Math activities for young children

Children use mathematical terminology throughout their daily play. While observing a group of children during play, one is likely to hear comments such as: He has more, These are my numbers, Jane has the biggest half, I'm bigger than you 'cause I'm five years old, Give me the round one, I gave each child one cupcake, and so on.Diane M. Kohl is Assistant Professor of Child and Family Development, The University of Georgia.     

New Contents for New Media: Pavia Project Physics

This hypermedial project deals with a historical and conceptual approach to physics. The core of the project is a certain number of case studies, namely problems or phenomena recounted together with their different interpretations. All case studies present two levels of investigation: the first level is devoted to high school students, the second level is devoted to university students and high school teachers. Our project is directed at a new and better understanding and appreciation of scientific culture.Our methodology is a historical methodology: teaching physics and the history of physics are fellow-subjects. We are not interested in adding the history of physics to teaching physics, as an optional subject: the history of physics is inside physics.Since textbooks usually give one and only one explanation of each physical phenomenon – the true explanation – we would like, on the contrary, to present the phenomena together with different interpretations that factually occurred in the history of physics. We offer four different approaches to the subject of the case study: A. Phenomena, B. Textbooks, C. History and D. Maps.The basic unit of the hypermedia is the presentation , namely a coherent set of information endowed with a definite and complete meaning. From the media point of view, a presentation consists of pictures and/or animations, key-words and/or key-sentences and a speaker explanation. Each approach consists of a certain number of presentations.     

Between epistemology and hermeneutics

In this paper I discuss the hermeneutic and epistemological dimensions of science, and investigate the role which this discussion might play in science education. After a brief review of two main variants of hermeneutic conceptions of science, a general outline is given of the existential-ontological notion of science. Regarding the degree of objectification, the theoretical ways of projecting the world as a scientific theme lie on a continuum between the poles of pure hermeneutics and pure epistemology. Finally, some conclusions for a new pedagogy are drawn.     

The applicability of democratic principles and the mission of the university

The university's mission of serving as a fortress for freedom of speech, inquiry, and criticism of established truths is inextricably connected with democracy. Such a mission can be pursued only in a climate of genuine political and academic freedom. Three other aspects of democracy in the university are discussed: equality of access, university governance, and the public utility of the university. It is argued that equal representation or one man one vote cannot be applied in university governance because it comes into conflict with the notion of competence—a conflict that cannot be resolved by taking votes. Interest groups inside and outside of the university cannot be allowed to interfere with the free pursuit of knowledge. The internal audit, that is, peer review (by, ultimately, the international community of scholars) has to take precedence over vertical review by government bureaucracy.     

Higher educational impact on student objectives: Longitudinal change in Clark-Trow “educational philosophies”

This study explores the impact of higher education on 3,942 arts and sciences students as measured by change in their freshman and senior ratings of four Clark-Trow educational philosophies: vocational, academic, collegiate, and nonconformist (Clark and Trow, 1966). A repeated measures analysis of variance was applied to each of the four philosophies, controlling for sex, entering year, major, parents' educational background, scholastic aptitude, and academic motivation. As expected from Clark-Trow theory, students showed significant increases in academic and nonconformist philosophies, and decreases in vocational and collegiate philosophies. Relationships between independent variables and freshman-senior change suggested post hoc reinterpretation of the dimensions underlying the Clark-Trow phenotypes: i.e., from identification with the college and involvement with ideas to social interests and academic interests (the latter suggested by Terenzini and Pascarella, 1977).     

The curriculum potential of Darwin's Theory of Evolution

Unity and diversity are best reconciled by Darwin's Theory of Evolution. Two major dilemmas related to the study of Evolution are described. The first, concerning pedagogy, can be solved by teaching the topic at an elementary level in the middle school so that the Theory may serve as an advanced oragnizer and returning with in-depth study in the last two years of high school. The second, concerning Faith, is a sensitive issue. Some successful approaches are discussed. The place of Darwin's Theory in the all-elective high school biology curriculum is described as well. The role of the Theory regarding explanations is especially highlighted.     

The instructor self-evaluation form: Development and validation of an ipsative forced-choice measure of self-perceived faculty performance

An ipsative forced-choice college faculty self-evaluation questionnaire was developed. The instrument was validated by comparing self-evaluation scores to student rating scores and by comparing superior and nonsuperior instructors on the basis of student ratings. Both analyses yielded positive, but modest, indications of validity. Implications are discussed relative to the questionnaire's utility in faculty development activities.     

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.     

Fostering Distributed Science Learning Through Collaborative Technologies

TACTICS (French and Spanish acronym standing for Collaborative Work and Learning in Science with Information and Communications Technologies) is an ongoing project aimed at investigating a distributed community of learning and practice in which information and communications technologies (ICT) take the role of collaborative tools to support social construction of knowledge. This community is composed of researchers, graduate students, and high-school teachers and their students, from six schools and four universities in Canada and Mexico. It set out in fall 2000 to develop a community around the general topic of integrating concepts in science school subjects. Once a prototype community is established, it can become a terrain where different aspects could be studied. Subsequently, researchers could gradually take a back seat allowing as well as ensuring the autonomy of the school members involved and, thereby, the viability of the learning community. The set up of the proposed prototype distributed science learning community was therefore an essential yet far from trivial first step. This paper discusses the process of setting up the community and the lessons learned.     

The Humanities in the Era of Cooperation: Beyond C. P. Snow's “Two Cultures”

During the forty years since C. P. Snow decried the existence of two cultures and castigated literary intellectuals for their lack of concern for humanity as a whole, an intellectual revolution in the humanities, driven in part by the intellectual obliteration of boundaries between disciplines and in part by globalization, has reoriented scholars toward engagement in the world and communication with scientists. A recognition that interdependence makes cooperation essential, whether among scholars or among nations, is bringing about an era of cooperation among disciplines and between academic and non-academic institutions.     

The role of reflection in mathematics learning

Reflective abstraction is central to the theory of constructivism as put forth by von Glasersfeld. In coming to know, persons make major cognitive advances by taking their actions as objects of thought. Leamers move beyond being in the action when they engage in reflection. There are serious limitations in the explain-practice method of instruction and active learning. Performing even self-generated mathematical operations does not have the power which results from reflecting on the activity. Problem-centered learning, an instructional strategy which has been shown to provide rich opportunities for reflection, is examined. The nature of reflection in mathematical activity is also considered.     

Using problem solving teaching styles to prepare candidates for the CXC basic proficiency examinations

Two Grade 10 classes in an urban Jamaican High School were taught over a period of one academic year in two problem solving styles: an Explicit Style derived from Charles, and an Implicit Style derived from Isaacs. At the end of the academic year there was no significant difference in their performance on a problem solving test, or on the Problem Solving Profile of the Caribbean Examinations Council's Basic Proficiency papers. The two classes performed much better than the population who sat the Basic papers on the tasks measuring Recall and Algorithmic Thinking but only moderately better than the population on tasks measuring Problem Solving.The teaching project described in this paper was supported in part by grants from the Research and Publications Fund Committee of the University of the West Indies (Mona), and the Wolmers Trust, Kingston. The author wishes to thank the Registrar and the Pro-Registrar of the Caribbean Examinations Council for permission to use the CXC papers and data in this study. A modified version of this paper was presented at the 63rd Annual Conference of the National Council of Teachers of Mathematics held in San Antonio, Texas in 1985.     

Reply to Bereiter's statement on Kohlberg's cognitive-developmental view

Bereiter's claim that the cognitive-developmental distinction between Type I structural reorganization and Type II content learning is a category error is based on his misunderstanding of the distinction. Bereiter misinterprets the distinction as one between the natural and invevitable and the taught. Some ways in which the distinction (and the existence of Type I change) may serve as a positive focus of early education are clarified.

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Résumé L'affirmation de Bereiter que la distinction cognitive-développementale entre la réorganisation structurale du Type I et l'acquisition des connaissances du Type II est une erreur de catégorie, s'explique par le fait qu'il a mal compris la distinction. Bereiter l'a mal interprétée comme une distinction entre ce qui est natural et inévitable et ce qui est enseigné. dans cet article, on explique comment cette distinction (et l'existence du changement du Type I) peut servir comme centre de'intérêt positif de l'éducation préscolaire.

     

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.     

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.     

Classroom control: Some cybernetic comments on the possible and the impossible

The application of basic cybernetic laws and information processing principles to the classroom situation suggests that traditional and modern teaching methods, regarded as control systems, are equivalent in terms of efficiency. As control structures, they embody different principles and are not decomposable. Examination of these principles reveals that the two methods are radically incompatible, in the sense that techniques developed in the one cannot be transferred to the other without dislocation of the system as a whole. Attempts to modernize the traditional method, or to formalize the modern method are ill-conceived. Such mixed methods violate basic laws of information and control, and cannot work. It is suggested that many of the problems underlying the Great Education Debate are a consequence of the impossible state of affairs created by the widespread introduction of mixed methods.     

Critical incidents and critical requirements in mentoring

Many traditional faculty now find themselves working with nontraditional students. New faculty models such as mentoring have emerged in response to the new student. The purpose of this study was to examine the mentoring role at Empire State College, State University of New York, on the basis of mentors' behavior responses to mentor-defined problems. The Critical Incident Technique was the method used to elicit reported and recalled incidents which either facilitated or impeded mentoring. Significant problems cited in the findings included communications gap in mentor/student relationship and the student's incompletion of academic work. Typical corresponding responses to such problems included providing support, demythologizing the learning process, setting behavior limits, and assessing and reassessing student performance. On the other hand, the critical requirements which were inductively derived from the critical incidents, as well as the practical implications which were gleaned from the study, revealed a definite extension of the traditional faculty role.The original document from which this article was adapted, including an extensive bibliography is on file with University of Microfilms International, Ann Arbor Michigan, 48108.     

Some new approaches to research and development funding

Some new approaches to research and development funding, adopted by the United Kingdom's National Development Programme in Computer Assisted Learning are described. The five-year, £2.5 million National Programme, sponsored by seven Government departments, was set up in 1973 at a time of widespread concern about government R & D funding. The funding strategy of the Programme is described in the hope that it might apply to the funding of other educational innovations. Four unusual features are discussed in detail, the aim of the Programme; the role of the Programme directorate in cooperative funding; the approach to evaluation; and the emphasis on project management.The main aim of the Programme, from which all other policy and management decisions derived, was the institutionalisation of innovation. The Programme directorate, by contrast to the central staff of research councils, was active and interventive in the formulation of policy, the design and selection of projects, and their evaluation. A cooperative approach to funding was adopted which permitted projects to combine national and local interests, in an effort to avoid the over-centralisation of some of the large schools curriculum development projects in the UK and the USA, and the parochialism of some higher education research funding. A major evaluation device used in the National Programme was the midterm evaluation of projects. Projects were step-funded for one or two years in the first instance, with continued funding dependent on the outcome of the midterm evaluation. A further novel feature of the evaluation was the existence of independent educational and financial evaluation. Project management skills were considered important in the Programme, and various techniques were adopted, such as virement, to improve project management and control.     

Special handling for special packages: Infant massage

There is a sigh of relief expressed when the notion of infant massage or, as it is sometimes called baby rub, is discussed among parents and professionals. The sigh of relief represents such feelings as, It's about time, or It makes so much sense, or I've been wondering about the very same ideas.illustrations by Barb DunnPhilip G. Rose is a special education teacher at the Early Learning Center in Oneida, NY.     

Different aspects in designing mathematics education: Three examples from the Freudenthal Institute

Three teaching designs are offered. They were developed for 12 to 16 year old pupils taking into account their personal differences in terms of gender (in Making Up the Cube), culture (in Mecca), knowledge, and use of calculators in The integrating calculator. The designs concern the representation of three-dimensional objects in the plane, directions and great circles on the sphere, and exploration of the integrating calculator.