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.     

La Croissance des depenses publiques d'education en Allemagne: 1829–1989

Résumé Le retournement de conjoncture du début des années 1970 s'est traduit par un renouveau des travaux relatifs aux cycles longs de type Kondratieff. Face à la fluctuation atypique de certaines variables (prix, production, etc ...), les acquis théoriques antérieurs semblaient avoir épuisé leur capacité explicative. Il devenait nécessaire d'énoncer et de vérifier des hypothèses nouvelles pour expliquer les traits originaux de la crise de structure qui se dessinait. Les résultats des travaux développés au sein du groupe de recherche en Histoire Quantitative et Théories du Long Terme de l'Université de Montpellier I répondent à cette nécessité. Ils introduisent une relation entre les dépenses engagées pour le développement des hommes (salaires, éducation, santé etc ...) et celles consacrées à la croissance matérielle.

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The downturn in the economic situation in the early 1970s gave rise to new work on long-term Kondratieff cycles. Given the atypical fluctuation in some variables (prices, production, etc.), previous theories appeared to have exhausted their ability to explain events. To explain the original features of the structural crisis that was developing, it has become necessary to put forward and test new hypotheses. The results of work carried out by the research group on Quantitative History and Long-Term Theories at the University of Montpellier I meet this requirement. They introduce a relationship between expenditure on human development (wages, education, health, etc.) and that devoted to material growth.

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Zusammenfassung Die Verschlechterung der wirtschaftlichen Situation in den frühen 70ern gab der Arbeit an langfristigen Kontratieff — Zyklen Aufschwung. In Anbetracht der atypischen Fluktuation einiger Variablen (Preise, Produktion, usw.) schienen vorangegangene Theorien die Ereignisse nicht mehr erklären zu können. Um die Ursachen der sich entwickelnden strukturellen Krise erklären zu können wurde es notwendig, neue Hypothesen aufzustellen und auszuprobieren. Die Ergebnisse der von der Forschungsgruppe über Quantitative Geschichte und Langzeittheorien an der Universität von Montpellier I durchgeführten Studien erfüllen diese Anforderungen. Sie stellen Ausgaben für die menschliche Entwicklung (Lohn, Bildung, Gesundheit usw.) und Ausgaben für materielles Wachstum in Relation.

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Resumen La degradación de la situación económica a comienzos de los a~nos setenta ha originado un nuevo trabajo sobre ciclos Kondratieff de largo plazo. Dada la fluctuación atípica de algunas variables (precios, producción, etc.), las teorías previas aparentemente habían agotado su capacidad de explicar los hechos. A efectos de explicar las características originales de la crisis estructural que se estaba desarrollando, surgió la necesidad de adelantar y comprobar nuevas hipótesis. Los resultados del trabajo realizado por el grupo de investigación de Historia Cuantitativa y Teorías de Largo Plazo de la Universidad de Montpellier I satisfacen estos requisitos. Ellos introducen una relación entre los gastos y esfuerzos destinados al desarrollo humano (salarios, educación, sanidad, etc.) y aquellos dedicados al crecimiento material.

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The Changing Debate on Internationalisation of Higher Education

Internationalisation, the growing border-crossing activities between national systems of higher education is losing ground to globalisation, increasing border-crossing activities of blurred national systems which is often employed to depict world-wide trends and growing global competition. This article addresses recent issues of knowledge transfer. It points out tensions between increasing diversity in higher education and efforts to facilitate recognition of prior studies on student mobility. It shows the diversity of steering and management policies with respect to internationalisation and globalisation. Finally, it asks whether globalisation of higher education has to be viewed as a manifestation of turbo-capitalism or could be viewed instead as a move towards global understanding.     

Can Mathematics Education and History of Mathematics Coexist?

Despite the wide interest in combining mathematics education and the history of mathematics, there are grave and fundamental problems in this effort. The main difficulty is that while one wants to see historical topics in the classroom or an historical approach in teaching, the commitment to teach the modern mathematics and modern mathematical techniques necessary in thepure and applied sciences forces one either to trivialize history or to distortit. In particular, this commitment forces one to adopt a Whiggish approach to the history of mathematics. Two possible resolutions of the difficulty are (1) radical separation – putting the history of mathematics on a separate track from the ordinary course of instruction, and (2) radical accommodation – turning the study of mathematics into the study of mathematical texts.     

Torsten Husén: A case of ethnocentrism in U.S. educational research?

This paper documents and discusses the lack of reference by U.S. educational researchers to the work of noted Swedish social scientist and educational researcher, Torsten Husén. The paucity of U.S. textbook or journal citations of Husén's writings and research is interpreted as an example of cultural ethnocentrism and academic imperialism in U.S. educational and psychological research. Crosscultural perspectives, interdisciplinary analyses, and global learning are proposed as methods of overcoming the methodological parochialism, overspecialization, and international fragmentation Husén describes as characteristic of much educational and social scientific research.     

The use of visual media in the service of enriching mental thought processes

Visual media of communication are not just convenient and indifferent technologies for the transmission of knowledge but also, and perhaps mainly, different languages for gathering, packaging and conveying knowledge. The real differences among the media are not so much in the kinds of knowledge they can convey, but rather in the languages, that is — the symbol systems — they uniquely employ. The experienced horrors of Clockwork Orange, or the possible better understanding of group processes after viewing Twelve Angry Men are greatly due to the visual mode and the unique languages of such films, not just the content (which can be read in a book).Media's different and often unique symbol systems have been studied in recent years. It has been found, for example, that different symbol systems call upon different kinds of mental skills and convey different meanings. But above all, media's unique symbol systems cultivate unique mental skills by either activating or overtly supplanting them. By doing so, these symbol systems offer new ways for internal, cognitive, representation. Thus, they can be seen as potentially serving as cultivators of mental abilities.This paper was presented at the IW APP Festival 1980, Amsterdam, The Netherlands, January 1980.     

Choosing competency-based,humanistic and self-directed programs: The contribution of personality and reasoning

Fifty-five college women enrolled in competency-based, humanistic or self-directed education programs completed their California Personality Inventory and listed five reasons for selecting their program. CPI results indicated that self-directed students scored lower than other students on the Femininity Scale (p.001). Using Chickering's seven vectors of change as a framework, the study found competency-based students identifying purpose and competence, humanistic students identifying inter-personal relationships and integrity, and self-directed student identifying autonomy and purpose as reasons for enrolling in their nontraditional programs. The study used these results to question the mythology that adherents to different programs are of different personality types and to argue that differences in perceptions of purpose in education distinguish students in the three programs.     

Modelling students' construction of energy models in physics

One of the main differences between novice and expert problem solving in physics is that novices mostly construct problem representations from objects and events in the experimental situation, whereas experts construct representations closer to theoretical terms and entities. A main difficulty in physics is in interrelating these two levels, i.e. in modelling. Relatively little research has been done on this problem, most work in AI, psychology and physics education having concentrated on how students use representations in problem solving, rather than on the complex process of how they construct them. We present a study that aims to explore how students construct models for energy storage, transformation and transfers in simple experimental situations involving electricity and mechanics. The study involved detailed analysis of problem solving dialogues produced by pairs of students, and AI modelling of these processes. We present successively more refined models that are capable of generating ideal solutions, solutions for individual students for a single task, then models for individuals across different tasks. The students' construction of energy models can be modelled in terms of the simplest process of modelling — establishing term to term relations between elements of the object/event world and the theory/model world, with underlying linear causal reasoning. Nevertheless, our model is unable to take into account more sophisticated modelling processes in students. In conclusion we therefore describe future work on the development of a new model that could take such processes into account.1. CHENE = CHaîne ENErgetique, or Energy Chain. (In French Chêne also means oak).2. Throughout the rest of the paper we use the following simple notation in order to avoid possible confusion between modelling as a process performed by the students, in the domain of physics, and AI modelling of the former modelling process: students' modelling in physics = modelling _SP ; AI modelling (of modelling _SP ) = modelling _AI .3. It has not been necessary to use more sophisticated strategies at the stage of our work reported here. The next system, modelCHENE, will directly address this issue.4. Note that what we refer to in this context as problem solving may in another context be viewed as construction of a qualitative representation for subsequent quantitative problem solving.5. The protocols indicate that students use this as a kind of anchor in their reasoning-some students returning to it in order to resolve impasses. As the current problem solver provides no mechanism for handling impasses we cannot model the reuse of information in any meaningful way.6. We are grateful to an anonymous reviewer for this example.7. This provides the minimum distinction for our initial needs.8. Though there is a difficult step in deciding that the moving object really is the last unassigned object-since that requires setting aside any need to assign roles to, for example, connecting strings etc.9. At the moment we have to provide psCHENE with slightly different rulesets: providing rules with priorities would be more convenient.     

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.     

The structure of subject matter content and its instructional design implications

This paper discusses the analysis of subject matter structure for purposes of designing instruction. The underlying assumption is that subject matter structures provide an important basis for deciding how to sequence and synthesize the modules of a subject matter area. Four types of fundamental structures are briefly described and illustrated: the learning hierarchy, the procedural hierarchy, the taxonomy, and the model. Then a theoretical framework is presented for classifying types of subject mater content — both modules and structures. Finally, some implications of these content classifications are discussed. The classification of modules is hypothesized to be valuable for prescribing strategies for the presentation of single modules, and the classification of structures is hypothesized to be valuable for prescribing strategies for selecting, sequencing, synthesizing, and summarizing related modules. The need to take into account more than one kind of structure in the process of instructional design is emphasized.     

Minority aspirations and the revival of indigenous peoples

The growing world-wide sensitivity to the aspirations of indigenous peoples is to be welcomed. However, there is still a tendency which should be avoided: to lump the claims of indigenous peoples with those of minorities. Indigenous peoples are the heirs of long-established political, social and cultural communities which have been oppressed for centuries or victimized by policies of genocide or forced assimilation into the approved language and religion of the dominating community. These forms of destruction can only be truly ended by returning to indigenous peoples a degree of autonomy which will ensure that they have real control over their future. Indigenous peoples should be able to create institutions, including schools, where their languages, religions and cultures are permitted to flourish without interference.

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Zusammenfassung Wachsende weltweite Sensibilisierung gegenüber den Bedürfnissen einheimischer Völker sind sicherlich begrüßenswert. Vermieden werden sollte jedoch die Tendenz, die Ansprüche einheimischer Völker mit denen der Minderheiten gleichzusetzen. Einheimische Völker sind Erben langansässiger politischer, sozialer und kultureller Gemeinden, die jahrhundertelang unterdrückt oder Opfer politisch motivierten Massenmordes wurden, oder aber die dazu gezwungen wurden, sich der Sprache und Religion der dominierenden Gruppe zu unterwerfen. Diese Art von Zerstörung kann nur dann endgültig beendet werden, wenn einheimischen Völkern die für eine wahre Kontrolle über ihre Zukunft nötige Autonomie zugestanden wird. Einheimische Völker sollten die Möglichkeit bekommen, Institutionen und Schulen einzurichten zur Pflege und Weiterentwicklung ihrer eigenen Sprache, Religion und Kultur ohne Intervention von dritter Seite.

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Resumen La creciente sensibilidad que se registra en todo el mundo ante las aspiraciones de los indígenas es un hecho muy positivo. Sin embargo, aun subsiste una tendencia que debe evitarse: no deben agruparse las reivindicaciones de los indígenas con las exigencias de minorías. Los indígenas son los herederos de communidades políticas, sociales y culturales establecidas desde hace mucho tiempo, que fucron oprimidas durante siglos o víctimas de políticas de genocidios o de asimilación forzada a la lengua y a la religión oficial de la comunidad dominante. Estas formas de destrución solamente podrán suprimirse devolviendo a los indígenas un grado de autonomia que les asegure un real control de su propio futuro. Los indígenas deberían recibir la posibilidad de crear instituciones, e incluso escuelas, donde sus lenguas, religiones y culturas puedan florecer sin sufrir interferencias.

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Résumé La sensibilisation croissante au niveau mondial pour les aspirations des populations autochtones doit être encouragée. Une tendance reste cependant à éviter: confondre les revendications des peuples autochtones avec celles des minorités. Les premiers sont les héritiers de communautés politiques, sociales et culturelles implantées de longue date, qui ont été opprimées pendant des siècles, ou sont devenues victimes de politiques génocides, ou encore forcées à l'assimilation de la langue et de la religion autorisées par la communauté dominatrice. On ne pourra mettre un terme définitif à ces formes de destruction que si les populations autochtones recouvrent un minimum d'autonomie qui leur assurera une maîtrise véritable de leur avenir. Les peuples autochtones devraient pouvoir créer des institutions, dont les écoles, où leurs langues, leurs religions et leurs cultures seraient libres de s'épanouir sans ingérence.

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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.     

Equity issues in local resourcing of education: Community financing of primary schools in Bhutan

Community financing is an important source of supplementary funds for education, particularly where governments are unable to meet all the needs of their peoples. While this is widely recognised, little empirical research has been conducted on the topic. This paper analyses patterns in Bhutan. It observes that until the 1990s few resources for education were provided by communities, but that the scale of financing has increased during the present decade. The paper notes that although communities have in general responded positively to government calls for local inputs, local resourcing has some problematic aspects. The paper focuses particularly on issues of regional, rural/urban and socio-economic equity, and shows how discussion of Bhutanese experiences contributes to the international literature.

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Zusammenfassung Finanzierungen über die Gemeinde sind eine wichtige Quelle der Bezuschussung von Bildung, besonders dort, wo Regierungen nicht in der Lage sind, den Bedürfnissen der Bevölkerung gerecht zu werden. Obwohl dies weitreichend bekannt ist, gibt es kaum empirische Studien zu diesem Thema. Dieser Artikel befaßt sich mit der Situation in Bhutan. Es wird festgestellt, daß die Gemeinden bis zu den 90ern kaum Gelder für die Bildung zur Verfügung stellten, daß aber der Rahmen der Finanzierung in diesem Jahrzehnt gestiegen ist. Der Autor beschreibt, daß trotz einer allgemein positiven Antwort seitens der Gemeinden auf Forderungen der Regierung nach lokalen Finanzbeiträgen, Probleme hinsichtlich lokaler Finanzierungen bestehen. Insbesondere befaßt sich der Artikel mit Themen über regionale, ländliche und städtische und sozialökonomische Gleichheit und zeigt, wie die Diskussion über die Erfahrungen in Bhutan zur internationalen Literatur beiträgt.

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Resumen La financiación a través de la comunidad es una fuente importante de recursos adicionales para la educación, particularmente allí donde los gobiernos son incapaces de satisfacer todas las necesidades de sus habitantes. Si bien este es un hecho ampliamente conocido, existen muy pocos estudios empíricos sobre este tema. El trabajo analiza los modelos existentes en Bhután y observa que hasta los años noventa, eran pocos los recursos financieros provistos por las comunidades, mientras que durante la década actual han aumentado estos niveles de financiación. El estudio observa que, a pesar de que las comunidades, en general, han respondido de forma positiva a las llamadas del gobierno a realizar inversiones locales, la creación de recursos locales tiene algunos aspectos problemáticos. El trabajo se concentra particularmente en problemas de equidad regional, rural/urbana y socioeconómica, demostrando cómo la discusión sobre experiencias bhutanesas presta su aporte a la literatura internacional.

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Résumé Le financement communautaire représente une source importante de fonds supplémentaires pour l'éducation, en particulier quand le gouvernement ne peut répondre à tous les besoins de la population. Bien que ce fait soit largement reconnu, il n'existe que peu de recherche empirique sur le sujet. Cet article analyse différents modèles existant au Bhoutan. Il constate tout d'abord que jusque dans les années 90, les communautés ne fournissaient qu'une faible partie des ressources de l'éducation, mais que cette forme de financement a augmenté au cours de la dernière décennie. Il relève également qu'en dépit de la réaction généralement positive de la part des communautés envers l'incitation du gouvernement à un financement local, ce modèle présente néanmoins des difficultés. L'article se concentre d'autre part sur les questions d'équitabilité entre régions, entre villes et provinces et entre niveaux socioéconomiques, et révèle que la discussion sur les expériences du Bhoutan contribue à enrichir la littérature internationale.

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Educational “excellence” versus teacher “professionalism”: Towards some conceptual clarity

The educational literature of the last several years is replete with both continuing calls for educational excellence reforms and for enhancing and upgrading the teaching profession. Importantly, both types of calls rely on the contribution of science. The educational research-and-development community continues to push for and believe in the notion that educational innovation is based on scientific advances in understanding child development and school functioning. Similarly, many teachers and teacher educators continually call for increased classroom autonomy and social status among teachers, based upon the supposedly scientific nature of their professional training. This paper takes issue with both of these points, arguing that the origin and success of most educationally innovative policies have as their origin the changing political, economic, and social forces visible in the country during the history of American education. Relatedly, since the science of teaching and learning takes a back seat in issues of school policy, teachers cannot and will not be able to convince the public and those in authority in the school that their insights and practices derive from any privileged understanding of the real needs of children. Arguing that teachers should, in fact, have more input into policy decisions in education, the paper concludes with a review and discussion of various strategies currently visible for improving the autonomy and control of classroom educators.     

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     

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.     

Towards a process theory of learning: Feeling the beauty of the world

Alfred North Whitehead's theory of learning is best understood in the overall context of his process philosophy. The rhythmic cycles of growth forming the basis of human learning (romance, precision, and generalisation) are organically connected to the characteristics of life typifying all entities in the universe (self-enjoyment, creative activity, and aim).The kind of balanced education which best enhances growth and connectedness is one in which art and aesthetic appreciation in the broadest sense are dominant. By experiencing the beauty of the sunset, for example, children and adults have access to feelings that flow through them from the world and connect them to distant events taking place in space and time. These bodily feelings at the base of all experience provide concrete ways in which human beings can appreciate the intrinsic value of the world around them.By way of contrast, the methods of 17th century science replace our concrete experience of the sunset with abstract categories that are used to measure the phenomena in question and deny the importance of that experience in understanding the world. Schools' and universities' emphasis upon this methodology produces an imbalanced education with minds in a groove.A renewal of balance in education helps us to understand the false dichotomy between child-centered and and curriculum-centered education. Education for Whitehead must pay attention to both. Moreover, he understands that the academic freedom enjoyed by bands of imaginative scholars in universities is not an article of commerce to be sold to the highest corporate bidder but something to be valued for its intrinsic worth.     

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.     

A two-dimensional analysis of student ratings of instruction

Student ratings of instruction were analyzed in terms of two global factors. One factor, which includes items on advanced planning, presentation clarity, and increased student knowledge, was named pedagogical skill. The other factor taps information about class discussion, grading, and the availability of help and was named rapport. Ratings on the skill factor did not covary with class size or the leniency of the instructor's grading but did correlate with a reasonable external criterion of student learning. Ratings of rapport correlated inversely with class size and directly with average class grade and showed only a weak relationship to the external criterion of student learning. The skill factor showed more interclass stability than the rapport factor. Previous research studies which have examined the reliability and validity of instructional ratings and their relationship to student grades and class size have reported inconsistent findings. These inconsistencies appear to result from an inappropriate unidimensional analysis of ratings which should be examined in terms of two of more separate attitude dimensions.     

The Effects of Storytelling and Story Reading on the Oral Language Complexity and Story Comprehension of Young Children

What began as a case study of intergenerational initiatives in university-based early childhood programs evolved into a comparative study of two different program implementation processes. Despite operating with the same goals, university partners, and resources, two early childhood centers pursued fundamentally different strategies for launching their intergenerational programs. One site followed what we call an explicit intervention with a set timeline and series of planned steps for finding, placing, and involving seniors in classroom activities. The other pursued what we call an emergent (or organic) strategy with no predetermined plan for finding senior volunteers and integrating them into classroom activities. Drawing on data collected from interviews with program staff and parents, and observations of intergenerational activities, this study serves to describe, compare, and contrast these alternative program initiation strategies. Both models are effective, but represent different approaches to valuing the contributions of older adults in the lives of young children.