Confidence is Everything” – Perspectives of Teachers and Students on Learning Mathematics

This paper problematises confidence as a frequently used explanation for performance in the mathematics classroom. I report on an interview-based study of how some English Advanced level (16+) students who have chosen to study mathematics, and their teachers, speak about confidence with respect to the learning of mathematics. I outline what constitutes confident learners for these teachers and, differently, for their students and what the students feel teachers could do to improve the students confident state. I discuss the implications of this for the education of prospective teachers of mathematics.     

HF: Working on mathematics education

First an impression will be given of the way Freudenthal worked on mathematics education during the period after WW II, until the early seventies. The sequence of events of that time form the leading principle of that period when important didactic concepts were being developed. In the following section the chronological order is set aside in an attempt to show how Freudenthal approached research, both in education and into mathematics education. In the next two sections two core themes are dealt with in detail: learning mathematics and developing mathematics education. Earlier didactic concepts are completed and further developed into key notions of a science of mathematics instruction.     

Connecting Teacher Beliefs to the Use of Children’s Literature in the Teaching of Mathematics

This article presents examples that illustrate how teachers use childrens literature in the teaching of mathematics. The examples are related to four curriculum ideologies that have influenced mathematics education in the USA for the last 75 years. It discusses why it is relevant to help teachers understand the ideological positions that influence their use of childrens literature during mathematics instruction, summarizes the four ideological positions, and presents results of a study of how teachers ideological positions relate to their use of childrens literature in the teaching of mathematics. The study examines two research questionsCan an instructional tool be developed that will highlight for teachers the different ways in which they and others use childrens literature to teach mathematics? and Can that instructional tool stimulate teacher discussion and reflection about their own beliefs and the ideological nature of the instructional environment in which they learned (as students) and teach (as teachers)? Study results indicate that both questions can be answered in the affirmative.     

Refugees and education in Canadian schools

This article summarizes some of the findings and recommendations of a research project focusing on the nature and needs of refugee students in Canadian schools. The school performance of refugee students is examined under the following headings: immigration regulations; initial identification, assessment, placement and monitoring; unaccompanied youngsters; at risk students; academic needs; the conflict of cultures. In particular, the article discusses the changing role of the school in the light of recent immigration trends. Many of the findings are applicable to other national settings.

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Zusammenfassung Dieser Artikel faßt einige der Ergebnisse und Empfehlungen eines Forschungsprojekts zusammen, das sich auf die Natur und die Bedürfnisse von Flüchtlingskindern in kanadischen Schulen konzentriert. Die Schulleistung der Flüchtlingskinder wird unter den folgenden Überschriften untersucht: Immigrationsvorschriften, ursprüngliche Identifizierung, Bewertung, Plazierung und Beobachtung, unbegleitete Schüler, Risiko studenten, akademische Bedürfnisse, der Konflikt der Kulturen. Der Artikel diskutiert im besonderen die sich ändernde Rolle der Schule hinsichtlich jüngster Immigrationstrends. Viele der Ergebnisse lassen sich auch auf andere nationale Gegebenheiten anwenden.

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Resumen Este artículo compendia algunos de los resultados y recomendaciones referentes a un proyecto de investigación que enfoca la naturaleza y las necesidades de estudiantes refugiados, en escuelas canadienses. El desempeño escolar de estudiantes refugiados se estudia bajo los siguientes aspectos: regulaciones de inmigración, identificación inicial, evaluación, colocación y asesoramiento; menores no acompañados, estudiantes de riesgo, necesidades académicas y el conflicto entre las culturas. En particular, el artículo trata del cambio que experimenta el papel de la escuela en vista de las tendencias de inmigración recientes. Muchos de estos resultados son aplicables a las circunstancias reinantes en otras naciones.

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Résumé Cet article présente un résumé des résultats et recommandations d'un travail de recherche, qui s'est penché sur les caractéristiques et les besoins de jeunes réfugiés fréquentant les écoles canadiennes. Les résultats scolaires de ces jeunes réfugiés sont étudiés par rapport aux critères suivants: réglementation de l'immigration; identification initiale, répartition, placement et suivi; mineurs non accompagnés; écoliers à risque; besoins intellectuels; conflits culturels. L'article examine en particulier l'évolution du rôle de l'école par rapport aux tendances apparues récemment dans la politique d'immigration. Nombre de ces résultats peuvent être appliqués à d'autres contextes nationaux.

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Child-methods in secondary mathematics

An earlier research project, the Concepts in Secondary Mathematics and Science (Mathematics) project, identified both a hierarchy of levels of understanding in different areas of secondary mathematics, and a number of particular errors which were made by significant proportions of the children tested. Preliminary consideration of these errors and the strategies which appear to have given rise to them suggests that the use of informal naive methods which are limited in their applicability is widespread even at fourth-year level. The suggestion is made that there may be two systems of mathematics coexisting in the secondary school classroom: the formal taught system, and a system of child-methods which are based upon a counting, adding-on or building-up approach, and by which children attempt to solve mathematical problems within a human-sense framework. The difficulties which some children appear to experience in mathematics is suggested to be due in part to these children's non-initiation into the formal taught system. The implication of such a view for teaching and research are indicated.     

The Pseudo-Conceptual and the Pseudo-Analytical Thought Processes in Mathematics Learning

This paper suggests a theoretical framework to deal with some well known phenomena in mathematical behavior. Assuming that the notions conceptual and analytical are clear enough in the domain of mathematical thinking, the notions pseudo-conceptual and pseudo-analytical are proposed and explained. Examples from mathematics classrooms, mathematics exams, and homework assignments are analyzed and discussed within the proposed theoretical framework.The notions pseudo-conceptual and pseudo-analytical proposed in this paper, actually narrow the extension of the notion cognitive by restricting it to the domain of meaningful contexts. Analysis of meaningless behaviors, it is claimed, requires a different theoretical framework. The attempt to analyze meaningless behaviors in the same way as meaningful behaviors is called here the cognitive approach fallacy.     

Socialist mathematics education: Does it exist?

A recent book by Frank Swetz and others has postulated the existence of the phenomenon socialist mathematics education. In this paper we consider critically Swet's arguments and assertions and suggest an alternative methodology whereby one might attempt to describe socialist mathematics education.     

Should Creationism be Taught in the Public Schools?

This article discusses philosophicalarguments relevant to the question of teachingcreationism, especially with regard to developments inthe debate since the early 1990s.Section 1 reviews the newfactions within the creationist movement, and theoverlapping views from young earth to intelligentdesign creationism, as well as non-Christianvarieties. It also considers what are the relevantdifferences for the policy question for private,public schools, and for home schoolers, as well aspossible differences in what it means to teachcreationism. Sections 2 & 3 discuss the main legal argumentsthat have ruled in the public school case, as well asarguments from academic freedom, fairness, censorship,parental rights and majority rule. Section 4 evaluates theepistemological issues regarding competing claims oftruth, and the contention that excluding whatChristians know (Alvin Plantinga) amounts toviewpoint discrimination (Phillip Johnson). Section 5argues that religious protection arguments actuallyfavor excluding creationism more than including it. Section 6 considers the goals of education, especiallyDewey's views on science education, and what theseimply regarding the teaching of a theistic science. In Section 7, I review a new argument of Alvin Plantingabased upon a purported Rawlsian basic right of aparent not to have her children taught anything thatviolates her comprehensive beliefs, and show whyRawlsian agents would reject it.     

A solid base for decisions

To gain insight into the use of the VSNU research quality evaluations (since 1993) in the practice of research and of institutional management in Dutch universities, interviews were held in eight cases evaluated in the first year of this procedure. The main conclusions are that use of these research evaluations is universal, both instrumentally (in decisions directly based on the judgements) and incrementally (in decision-making processes not directly linked to the evaluation). Underlying this is conceptual use: an important change in deans and rectors views of their role in managing research, which they now can realise, because the VSNU research evaluations give them, for the first time, solidly legitimate arguments on which to base strategic decisions. Next to use, other effects can be discerned within universities, pointing to a growing dependency of researchers on managers, necessitating amongst others ever more consciously strategic publication behaviour. Whether quality of research improves in this way, cannot be answered here, but certainly it is more difficult for academics not to engage in research.     

Hierarchies in mathematics education

In mathematics education literature the term hierarchy is used in a number of ways. It is important that the mathematics educator consider the usefulness of the hierarchies presented by various researchers and theorists, in the light of their application to teaching. Current works on mathematical learning hierarchies are illustrated and in particular the work of the mathematics team of the research project Concepts in Secondary Mathematics and Science is examined.     

The decline of the nation-state and the education of national minorities

Many forces are shifting the role of the nation-state and altering our fundamental understanding of how it should function. The author argues that the transplanted European model of the nation-state has become dysfunctional, creating national minorities, serving as an ideological cloak for various forms of oppression and opposing forms of education that would promote diversity of languages and cultures. The decline of territorial sovereignty under the forces of globalization, the move to supranational forms of organization and the emergence of sub-national areas of economic and social development (often city-regions) provide a new range of opportunities for development of minority schooling.

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Zusammenfassung Viele Kräfte verändern die Rolle des Nationenstaates und ändern damit auch unser grundsätzliches Verständnis zu dessen Funktion. Der Autor argumentiert, daß das übertragene europäische Modell des Nationenstaates außer Funktion gesetzt und damit nationale Minderheiten geschaffen wurden. Somit besteht ein ideologischer Deckmantel für verschiedene Arten von Unterdrückung und Widerstand gegen Erziehungsarten, die eine Vielfalt der Sprachen und Kulturen fördern würden. Der Verfall territorialer Unabhängigkeit unter den Kräften der Globalisierung, die Bewegung hin zu einer supranationalen Form der Organisation und die Schaffung regionaler Gebiete wirtschaftlicher und sozialer Entwicklung (oft Stadtbezirke) bieten neue Entwicklungsmöglichkeiten hinsichtlich der Schulbildung für Minderheiten.

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Resumen Son muchas las fuerzas que están cambiando el papel que desempeña el estado-nación y que alteran nuestro concepto básico de cómo este debería funcionar. El autor argumenta que el modelo europeo trasplantado del estado-nación se ha vuelto disfunctional, creando minorías nacionales y sirviendo de manto ideológico para encubrir diferentes formas de opresión y de oposición a una educación que intenta promover la diversidad de lenguas y culturas. El ocaso de la soberanía territorial bajo las fuerzas de globalización, el cambio hacia formas de organización supranacionales y el surgimiento de sectores subnacionales de desarrollo económico y social (frecuentemente en regiones urbanas) proveen un nuevo tipo de oportunidades para el desarrollo de una educación escolar de minorías.

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Résumé De nombreuses pressions modifient le rôle de l'Etat-nation et transforment notre conception fondamentale de son fonctionnement. L'auteur expose que le modèle européen d'Etat-nation qui a éé transposé dans d'autres régions est maintenant atteint de dysfonctionnement, car il crée des minorités nationales, sert de prétexte idéologique à différentes formes d'oppression et fait obstacle à des modèles d'éducation qui encourageraient la diversité des langues et des cultures. Le déclin de la souveraineté territoriale sous la pression de la mondialisation, l'évolution vers des formes d'organisation supranationales et l'apparition de concentrations régionales du développement éconnomique et social (souvent en tant que régions urbanisées) constituent de nouveaux stimulants pour l'élaboration d'une scolarité adaptée aux minorités.

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‘Discrete analysis’ — An approach to fundamental ideas of analysis

The paper investigates conceptual relationships between the Continuous and the Discrete. Differentiation, integration and the fundamental theorem of calculus are based on corresponding operators and a corresponding theorem with functions on finite domains (discrete functions). The final section discusses the possibilities for introducing elements of a discrete analysis into the mathematics curriculum.     

Selbstorganisation: ein neues Paradigma für die Schulpädagogik — oder alter Wein in neuen Schläuchen?

Zusammenfassung Die Schulpädagogik ist seit langem daran gewöhnt, mit Theorieangeboten aus anderen Wissenschaftsdisziplinen konfrontiert zu werden. Mit dem Paradigma der Selbstorganisation liegt gegenwärtig eine sehr komplexe Konzeption bereit, die die Schulpädagogik zur Reflexion über ihren Gegenstand Schule anregen kann. Eine von diesem Paradigma motivierte differenztheoretische Betrachtungsweise von Systemen schärft den Block für die Möglichkeiten, aber vor allem für die Grenzen eines modernene Sozialsystems, wie es die Schule heute ist. Die Fragen, ob Schule kompensatorische Erziehungsleistungen für das Familiensystem erbringen kann, ob unterrichtliches Handeln auch therapeutisches Handeln sein kann, können aus der Perspektive dieses Paradigmas beantwortet werden.

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School education has long been accustomed to accommodating theories from other scientific disciplines. The paradigm of self-organization provides a complex concept which will stimulate reflection on the phenomenon of schools within educational science. Analysis of systems in the light of different theory, motivated by this paradigm, can give a clearer view of the potential and limitations of a modern social system, which is what a school now is. By employing this paradigm, answers can be found to the questions whether schools can deliver education that compensates for family systems, and whether teaching can also provide therapy.

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Resumen La educación escolar desde hace mucho tiempo se ha acostumbrado a adaptar teorías de otras disciplinas científicas. El paradigma de la auto-orgnización provee un concepto complejo que estimulará la reflexión acerca de fenómeno de las escuelas dentro de la ciencia de la educación. El análisis de sistemas a la luz de una teoría diferencial, motivada por este paradigma, podrá proporcionar una visión más clara del potencial y de las limitaciones de un sistema social moderno, de lo que es una escuela ahora. Aplicando este paradigma, podrán encontrarse soluciones a los interrogantes de si las escuelas pueden proporcionar una educacíon que compense sistemas familiares, y si la enseñanza puede también redundar en terapia.

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Résumé L'éducation scolaire est depuis longtemps habituée à assimiler les théories d'autres disciplines scientifiques. Le modèle de l'autogestion fournit un concept complexe qui donnera aux sciences de l'éducation matière à réflexion sur le phénomène de l'école. Une analyse des systèmes à la lumière de la théorie différentielle soutenue par ce modèle peut donner une vision plus claire des possibilités et des limites d'un système social moderne, comme l'est l'école aujourd'hui. Dans l'optique de ce modèle, des réponses peuvent être apportées aux questions si l'école peut remplir un rôle compensatoire par rapport au système familial, et si l'enseignement constitue aussi une action thérapeutique.

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Minority workers or minority human beings? A European dilemma

European identities may be politonymic, toponymic, ethnomyic or linguonymic (Bromley 1984). Each dimension may affect whether migrant minorities are treated as European, and influence their schooling, integration and rights. Treatment and terminology vary in different states and periods of migration. However, the position for immigrated minorities is that they are still largely seen as workers rather than human beings with equal rights. Lack of success in schools is blamed on the migrants themselves rather than the educational system. This construction of migrants as being deficient is parallel to educational practice which falls within a UN definition of linguistic genocide, and contributes to mis-education. If current efforts in international bodies to codify educational linguistic human rights were to lead to greater support for minorities, this could assist in a redefinition of national identities and a reduction of racism and conflict.

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Zusammenfassung Europäische Identitäten können politonym, toponym, ethnonym oder linguonym sein (Bromely 1984). Jede Gruppe kann darauf Einfluß haben, ob Migrantenminderheiten als Europäer behandelt werden und Schulwesen, Integration und Rechte respektiert werden. Noch werden immigrierte Minderheiten jedoch weitgehend als Arbeiter und nicht als Menschen mit gleichen Rechten angesehen. Schulische Mißerfolge werden eher ihnen selbst als dem Bildungssystem angelastet. Diese Darstellung von Migranten als defizitär entspricht derjenigen Handlungsweise im Bildungsbereich, welche unter die Kategorie des linguistischen Genozids definiert wird und welche zu einer mis-education beiträgt. Wenn gegenwärtige Bemühungen internationaler Gremien um die Kodifizierung der Rechte der Menschen auf ihre Sprache Minderheiten unterstützen, könnte dies zu einer Umdefinition nationaler Identitäten und einer Reduzierung von Rassismus und Konflikten führen.

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Resumen Las identidades de los Europeos pueden ser politonímicas, toponímicas, etnomímicas o linguonímicas (Bromley 1984). Cada una de estas dimensiones puede influir en que minorías de inmigrantes scan tratadas de Europeos y con ello en su educación escolar, en su integración y en sus derechos. El tratamiento y la terminología varían conforme a los períodos y las circunstancias de la inmigración. No obstante, la posición que se adopta frente a las minorías inmigrantes es la de considerarlos en gran medida como trabajadores y no tanto como seres humanos de iguales derechos. La falta de éxito en los estudios se atribuye a los inmigrantes mismos, más que al sistema de educación. Esta consideración de los inmigrantes como inferiores es paralela a una práctica de la educación que cae bajo una definición de la Naciones Unidas de genocidio lingüístico y contribuye a la educación deficiente. Si los esfuerzos actuales que las organizaciones internacionales ponen en codificar los derechos humanos lingüísticos de la educación estuvieran destinados a brindar un mayor apoyo a las minorías, esto podría ayudar a definir con mayor precisión las identidades nacionales y a reducir el racismo y los conflictos.

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Résumé Les identités européennes peuvent être politonymiques, toponymiques, ethnonymiques ou linguonymiques (Bromley 1984). Selon leurs affinités avec chacun de ces domaines, les personnes appartenant aux minorités migrantes sont considérées ou non comme européennes, et cela influence leur scolarité, leur intégration et leurs droits. La façon dont ces personnes sont traitées et la terminologie évoluent selon les différentes étapes et périodes de migration. Mais le plus souvent, les minorités immigrantes sont encore davantage considérées comme des travailleurs que comme des personnes bénéficiant des mêmes droits. Les échecs scolaires sont mis sur le compte des migrants eux-mêmes et non sur celui du système éducatif. Le fait que l'on considère les migrants comme inférieurs se reflète dans une pratique éducative que les Nations Unies appellent génocide linguistique et se traduit par une éducation inadéquate. Si les efforts actuels de la part des institutions internationales pour codifier les droits de l'homme en matière de pédagogie linguistique apportaient un plus grand soutien aux minorités, cela contribuerait à donner une rédéfinition des identités nationales et à réduire le racisme et les conflits.

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The effects of educational reform on the content and status of the social subjects in England and wales and the USA: A case study

Over the past decade educational reform has been taking place in the USA and in England and Wales. This paper traces the political pressures to change the social subjects curriculum on both sides of the Atlantic. In England and Wales the new National Curriculum aims to raise educational standards and to increase accountability through a national assessment system. In the USA the Federal Government has set to work on establishing national goals. There is evidence in both countries that the new curricula are emerging from a political process which imposes content and structures upon teachers with little consultation. The paper concentrates on how the social studies curriculum has been affected in this process. It explores the politics of curricular reform by comparing events in the USA and England and Wales and outlines the ways, particularly in the British context, in which the teaching profession has explored the limits of its power and has fought back against central control to make its voice heard.

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Zusammenfassung In den letzten zehn Jahren gab es eine Bildungsreform in den USA, sowie in England und Wales. Dieser Bericht studiert den politischen Druck, der zu einer Änderung des Curriculums in den Sozialfächern auf beiden Seiten des Atlantiks geführt hat. In England und Wales soll das neue nationale Curriculum den Bildungsstandard anheben und die Verantwortlichkeit durch ein nationales Bewertungssystem steigern. In den USA begann die Bundesregierung mit der Festsetzung nationaler Ziele, die den Lehrern Inhalte und Strukturen mit wenig Mitbestimmungsrecht auferlegt. Der Artikel konzentriert sich auf die Auswirkungen dieses Prozesses auf das Curriculum der Sozialstudien. Er untersucht die Politik der Curriculums-Reform, in dem Ereignisse in den USA, England und Wales verglichen werden. Insbesondere im britischen Kontext werden Wege aufgezeigt, auf denen der Lehrberuf die Grenzen seiner Macht erforscht und sich gegen eine zentrale Kontrolle gewehrt hat, um Aufmerksamkeit auf sich zu ziehen.

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Resumen Durante la última década se ha realizado una reforma de la educación en los EEUU, Inglaterra y Gales. Este trabajo esboza las presiones políticas de cambiar los planes de estudio de los sujetos sociales a ambos lados de Atlántico. En Inglaterra y Gales, elNew National Curriculum aspira a crear estándares de la educación y a incrementar la responsabilidad a través de un sistema nacional de valoración. En los EEUU, el Gobierno Federal ha comenzado a trabajar en la fijación de objetivos nacionales. Es evidente que en ambos países los nuevos planes de estudios están emergiendo de un proceso político que impone contenidos y estructuras a los maestros, consultándolos poco o nada. El trabajo se concentra en el impacto que ha sufrido el curriculo de estudios sociales en este proceso. Explora la política de la reforma curricular comparando acontecimientos de los EE UU y de Inglaterra y Gales y proporciona una idea general de los modos, particularmente en el contexto británico, en los que la profesión de enseñanza ha explorado los límites du su poder y se ha defendido contra el control central para hacerse escuchar.

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Résumé Au cours de la dernière décennie, une réforme éducative a été engagée aux Etats-Unis, en Angleterre et au pays de Galles. Cet article retrace les pressions politigues qui ont été exercées pour remanier les thèmes sociaux dans les programmes des deux côtés de l'Atlantique. En Angleterre et au pays de Galles, le nouveau curriculum national a pour but d'élever les niveaux de l'enseignement et d'augmenter la responsabilité par un système national d'évaluation. Aux Etats-Unis, le gouvernement fédéral a entrepris d'établir des objectifs nationaux. Il est évident que dans les deux pays, les nouveaux programmes sont nés d'un processus politique qui a imposé aux enseignants des contenus et des structures en les consultant à peine. L'article se concentre sur les retombées de ce processus sur les programmes d'études sociales. Il étudie la politique de la réforme curriculaire en comparant les événements intervenus aux Etats-Unis et en Angleterre-pays de Galles et souligne, en particulier dans le contexte britannique, la façon dont le corps enseignant a épuisé les limites de son pouvoir et a résisté au contrôle central pour se faire entendre.

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Language in education: Minorities and multilingualism in India

The question of education in India cannot be properly discussed without referring to its socio-linguistic context. This paper provides background information on the linguistic profile of India. The term minorities in the Indian context is defined, and the protection offered to linguistic minorities in the Indian Constitution is examined. A discussion of language policy in Indian education follows in which the recommendations of the different education commissions are analysed. The important issues covered include: the number of languages that are taught, the medium of instruction, and the educational policies regarding speakers of minority languages. The article also discusses different language movements and their impact on Indian education.

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Zusammenfassung Die Frage der Bildung in Indien kann ohne einen Bezug zum sozial-linguistischen Kontext nicht hinreichend diskutiert werden. Dieser Artikel liefert Hintergrundinformationen zum linguistischen Profil Indiens. Der Begriff Minderheiten wird im Zusammenhang mit Indien definiert und der den Sprachminderheiten in der indischen Verfassung zugestandene Schutz untersucht. Anschließend wird die Sprachpolitik im indischen Bildungssystem angesprochen und die Empfehlungen unterschiedlicher Bildungskommissionen werden analysiert. Die wesentlichen abgehandelten Themen beinhalten folgende Bereiche: die Anzahl der unterrichteten Sprachen, die Unterrichtssprache und die Bildungspolitik hinsichtlich der Sprachminderheiten. Der Artikel befaßt sich außerdem mit unterschiedlichen Sprachbewegungen und ihrem Einfluß auf die indische Bildung.

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Resumen La cuestión de educación en la India no podrá discutirse adecuadamente sin hacer referencia a su contexto sociolingüístico. Este trabajo provee informaciones de fondo sobre el perfil lingüistico de la India. Define el término de minorias en el contexto indio y examina la protección que la Constitución de la India ofrece a las minorías lingüísticas. A ello se agrega una discusión de la política lingüística en la educación india, en la que se analizan las recomendaciones de las diferentes comisiones de educación. Fntre otras cosas, los puntos tratados son: el número de lenguas que se enseñan, el medio de instrucción, y las políticas de educación referentes a las personas que hablan lenguuas minoritarias. El artículo también trata los diferentes movimientos lingüísticos y sus impactos en la educación en la India.

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Résumé On ne peut vraiment débattre la question de l'éducation en Inde sans la replacer dans son contexts socio-linguistique. Cet article fournit une information de base sur le profil linguistique de l'Inde. Il y définit le terme de minorités dans le contexte de ce pays et étudie la protection que la Constitution indienne assure aux minorités linguistiques. Il s'ensuit un exposé de la politique linguistique dans l'enseignement de ce pays, incluant une analyse des recommandations des différentes commissions pédagogiques. Les points essentiels traités portent sur le nombre de langues enseignées, la langue d'enseignement et les politiques pédagogiques touchant les locuteurs de langues minoritaires. L'article analyse enfin les différents mouvements linguistiques et leur influence sur l'éducation en Inde.

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Memory in mathematical understanding

Whatever cognitive processes are involved in understanding mathematics, it is clear that one of them is learning. No one is born with an understanding of measure theory, abstract algebra or general topology; the very name mathematics means that which is to be learned (Boyer, 1968). One of the outcomes of learning is remembered knowledge. Indeed it is our contention that memory plays an essential role in the understanding of mathematics, However, what it is that is remembered by students who understand mathematics in contrast to those who do not is by no means a trivial question. In fact, we would like to suggest that there is a gap in this connection between recent developments in memory research and the theory and practice of mathematics education. A second purpose of the present article is to survey briefly the orgins of this gap.     

Curriculum matters: Creating a positive climate for diversity from the student perspective

The purpose of this paper is to identify the factors that predict students perceptions of their institutions success in achieving a positive climate for diversity. This study examines a sample of 544 students at a large, public, predominantly White Mid-Western institution. Results show that students perceptions of the institutions ability to achieve a positive climate for diversity is a reflection of students precollege interactions with diverse peers and the institutions ability to incorporate diversity-related issues into its curriculum. Results also indicate that these perceptions differ by race and gender. Implications for institutional researchers are discussed.     

Mathematics education as a ‘design science’

Mathematics education (didactics of mathematics) cannot grow without close relationships to mathematics, psychology, pedagogy and other areas. However, there is the risk that by adopting standards, methods and research contexts from other well-established disciplines, the applied nature of mathematics education may be undermined. In order to preserve the specific status and the relative autonomy of mathematics education, the suggestion to conceive of mathematics education as a design science is made.Revised and extended version of the paper Mathematikdidaktik als design science, published inJournal für Mathematikdidaktik 13 (1992), 55–70. I am indebted to Jerry P. Becker, P. Bender, H. Besuden, W. Blum, E. Cohors-Fresenborg, Th.J. Cooney, L. Führer, H.N. Jahnke, A. Kirsch, G.N. Müller, H._Chr. Reichel, H. Schupp, Ch. Selter, H.-J. Vollrath, J. Voigt, G. Walther and H. Winter for critical remarks to earlier drafts.     

Cognitive demand of secondary school mathematics items

Items from ten mathematics tests developed at Chelsea College by members of the SSRC sponsored research programme Concepts in Secondary school Mathematics and Science are examined to see whether general dimensions can be found to explain differences and similarities in facility within and across tests.