Proving is convincing and explaining

In mathematical research, the purpose of proof is to convince. The test of whether something is a proof is whether it convinces qualified judges. In the classroom, on the other hand, the purpose of proof is to explain. Enlightened use of proofs in the mathematics classroom aims to stimulate the students' understanding, not to meet abstract standards of rigor or honesty.     

Normative Support for Improving Undergraduate Education in Teaching-Oriented Colleges

A number of recommendations to improve undergraduate education have been put forth in the higher education literature. However, we maintain that the implementation of these recommendations at our colleges and universities is unlikely if norms or group standards of appropriate and inappropriate behavior do not support these recommendations. Consequently, this study investigated the normative support for 6 selected recommendations to improve undergraduate education at teaching-oriented colleges. Results indicate support for 3 of the 6 recommendations: systematic program of advisement, providing students with prompt, formative feedback on assignments, and fostering an egalitarian classroom climate. These are the same recommendations supported by norms at higher education institutions that are more focused toward research and graduate education. The implications suggest that the normative structure that supports teaching improvement efforts may be more similar among various institutions than previous research might have indicated.     

Capturing congruence with a turtle

This note compares turtle geometry and Euclidean geometry with respect to their treatment of similarity and difference of plane figures. It is observed that while the Euclidean notion of congruence faithfully captures a common perception of sameness, the turtle expression of this idea is too weak. To deal with this insufficiency we add a new turtle operation, FLIP, which turns the turtle upside down. This brings the turtle's power to express invariance of shape up to Euclid's.The problem and its solution are viewed briefly from the perspectives of mathematics, computer science and education. The mathematical discussion compares the turtle group and the Euclidean group. The computational discussion focuses on the issue of expressive power of a language and how it may be enhanced. The educational discussion suggests a classroom implementation of the above ideas.     

College presidents' role performance and faculty satisfaction

This research analyzed faculty evaluations of college presidents' role performance with the intent of identifying underlying dimensions and to ask further which dimensions predicted faculty satisfaction with presidents. Data were gathered from 896 faculty members from two technical colleges, three community colleges, two private universities and three public universities in a Western state. The factor analysis revealed three relatively independent dimensions of the presidential role: personal-public image, faculty and student interaction with presidents, and absence of autocratic leadership style. The personal-public image was the most important dimension and predicted faculty satisfaction across the four types of institutions of higher learning. Faculty-student interaction with the president, while not as important a dimension of the presidential role, predicted faculty satisfaction in three institutional types, but not in public universities. The absence of autocratic leadership style predicted satisfaction in community and technical colleges.     

Certifying effect and consumer effect: Some remarks on strategies employed by higher education institutions

The term certification, as used in discussions concerning higher education, is clarified and a distinction made between terminal awards which do have a genuine certifying effect in the sense of procuring admission to a profession and those which do not. Institutions wishing to increase the value of the certifying effect of their awards, seek to do this by stimulating applications for entry to their institution. The longer the queue at the gate the greater the prestige of the terminal award. The ability to influence the certifying effect of an award does not, however, lie with the teaching institutions alone; business, the employers and the professions can, and increasingly do, determine the relative value of awards and of different ways of preparing for the exercise of a particular profession. The case of the business schools in France is described to illustrate how teaching institutions once they are established seek to increase the certifying effect of the diplomas they award by actually reducing the number of graduates. The numerus clausus, as applied to medical schools, provides another example of the same phenomenon. Such strategies lead to what the author describes as consumer effect. Once admittance to a prestige institution has been gained, entry to a position of influence and possibly affluence, is more or less assured. Students in such institutions, in both capitalist and communist countries, have exploited this by persuading teaching staff to acquiesce in a reduction of the demands made by the course, though some directors of institutions have begun to respond by failing more students, seeking to re-establish positions surrendered in the days of student unrest and by these and other means seeking to reduce consumer effect. Teacher training colleges provide an interesting example of institutions having a low but certain certifying effect, producing a high consumer effect. The possibility of deriving a general theory from the proposition put forward in the article is discussed.This is an improved version of an article published earlier in French: Effet certifiant et effet clientèle. Quelques remarques sur les stratégies des institutions d'enseignement supérieur dans les pays développés, ESPRIT, nov./dec. 1978. Translation: Sylvia Collot.     

Retired professors and professional activity: A comparative study of three types of institutions

This study compares the professional activities of retired professors from liberal arts colleges, a comprehensive university, and a major research university. Results show that a large majority of faculty continue to perform professional roles and that strength of ties to colleagues and professional organizations outside the institution are correlated with professional activity at all types of institutions. Major differences among institutions are: (1) liberal arts college and research university faculty show consistency between pre- and postretirement professional activity levels, whereas comprehensive university faculty do not; (2) university faculty show higher levels of participation in a number of professional activities than do liberal arts college faculty; (3) rated importance of research or other creative work is related to professional activity for comprehensive university faculty and rated importance of consulting and university service are related to professional activity for research university faculty.     

More Than a Pipeline Problem: Labor Supply Constraints and Gender Stratification Across Academic Science Disciplines

Employing a nationally representative sample of science faculty in U.S. colleges, we investigate 3 explanations for persisting differences in women's faculty representation across science fields even after adjusting for women's variable representation among doctoral recipients. First, we examine labor market factors: (a) differential growth rates and critical mass in the supply of women doctoral recipients, (b) growth or contraction in academic and nonacademic job opportunities, and (c) presence of foreign-born scholars. Second, we control for institutional explanations such as differential rates of faculty unionization and less receptivity to women at prestigious or research-oriented universities and fields that are applied, soft, or nonlife sciences. Third, gender role explanations are addressed by controlling for gender differences in work experience, work interruptions, and the prestige of doctoral credentials. After finding that none of these explanations account fully for distinctive patterns among science fields in the faculty gender composition, we discuss how they may reflect differences in academic cultures.     

Paranoia: A few final remarks

Paranoid is given a tolerably clear meaning. It is suggested that conceptual understanding must be the first step before seeing how far unconscious or other pressures distract teachers and others from retaining a firm grasp of concepts. Concepts are not relative.     

The American mixture of higher education in perspective: four dimensions

Several nations are currently considering privatization of parts of their higher education systems. This paper, mainly based on the American experience, examines privatizing public institutions as an alternative to establishing solely private institutions.Institutions are analyzed along four dimensions: (1) ownership (public or private); (2) control (external or internal); (3) financing (public or private funds); and (4) mechanisms for public financing (who controls fund distribution and how). There are varying mixtures along these four dimensions both within countries and around the world, with the American system exhibiting the widest range of combinations. Six categories are described, including four common in the U.S.: I. Independent private, where institutions are independent in ownership, in control, and in basic financing; II. Dependent private, independent in ownership and financing but dependent in control; III. Independent public, dependent in ownership but independent in control and substantially independent in financing; IV. Semi-independent public (state/guild type), dependent in ownership, mixed in control, and heavily dependent in financing (less common in the U.S., but typical of Italy and Latin America); V. Semi-independent public (state/trustee/guild type), where control is shared among state, academic guilds and lay boards of trustees but with mainly state-controlled financing; and VI. Dependent public, the model in the Communist nations.Kerr traces the historical path that led to the mixed American system and examines some of its positive consequences, which include institutional autonomy, diversity, and flexibility. Negative results include possible over-responsiveness to short-term pressures, as from the labor market or student preferences for courses of study, and from supporting business or industry.The author concludes that the American experience with privatized public institutions may serve as a model for those elsewhere who now seek greater institutional differentiation, autonomy, and flexibility within national systems of higher education.     

The higher education – economic development ‘connection’ in Massachusetts: Forging a critical linkage?

This paper examines the "connection"between higher education and economic development in Massachusetts, a state whose renowned academic institutions have fueled the rise of a premier high technology industrial district. But in the aftermath to the abrupt demise of the Massachusetts Miracle, the state higher education system sought to develop a new mandate for public service in the 90s keyed to upgrading the state's industrial base and coordinating with labor market needs. These growing involvements in manifestly vocational endeavors seem to reflect a major shift in the models that articulate the higher education-economic development connection in Massachusetts. Thus, it appears that the elite model of the world-class research university sparking numerous industry spin-offs has been joined by newer diffusion-oriented models of academic outreach that extend out from the community colleges into the workplace and even into the K-12 schools.     

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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Science, Society, and Technology—Three Cultures and Multiple Visions

The article reviews the strikingly divergent viewpoints of intellectuals—scientists and non-scientists—about Science and Technology. It shows that while scientists implicitly accept the difference between Science and Technology, to non-scientists that difference is irrelevant. The most important differences between Science and Technology that lie in their relative scales, outputs and accuracy of predictions are highlighted. The complexity of and difficulty in trying to quantify the contribution of science and technology to economic growth are discussed. Views of science and technology that include their societal perceptions are recommended.     

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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The meaning of response categories: How often is “occasionally,” “often,” and “very often”?

Samples of undergraduates from 30 colleges and universities responded in two ways to statements about how often they had engaged in various activities: first by indicating never, occasionally, often, or very often, and second by indicating the number of times they had engaged in the activity. Comparisons of the two sets of responses indicates that: (1) there are wide individual differences in the meaning attributed to each response category; (2) despite individual differences, the group data show clear modal differences between occasionally and often and between often and very often; (3) the median difference in the meaning of each of the response categories is very small between one institution and the next and between types of institutions; and (4) based on the present data, there is no compelling need to develop separate norms for different types of institutions.Presented at the 1981 Annual Meeting of the American Educational Research Association, April 13–17, Los Angeles.     

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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Growth and development of college administrative structures

Current research suggests that organizations tend to move through distinct growth stages from a more person-centered to a more task-oriented bureaucracy. The study reported here examined the structural characteristics of community colleges at regular intervals. Five major growth stages were found, each similar to a theoretically derived growth period.The colleges progressed from having, in their early years, decentralized decision-making, few and flat reporting spans, and few structured and controlled activities, to having, in their later years, many tall reporting spans and many structured and controlled activities. They moved toward centralized decision-making in the middle years and then reverted to decentralized forms in later years.     

Whitehead and a new look at teaching elementary science

If Whitehead is right, science teachers who try to increase student interest by making the science they teach more pure and by covering more material are going about their work in just the wrong way. Science, for purposes of precision in measurement, translates the dynamic world of feeling and force, of causal efficacy (for example, the San Francisco earthquake), into a static representation spatialized and given presentational immediacy (for example, the Richter scale). But notice that the Richter scale isn't very interesting (even as abstract art) apart from its connection, via symbolic reference, to the earthquake. Such reference is essential to give both a sense of reality and a feeling of interes to the subject, but it makes the science less pure, and it takes more time to cover the material. An example of teaching pure and impure formal logic is given as a case study.     

Informal interaction and faculty projections of student ratings of the institutional climate

This study employed the Semantic Differential technique to investigate the relationship between informal interaction with students and the accuracy with which faculty members project students' perceptions of the institutional climate at two colleges of Arts and Sciences. When subdivided into nominal categories of high, moderate, and low interactors on the basis of their frequency of informal, out-of-class contacts with students, high interactors were found to project consistently more accurate student ratings of the climate on a bureaucracy factor than low interactors. A similar, though not consistent, relationship was found between high and low interactors on an intellectualism/scholarship dimension.     

Exploring the Concept of ‘Habitus’ with Preservice Teachers Through the Use of Popular School Films

The thesis of this paper is that it is a productive venture to introduce preservice students to social theories that are typically not a part of teacher preparation programs. Examples of these theories are those associated with terms such as habitus, the carnivalesque, power / knowledge, seduction, detournement, the spectacle,la perruque, (the wig), and the art of making do,as well as others. In this paper, I describe a project that involved exploring the theory of habitus to problematize the tendency of preservice students to not think in terms of relations between what goes on in the classroom and what goes on in society. I introduced habitus by having preservice students read selected print materials and by having them view, analyze, and respond in writing to popular school films. Students also analyzed their experiences in classrooms in terms of habitus, making a connection between theory and practice.     

Personality development and the college experience

Studies of freshman-senior data on undergraduates show that, despite major differences among institutions and students, the direction of net change was basically the same in several diverse colleges. Institutional freshmen means spanned a wide range, yet students became more autonomous, more aware, more integrated, more aesthetically sensitive, more tolerant, more liberal in religious views, and less concerned about material possessions. Although all students tended to change in the same direction at all colleges, they did not become more similar; diversity increased for the total group and, more often than not, diversity increased within each college.When sub-groups of similar students were examined within institutions, different patterns of change appeared, and were systematically related to such factors as college climate, student characteristics, teaching practices and study activities, and student-faculty relationships. Thus, differential change occurred as a function of institutional fit. When there is a close fit change proceeds along lines indicated by cultural and genetic forces and is consistent among diverse colleges. Where there is a misfit — students who have not developed to the general level at which a college operates, or whose development has gone beyond the operating level of a college — significant changes occur which are strongly associated with varied college characteristics and educational practices.The research reported here was supported by NIMH Grant #MH14780-05