue stressing the use of mathematical language and vocabulary in my classroom and will try to develop new ways to help students to read, understand, and remember mathematical language they find daily in their textbooks.

Expressiveness of Concurrent Languages

The aim of this thesis is to go through different approaches for proving expressiveness properties in several concurrent languages. We analyse four different calculi exploiting for each one a different technique. We begin with the analysis of a synchronous language, we explore the expressiveness of a fragment of CCS! (a variant of Milner's CCS where replication is considered instead of recursion) w.r.t. the existence of faithful encodings (i.e. encodings that respect the behaviour of the encoded model without introducing unnecessary computations) of models of computability strictly less expressive than Turing Machines. Namely, grammars of types 1,2 and 3 in the Chomsky Hierarchy. We then move to asynchronous languages and we study full abstraction for two Linda-like languages. Linda can be considered as the asynchronous version of CCS plus a shared memory (a multiset of elements) that is used for storing messages. After having defined a denotational semantics based on traces, we obtain fully abstract semantics for both languages by using suitable abstractions in order to identify different traces which do not correspond to different behaviours. Since the ability of one of the two variants considered of recognising multiple occurrences of messages in the store (which accounts for an increase of expressiveness) reflects in a less complex abstraction, we then study other languages where multiplicity plays a fundamental role. We consider the language CHR (Constraint Handling Rules) a language which uses multi-headed (guarded) rules. We prove that multiple heads augment the expressive power of the language. Indeed we show that if we restrict to rules where the head contains at most n atoms we could generate a hierarchy of languages with increasing expressiveness (i.e. the CHR language allowing at most n atoms in the heads is more expressive than the language allowing at most m atoms, with mlanguage similar but simpler than CHR. The kappa-calculus is a formalism for modelling molecular biology where molecules are terms with internal state and sites, bonds are represented by shared names labelling sites, and reactions are represented by rewriting rules. Depending on the shape of the rewriting rules, several dialects of the calculus can be obtained. We analyse the expressive power of some of these dialects by focusing on decidability and undecidability for problems like reachability and coverability.

CLIL materials in Secondary Education: focusing on the language of instruction in the subject area of Mathematics

[EN]Applying a CLIL methodological approach marks a shift in emphasis from language learning based on linguistic form and grammatical progression to a more ‘language acquisition’ one which takes account language functions. In this article we will study the elements of the “language of instruction” of the area of Maths in Secondary Education, by focusing on the analysis of the communicative functions, and the lexical and the cultural items present in the textbook in use. Our aim is to present the CLIL teacher with the linguistic and didactic implications that he or she should take into consideration when implementing the bilingual syllabuses with their students. In order to do that, we will present our conclusions emphasizing the need for coordination in different content areas, linguistic and communicative contents, between the foreign language teacher and the CLIL subject one.

The universal language of Freemasonry

Freimaurer verwenden eine spezielle Art von Kommunikation: Zeichensprache, Metaphern, Symbole, Neologismen, Fachsprachen, rituelle 'Reisen' usw. Untersucht werden soll hier der masonische Anspruch, eine 'Universalsprache' zu besitzen. Das Gerüst dieser Dissertation ist ein Vergleich der ganzen Bandbreite der Freimaurerei - Orden für Männer, Frauen, Jugendliche, Farbige, sowie quasi-masonische Freizeitclubs - mit nachahmerischen Fraternitäten, wie z.B. den frühen amerikanischen Versicherungsgesellschaften und deren Kommunikationsmodellen. Die experimentelle Methode der Autorin schließt die Erforschung freimaurerischer und anderer bruderschaftlicher Quellen der letzten drei Jahrhunderte ein, sowie Besuche freimaurerischer Institutionen und Interviews mit Freimaurern. Diese Aktivitäten führten zu dem Ergebnis, daß - während die Symbole allgemein anwendbar sind - die schriftliche Freimaurersprache nicht in allen Ländern uniform ist. Die ethischen Lehren, die aus der symbolischen Freimaurerkommunikation gezogen werden sollen, haben einen internationalen Standard erreicht. So ist die Freimaurersprache seit der offiziellen Gründung der Freimaurerei im Jahre 1717 immer noch lebendig. Die rituelle Phraseologie der frühen nordamerikanischen Gewerkschaften und Versicherungsgesellschaften hingegen ist entweder verloren gegangen oder stellt nur noch pompöse Worthülsen dar, die sich um ein weltliches Thema - wie Versicherungen - ranken.

Meta-Environment and Executable Meta-Language using Smalltalk: an Experience Report

Object-oriented modelling languages such as EMOF are often used to specify domain specific meta-models. However, these modelling languages lack the ability to describe behavior or operational semantics. Several approaches have used a subset of Java mixed with OCL as executable meta-languages. In this experience report we show how we use Smalltalk as an executable meta-language in the context of the Moose reengineering environment. We present how we implemented EMOF and its behavioral aspects. Over the last decade we validated this approach through incrementally building a meta-described reengineering environment. Such an approach bridges the gap between a code-oriented view and a meta-model driven one. It avoids the creation of yet another language and reuses the infrastructure and run-time of the underlying implementation language. It offers an uniform way of letting developers focus on their tasks while at the same time allowing them to meta-describe their domain model. The advantage of our approach is that developers use the same tools and environment they use for their regular tasks. Still the approach is not Smalltalk specific but can be applied to language offering an introspective API such as Ruby, Python, CLOS, Java and C#.

Law in a Linguistic Battlefield: The Language of the New State Versus the ‘Language of the Oppressors’ in Ukraine

Article 10 of the 1996 Ukrainian Constitution proclaims that “The state language of Ukraine shall be the Ukrainian language” but continues: “Free development, use, and protection of Russian and other languages of national minorities of Ukraine shall be guaranteed in Ukraine.” Consolidating the position of the state language was at the centre of the "Orange Revolution", but President Yanukovich, elected in February 2010, has committed himself to a defence of the Russian language, as a regional language of Ukraine, and the battle is on to replace the Law on Languages of the Ukrainian SSR of 1989, which is still in force. Ukraine has ratified the Council of Europe’s European Charter for Regional or Minority Languages. This article reflects on the relation between language and law, and endeavours to bring clarity to a situation which at times resembles an overheated kettle about to explode.

The sociolinguistic situation of ǂHoan, a moribund 'Khoisan' language of Botswana

In 2010, we conducted a sociolinguistic survey on the moribund 'Khoisan' language ǂHoan (Ju-ǂHoan), spoken in Botswana at the fringe of the Kalahari Desert. The survey aimed at investigating language use, degrees of multilingualism and language attitude among the ǂHoan speakers. Data collection was done on the basis of a questionnaire. We found that the positive language attitude of individuals towards ǂHoan often conflicts with the community's attitude towards this language, resulting in a split of actual language use between the family and more formal situations. All ǂHoan speakers are at least bilingual speaking the local lingua franca Kgalagadi (Bantu) besides ǂHoan. Most of them are in fact even trilingual, speaking Gǀui (Khoe-Kwadi) in addition to ǂHoan and Kgalagadi. Most of our results stand in line with an earlier sociolinguistic survey on ǂHoan by Batibo (2005a) which was carried out in 2003. In comparing Batibo's results to ours, changes in the sociolinguistic situation of ǂHoan as well as differences between the different villages will be pointed out.

Gender-fair language in the context of leadership: Preventing the lack of fit for women

Women are still underrepresented in leadership due to a perceived a ‘lack of fit’. Thus, women are hired less likely, evaluated unfavorably or are less willing to take over a leadership role than their male counterparts. Because gender-fair language (e.g., feminine-masculine word pairs, German: ‘Geschäftsführerin/Geschäftsführer’, CEO, fem./CEO, masc.) leads to a higher mental inclusion of women compared to generic masculine forms (German: ‘Geschäftsführer’, CEO,masc.), we argue that masculine forms endorse the ‘lack of fit’ for women in leadership, whereas gender-fair language reduces it. Three studies support our assumption. Masculine forms led to a ‘lack of fit’ for women in leader selection: they were hired less likely (Study 1) and evaluated less favorably (Study 2) than their male counterparts. Moreover, women showed less willingness to apply when masculine forms were used in the advertisement for a leadership position. Contrary, no such gender-bias was obtained in case of gender-fair language.

Gender-Fair Language in Organizations: Attracting Potential Leaders and Promoting the Organizational Image of Gender Equality

In many languages, masculine generics are the traditional way of referring to women and men. However, gender-fair forms (e.g., feminine-masculine word pairs) can enhance gender equality: for instance, they counteract male biases in mental associations (Stahlberg et al., 2007) and evoke more neutral perceptions of gender-stereotypical professions (Merkel et al., 2013). Compared to masculine forms, use of gender-fair language in advertisements for leadership positions also helps to achieve gender equality in hiring decisions (e.g., use of German Geschäftsführerin/Geschäftsführer 'CEO fem/masc' instead of Geschäftsführer 'CEO masc', cf. Horvath & Sczesny, 2012). The present research investigates how potential applicants react to the use of gender-fair vs. masculine forms in German job ads for leadership positions (Study 1) and how the respective organization is perceived in response to these forms (Study 2). In Study 1, 251 participants showed higher intentions to apply for a leadership position when it was advertised with a feminine-masculine word pair instead of a masculine form; this was mediated by job appeal and organizational attraction. In Study 2, 154 participants perceived the organization as more discriminatory when masculine forms were used. This was mediated by the organizational image of gender equality. Thus, gender-fair language affects the social perception of a job and the respective organization and can impact social behavior in an organizational context.

Retirement as a “language related major life event” and its consequences on the multilingualism of migrants

The present study investigates life stories of established Italian workforce migrants living in the city of Berne, Switzerland, in regard to “language related major life events” (De Bot, 2007). These events are important in terms of changes happening in the linguistic setting during the life span and influence language development. In this sense, during the process of retirement, a new phase of life begins, which, amongst other things, has to be reorganized in relation to social contact and language use. One of my main questions is how the subjects handle the changes happening within and after the process of retirement in respect to the use of different languages and how this “language related major life event” is constructed and described by the migrants. One of these changes happens due to the fact that, after retirement, the social network at the workplace (the primary source of language input) can get (partially) lost and with it, the use of the local language. The fact that migrants living in Berne are confronted with diglossia (Standard German and Swissgerman), that the Canton of Berne is bilingual (German and French) and that the migrants' mother tongue (Italian) is one of the Swiss national languages, makes this question even more interesting. A second question will consider the influence of the fact that most of the subjects in question lived with the idea of return migration, but as shown in a previous study (Alter/Vieillesse/Anziani, NFP 32, 1999), only a third returned back while another third remained in the host country and the final third chose the commuting option. I will first examine these processes, changes and influences by using quantitative questionnaires in order to obtain general information on demographic data, the social situation, and a self-assessment of linguistic skills. Secondly, I will use qualitative interviews to get in-depth information of the subjects’ life stories and language biographies. The results of this project are meant to deliver insight into different aspects that have not been looked at in detail to this point: which factors of the life stories of Italian workforce migrants, who decided to remain in Switzerland after retirement, influence the linguistic changes in general and the ones happening around retirement in particular.

Prometheus on Mars: Nineteenth-Century Science Fiction and the Language of Romanticism

The development of astrophysics in the nineteenth century drew mankind closer to the planets. For the first time, it was possible to give serious scientific consideration to the possibilities for life on other planets. The greatest leap, however, was in recognizing what was not known, and acknowledging the limits of human intuition. ‘Ideas,’ wrote Agnes M. Clerke, ‘have all at once become plastic’. As the scientific community tested the limits of scientific understanding, it became the role of science-fiction writers to imagine the universe beyond these limits. This paper will examine the ways in which nineteenth-century science fiction used the inheritance of the poetic language of Romanticism to reinstate the centrality of human being in the universe. I will explore the ways in which writers such as Edward Bulwer-Lytton (The Coming Race, 1871) and W. S. Lach-Szyrma (Aleriel, 1883) extended the Byronic hero to envisage extra-terrestrial utopias. The Hegelian systematic mythology described by Byron and Shelley had reimagined paradise and redemption on earth. Through science fiction, this mythology extended out towards the stars. A discourse on the possibilities of extra-terrestrial life became a Romantic discourse on the possibilities of being. The Byronic hero could now find a home not by escaping the shackles of religion, but as an angelic citizen of Venus or Mars. In this way, the paper will explore how science-fiction writers appropriated the language of Romantic poetry to build a bridge between the framework of scientific knowledge and the extent of human imagination.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

Leaving Home: Philo of Alexandria on the Exodus.

For Jewish-Hellenistic authors writing in Egypt, the Exodus story posed unique challenges. After all, to them Egypt was, as Philo of Alexandria states, their fatherland. How do these authors come to terms with the biblical story of liberation from Egyptian slavery and the longing for the promised land? In this chapter I am taking a close look at Philo’s detailed discussion of the Exodus and locate it within the larger context of Jewish-Hellenistic literature (Wisdom of Solomon, Ezekiel’s Exagoge). In Philo’s rewriting of the Exodus the destination of the journey is barely mentioned. Contrary to the biblical narrative, in the scene of the burning bush, as retold by Philo, God does not tell Moses where to go. Philo’s main concern is what happens in Egypt: both in biblical times and in his own days. The Exodus is nevertheless important to Philo: He reads the story allegorically as a journey from the land of the body to the realms of the mind. Such a symbolic reading permitted him to control the meaning of the Exodus and to stay, literally and figuratively, in Egypt.

Evaluation of a User-Adapted Spoken Language Dialogue System: Measuring the Relevance of the Contextual Information Sources

We present an evaluation of a spoken language dialogue system with a module for the management of userrelated information, stored as user preferences and privileges. The flexibility of our dialogue management approach, based on Bayesian Networks (BN), together with a contextual information module, which performs different strategies for handling such information, allows us to include user information as a new level into the Context Manager hierarchy. We propose a set of objective and subjective metrics to measure the relevance of the different contextual information sources. The analysis of our evaluation scenarios shows that the relevance of the short-term information (i.e. the system status) remains pretty stable throughout the dialogue, whereas the dialogue history and the user profile (i.e. the middle-term and the long-term information, respectively) play a complementary role, evolving their usefulness as the dialogue evolves.

Automatic compile-time parallelization of logic programs for restricted, goal-level, independent and-parallelism.

A framework for the automatic parallelization of (constraint) logic programs is proposed and proved correct. Intuitively, the parallelization process replaces conjunctions of literals with parallel expressions. Such expressions trigger at run-time the exploitation of restricted, goal-level, independent and-parallelism. The parallelization process performs two steps. The first one builds a conditional dependency graph (which can be implified using compile-time analysis information), while the second transforms the resulting graph into linear conditional expressions, the parallel expressions of the &-Prolog language. Several heuristic algorithms for the latter ("annotation") process are proposed and proved correct. Algorithms are also given which determine if there is any loss of parallelism in the linearization process with respect to a proposed notion of maximal parallelism. Finally, a system is presented which implements the proposed approach. The performance of the different annotation algorithms is compared experimentally in this system by studying the time spent in parallelization and the effectiveness of the results in terms of speedups.