A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

The Vernacular Discourse of the "Arab Spring:" An Analysis of the Visual, the Embodied, and the Textual Rhetorics of the Karama Revolution

The Vernacular Discourse of the "Arab Spring" is a project that bridges the divide between the East and the West by offering new readings to Arab subjectivities. Through an analysis of the "Arab Spring" through the lens of vernacular discourse, it challenges the Euro-Americo-centric legacies of Orientalism in Western academia and the new wave of extremism in the Arab world by offering alternative representations of Arab bodies and subjectivities. To offer this new reading of the "Arab Spring," it explores the foundations of critical rhetoric as a theory and a practice and argues for a turn towards a critical vernacular discourse. The turn towards critical vernacular discourse is important as it urges the analyses of different artifacts produced by marginalized groups in order to understand their perspectives that have largely been foreclosed in traditional cultural studies research. Building on embodied/performative critical rhetoric, the vernacular discourses of the Arab revolutionary body examines other forms of knowledge productions that are not merely textual; more specifically, through data gathered in the Lhbib Bourguiba, Tunisia. This analysis of the political revolutionary body unveils the complexity underlining the discussion around issues of identity, agency and representation in the Middle East and North Africa, and calls for a critical study towards these issues in the region beyond the binary approach that has been practiced and applied by academics and media analysts. Hence, by analyzing vernacular discourse, this research locates a method of examining and theorizing the dialectic between agency, citizenry, and subjectivity through the study of how power structure is recreated and challenged through the use of the vernacular in revolutionary movements, as well as how marginalized groups construct their own subjectivities through the use of vernacular discourse. Therefore, highlighting the political prominence of evaluating the Arab Spring as a vernacular discourse is important in creating new ways of understanding communication in postcolonial/neocolonial settings.

Sovereignty and Intervention in the Middle East: From the Fall of the Ottoman Empire to the Arab Spring

This research provides an institutional explanation of the practices of external intervention in the Arab state system from the fall of the Ottoman Empire in 1922 to the Arab Spring. My explanation consists of two institutional variables: sovereignty and inter-state borders. I examine the changes in regional and international norms of sovereignty and their impact on the practices of external intervention in the Arab state system. I also examine the impact of the level of institutionalization of inter-state borders in the Arab World on the practices of external intervention. I argue that changes in regional and international norms of sovereignty and changes in the level of institutionalization of inter-state borders have constituted the significant variation over time in both the frequency and type of external intervention in the Arab state system from 1922 to the present. My institutional explanation and findings seriously challenge the traditional accounts of sovereignty and intervention in the Arab World, including the cultural perspectives that emphasize the conflict between sovereignty, Arabism, and Islam, the constructivist accounts that emphasize the regional norm of pan-Arabism, the comparative politics explanations that focus on the domestic material power of the Arab state, the post-colonial perspectives that emphasize the artificiality of the Arab state, and the realist accounts that focus on great powers and the regional distribution of power in the Middle East. This research also contributes to International Relations Theory. I construct a new analytical framework to study the relations between sovereignty, borders, and intervention, combining theoretical elements from the fields of Role Theory, Social Constructivism, and Institutionalization. Methodologically, this research includes both quantitative and qualitative analysis. I conduct content analysis of official documents of Arab states and the Arab League, Arabic press documents, and Arab political thought. I also utilize quantitative data sets on international intervention.

Validation of the Item-Attribute Matrix in TIMSS-Mathematics Using Multiple Regression and the LSDM

The purposes of this study were (1) to validate of the item-attribute matrix using two levels of attributes (Level 1 attributes and Level 2 sub-attributes), and (2) through retrofitting the diagnostic models to the mathematics test of the Trends in International Mathematics and Science Study (TIMSS), to evaluate the construct validity of TIMSS mathematics assessment by comparing the results of two assessment booklets. Item data were extracted from Booklets 2 and 3 for the 8th grade in TIMSS 2007, which included a total of 49 mathematics items and every student's response to every item. The study developed three categories of attributes at two levels: content, cognitive process (TIMSS or new), and comprehensive cognitive process (or IT) based on the TIMSS assessment framework, cognitive procedures, and item type. At level one, there were 4 content attributes (number, algebra, geometry, and data and chance), 3 TIMSS process attributes (knowing, applying, and reasoning), and 4 new process attributes (identifying, computing, judging, and reasoning). At level two, the level 1 attributes were further divided into 32 sub-attributes. There was only one level of IT attributes (multiple steps/responses, complexity, and constructed-response). Twelve Q-matrices (4 originally specified, 4 random, and 4 revised) were investigated with eleven Q-matrix models (QM1 ~ QM11) using multiple regression and the least squares distance method (LSDM). Comprehensive analyses indicated that the proposed Q-matrices explained most of the variance in item difficulty (i.e., 64% to 81%). The cognitive process attributes contributed to the item difficulties more than the content attributes, and the IT attributes contributed much more than both the content and process attributes. The new retrofitted process attributes explained the items better than the TIMSS process attributes. Results generated from the level 1 attributes and the level 2 attributes were consistent. Most attributes could be used to recover students' performance, but some attributes' probabilities showed unreasonable patterns. The analysis approaches could not demonstrate if the same construct validity was supported across booklets. The proposed attributes and Q-matrices explained the items of Booklet 2 better than the items of Booklet 3. The specified Q-matrices explained the items better than the random Q-matrices.

A Cross-Cultural Examination of the Use of Multimodal Metaphor in English and Arabic Cartoons of the ‘Arab Spring’ in Egypt

El estudio de Lakoff y Johnson Metáforas de la vida cotidiana (1980) ha dotado al campo de la metáfora de un renovado interés, y a éste siguieron numerosas publicaciones abordándolo desde diversas perspectivas. Lakoff y Johnson (1980) aseguran que la metáfora es, de hecho, una característica del pensamiento y, por consiguiente, ya no es una propiedad exclusiva del lenguaje. La metáfora sería en realidad un reflejo de cómo concebimos e interpretamos el mundo en que vivimos, en la medida en que está conformada por nuestras experiencias corporales, un fenómeno al que Lakoff y Johnson se refieren como la “mente corpórea”. La metáfora cumple la función de “comprender” y facilitar la interpretación de un ámbito o experiencia en los términos de otro ámbito o experiencia (Lakoff & Johnson, 1980: 36). Los conceptos abstractos son difíciles de ser pensados per se; consecuentemente, las personas recurren a la metáfora para concebirlos en los términos de otras nociones más concretas que están, en cierto grado, vinculadas a nuestras experiencias somáticas. Si bien no escasean las investigaciones en el campo de las metáforas, parece haber, sin embargo, cierto vacío en lo tocante a la manifestación de la metáfora en modos distintos del modo verbal. Forceville (2009: 19) afirma que uno de los principios fundamentales de la Teoría de la Metáfora Conceptual es la idea de que el variado empleo de metáforas por parte del ser humano sugiere “que piensa en gran medida metafóricamente”. Esto lleva a la conclusión de que la manifestación de la metáfora debería estar presente en los diversos modos del pensamiento, y no únicamente en el verbal. Estos otros modos de pensamiento incluyen, entre otros, las imágenes, la música, los sonidos y los gestos. Asimismo, la mayoría de estudios que se han realizado en el área de las metáforas multimodales ha sido aplicada al terreno de la publicidad. Los anunciantes parecen advertir el ! 2! poder que se invierte en las metáforas, y las usan profusamente para transmitir mensajes a los consumidores. No obstante, recientemente existe un nuevo interés por investigar el uso de metáforas multimodales en las caricaturas (véase, por ejemplo, El Refaie 2003, 2009; Schilperoord y Maes 2009; Yus 2009; Bergen 2003; Marin Aresse 2008). Las tiras cómicas se distinguen de los anuncios principalmente por el hecho de que las caricaturas transmiten una postura negativa frente a un sujeto particular, mientras que los anuncios presentan una actitud positiva. Igualmente, les diferencia el hecho de que las tiras cómicas requieren un conocimiento social y político específico. El presente escrito examina y compara el uso de metáforas multimodales en caricaturas políticas – tanto inglesas como árabes – que retratan la Primavera Árabe en Egipto, con el fin de determinar: (1) si la mayoría de caricaturas son conceptualmente específicas o culturalmente específicas; (2) los principales dominios fuente empleados por los caricaturistas ingleses y árabes para interpretar la Primavera Árabe; (3) si hay semejanzas o diferencias entre las caricaturas inglesas y las árabes en su elección del dominio meta; y (4) observar también cómo los distintos modos (aquí esencialmente los modos verbal y pictórico) contribuyen a representar la Primavera Árabe. El corpus para este estudio se compone de un total de 50 tiras cómicas, 25 de ellas inglesas y las 25 restantes árabes. En cada una de estas tiras debe haber al menos una metáfora que representa la Primavera Árabe o alguno de sus subtemas. Las tiras han sido seleccionadas aleatoriamente a través de Internet. Para el análisis, la investigadora ha seguido el marco teórico propuesto por Bounegru y Forceville (2011) en cuanto a la determinación de metáforas en general, así como la determinación de metáforas multimodales de tipo verbovisual en particular. Por cada tira cómica se ha llevado a cabo un análisis independiente, determinando el dominio fuente y el dominio meta, las metáforas, las asignaciones, qué se está representando verbalmente y qué se representa pictóricamente. Además, la autora ha analizado ! 3! posteriormente si estas metáforas son culturalmente específicas o no, y/o si están relacionadas con metáforas más genéricas o universales. El análisis que comprende este trabajo se divide en dos secciones. La primera parte es un estudio detallado de los dos corpora, abordando los distintos escenarios de los dominios fuente empleados por los dibujantes según su similitud. Esta sección presenta a su vez un análisis de los diversos modos que se utilizan para revelar el dominio fuente así como el dominio meta. Del mismo modo, se incluyen las metáforas específicas manejadas en cada tira cómica y, cuando se da el caso, aquellas metáforas genéricas o universales a las que remite. La segunda sección del análisis presenta una comparativa entre ambos corpora basada en el análisis expuesto en la primera parte. Además, trata varios de los fenómenos lingüísticos a los que han recurrido frecuentemente los dibujantes ingleses y árabes. Estos fenómenos son principalmente la metonimia y la personificación. Igualmente, en esta sección la autora investiga en mayor profundidad las metáforas usadas por los dibujantes ingleses y los árabes, determinando si son ora conceptualmente específicas, ora culturalmente específicas, a partir del hecho de que las metáforas sirven como herramienta para reconocer la forma en que personas distintas, o bien culturas distintas, interpretan varias cuestiones. Por ejemplo, a la hora de conceptualizar el futuro, algunas culturas lo representan espacialmente como delante del hablante, mientras que otras se refieren al mismo como localizado detrás del sujeto (Lakoff y Johnson 1980: 14). Este trabajo ha permitido varios hallazgos. En cuanto a las metáforas empleadas para representar la Primavera Árabe, tanto las tiras inglesas como las árabes han recurrido a una cierta variedad de metáforas. Algunas de las tiras presentan más de una metáfora operando a la vez. Los dibujantes ingleses y árabes parecen haberse apoyado siempre en el modo pictórico para presentar el dominio fuente, así como en el modo verbal para mostrar el dominio meta. ! 4! Además, respecto a la naturaleza de las metáforas que figuran en sendos corpora, casi todas las metáforas son conceptuales en cuanto que se corresponden con nuestras experiencias corporales; no hay, por otro lado, ninguna metáfora culturalmente específica. Asimismo, la única diferencia a este respecto entre ambos corpora es una variación en lo que constituye el prototipo de una categoría particular – aquí concretamente la categoría “primavera” en cada una de las culturas –. En las tiras inglesas, una flor es empleada para representar la primavera, mientras que en las árabes el elemento natural más frecuente para simbolizar la primavera es un árbol.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

A structural model of cognitive-motivational variables as explanatory factors of academic achievement in Spanish Language and Mathematics

In recent years, several explanatory models have been developed which attempt to analyse the predictive worth of various factors in relation to academic achievement, as well as the direct and indirect effects that they produce. The aim of this study was to examine a structural model incorporating various cognitive and motivational variables which influence student achievement in the two basic core skills in the Spanish curriculum: Spanish Language and Mathematics. These variables included differential aptitudes, specific self-concept, goal orientations, effort and learning strategies. The sample comprised 341 Spanish students in their first year of Compulsory Secondary Education. Various tests and questionnaires were used to assess each student, and Structural Equation Modelling (SEM) was employed to study the relationships in the initial model. The proposed model obtained a satisfactory fit for the two subjects studied, and all the relationships hypothesised were significant. The variable with the most explanatory power regarding academic achievement was mathematical and verbal aptitude. Also notable was the direct influence of specific self-concept on achievement, goal-orientation and effort, as was the mediatory effect that effort and learning strategies had between academic goals and final achievement.

The representation of the world in national Arab news agencies: an exploration of (trans)national networks in the official Arab media

The purpose of this paper is to draw a map of the representation of the world and of Arab states as reflected by the countries of the region. To do so, we have analysed the news (4,093 news randomly collected on February and August 2005) produced by the governments of the Arab states through their national news agencies. Several regional and world maps had been constructed to show the official Arab representation of the World, the Arab countries conflict agenda, the persistence of colonial ties (with the European metropolis) and the emergence of new relationships (Asian countries). The representation of the world that appeared in the analysis focuses its interest on the USA, the war in Iraq, the Israel-Palestine conflict, the United Kingdom, France, and Iran. The Arab regional powers organise the flow of information (Saudi Arabia and Egypt) and the colonial past determines the current structure of communication (French-speaking bloc and English-speaking bloc).

Mathematics Game e-Library for Elementary School, study case: Mexico

One of the most relevant subjects for the intellectual formation of elementary school students is Mathematics where its importance goes back to ancient civilizations and which its importance is underestimated nowadays. This phenomenon occurs in Mexico, where 63.1% of the total population of elementary school students between the third and sixth grade have insufficient/elemental level of mathematics knowledge. This has resulted in the need to use a new mechanism to complement student’s classroom learning. With the rapid growth of wireless and mobile technologies, the mobile learning has been gradually considered as a novel and effective form of learning due to it inherits all the advantages of e-learning as well as breaks the limitations of learning time and space occurring in the traditional classroom teaching. This project proposes the use of a Mathematics Game e-Library integrated by a set of games for mobile devices and a distribution/management tool. The games are developed for running on mobile devices and for cover the six competencies related with the mathematics learning approach established in Mexico. The distribution/management tool allows students to reach contents according to their needs; this is achieved through a core engine that infers, from an initial profile, the games that cover the user’s knowledge gaps.

The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.

Do first-year university students understand the language of mathematics?

The aim of the project is to determine if the understanding of the language of Mathematics of students starting university is propitious to the development of an appropriate cognitive structure. The objective of this current work was to analyse the ability of first-year university students to translate the registers of verbal or written expressions and their representations to the registers of algebraic language. Results indicate that students do not understand the basic elements of the language of Mathematics and this causes them to make numerous errors of construction and interpretation. The students were not able to associate concepts with definitions and were unable to offer examples.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

Mathematics notebook, ca. 1714-1718

This heavily illustrated notebook contains extensive notes on spheric triangles and spheric angles. These include rules and examples with their solutions.