bluuebunny/crossref_metadata_2025 huggingface dataset:
Die Betroffenenrechte nach der DS-GVO und ihre Umsetzung in der kommunalen Praxis
Authors: Buten Sebastian
Published: January 2021

Das Thema Datenschutz hat in der jüngeren Vergangenheit deutlich an Bedeutung gewonnen. Dies ist einerseits begründet durch den Erlass der Datenschutz-Grundverordnung (DS-GVO) und damit der EU-weiten Harmonisierung des Datenschutzrechts, andererseits jedoch auch durch Ereignisse, die mediale Aufmerksamkeit auf sich gezogen haben.

Wie sich am Beispiel von Cambridge Analytica zeigt, wurden bereits in der Vergangenheit verschiedenartige personenbezogene Daten unzulässigerweise verarbeitet. Jedoch können Daten auch bei einer zulässigen Verarbeitung kompromittiert werden. Der effektive Schutz und die ordnungsgemäße Verarbeitung personenbezogener Daten gemäß der DS-GVO sind daher wichtig, um schädliche Ereignisse für betroffene Personen zu verhindern. Ein solcher Schutz ist insbesondere bei der Datenverarbeitung durch Kommunen wichtig, da hier nicht nur einfache Kundendaten, sondern auch sensible Daten (z. B. Sozialdaten gem. § 35 SGB I, § 67 SGB X) verarbeitet werden.

In dieser Arbeit werden die Voraussetzungen einer transparenten und ordnungsgemäßen Erfüllung der Betroffenenrechte betrachtet und herausgestellt (Betroffenengerechtigkeit). Die Arbeit soll darüber hinaus Kommunen die Erfüllung der Betroffenenrechte erleichtern und als Arbeitshilfe dienen, damit die datenschutzrechtlichen Vorgaben praxisgerecht umgesetzt werden können.
The Future of Family Values
Authors: Proietti Pamela Werrbach ,   Institute for Interdisciplinary Research
Published: January 2021

John Paul II's encyclical, Fides et Ratio, describes a profound and causal connection between the teaching of modem Western philosophy and contemporary spiritual dilemmas. The Pope argues persuasively that modem philosophy has led modern man to a loss of faith in the nobility of human reason and the possible existence of meaningful human truths. Modem political philosophers wanted to bring the divine law of revealed Scripture into service of modem philosophic principles of the autonomy of human reason and freedom. John Locke sought to reorganize family life in accordance with such modem principles. Locke clearly modified Biblical teaching to allow for more liberty for the autonomous individual in his imagined liberal democratic society of the future. John Paul II is among those who urge Christians in the West to examine our present social disintegration in light of the foundational ideas that have formed modem liberal societies. We must understand how these ideas have contributed to our present social problems, and determine how to chart the best course for liberal democracy in the new Millennium.
Peirce, Habermas and Moral Absolutes
Authors: Seeman Bradley N. ,   Institute for Interdisciplinary Research
Published: January 2021

Drawing on C. S. Peirce's notion of an "unlimited community of investigators," Jürgen Habermas seeks to construct binding moral norms apart from independently existing moral absolutes. But Habermas fatally compromises the usefulness of an unlimited community for his project. Where Peirce relied on the notion of a uniform "outward clash" with external reality or "secondness" to lead all members of his unlimited community of investigators to a "predestinate" point of convergence, Habermas lacks any notion of an independent moral reality to bring about this convergence throughout his unlimited community of constructors. Apart from devising a substitute secondness to replace the clash with external moral reality, Habermas' unlimited community will spin apart into countless divergent moral constructs, Habermas' attempts to devise a substitute secondness fouruier on a lifeworld dilemma he never resolves, Habermas' difficulties are instructive, suggesting a possible way forward.
The American Experiment and the Crisis of Community
Authors: Meagher Michael M. ,   Institute for Interdisciplinary Research
Published: January 2021

The American experiment with democracy faces challenges due to the waning of the moral and religious underpinnings of the original social contract. Religion has played a key role in the development of an American civil society from the pre-revolutionary era to the present. The lessons of historical interpretation have much to offer in illuminating the nation's civil society. This essay evaluates Gordon S. Wood's thought, contrasting it with Alexis de Tocqueville and others, in light of the American tradition of political thought. Wood is a proponent of the civic republican approach to history, which advocates an expanded public sphere and is sceptical of the private realm of civil society. This approach, however, is outside the mainstream of American thought, for civil society has formed an essential component of American life from the earliest days of the colonial and national periods. A promising way to repair the breach in the American social contract is through a renewed awareness of the role of Christianity in the nation's genesis.
Freedom of Religion in Post-Soviet Russia
Authors: Kazmina Olga ,   Institute for Interdisciplinary Research
Published: January 2021

The religious situation in Russia has changed greatly following the collapse of communism in 1991. Although the process was more difficult and contradictory than expected in the early 1990s, Russia has made considerable progress on its way to religious freedom. Now, people can openly profess their faith. To evaluate the degree of religious freedom in contemporary Russia, it is necessary to examine legal acts such as the Constitution arui laws on religion, and how they are implemented, the dynamics of the denominational structure of the population, and the status of different denominations in society. During the 1990s, there were crucial changes in such spheres as the principles of church-state relations, religious legislation, and the role of religion in the social, political, and cultural life of the country. Religion is recovering its place in society lost during the Soviet period, and can play a significant role in overcoming the social crisis and contribute to building a civil society. The growing interest in religion can be reconciled with freedom, pluralism, and tolerance.
Civil Society and Religion in Post-Communist Hungary
Authors: Kamarás István ,   Institute for Interdisciplinary Research
Published: January 2021

How can the churches in Hungary today help in building civil society without becoming politicised or submerged in a secular world? This essay focuses on the different roles and activities of larger and smaller churches in Hungarian civil society, especially Catholic congregations and smaller communities, new religious movements and groups, the "official church," and the "civil church," Churches and religious communities in Hungary are still too rigid in their institutional forms to become an organic part of civil society. To preserve their unique calling churches have to play the role as a participant of a special form of civil society--the "contrast-society." Only churches institutionalized in an appropriate way will be able to accommodate civil society without being assimilated by it. Thus, churches can become part of civil society mainly in the form of a dialogue. Hungarian churches, religious groups, and movements are just at the beginning of a promising process.
Renewing the Liberal Arts
Authors: Gruenwald Oskar ,   Institute for Interdisciplinary Research
Published: January 2021

This essay explores the conceptual foundations of C. S. Lewis' pilgrimage to a Christian worldview and its implications for Christian scholarship in the Third Millennium. C. S. Lewis' essential Christian worldview has three distinct yet complementary strands: The Tao, Natural Law, or the moral sense; the ecumenical inspiration of Mere Christianity; and the quest for truth and authentic values in the real world. These three strands converge in Lewis' own pilgrimage and witness to the immediacy and relevance of religious experience. Curiously, the reality and truth of the Christian vision finds eloquent exposition in Lewis' lucid prose In the recounting of this consummate storyteller, the Christian worldview emerges as both real and transcendental or "numinous," whose truth is found in historical evidences and lived experience. It is for this reason that Lewis is aptly called an apostle to the sceptics. Lewis' literary imagination thus provides inspiration for a Christian humanist paideia as propaedeutic to renew both liberal arts education and the culture of liberalism.
Naturalism, Theism and Objective Knowledge
Authors: Byl John ,   Institute for Interdisciplinary Research
Published: January 2021

This essay proposes that various forms of relativism and naturalism are self-refuting. The rational defense of any worldview requires the prior acceptance of the existence of other rational minds, mental causation and free will, an objective language, and objective logical and rational standards, A worldview is self-refuting if its defense necessarily presumes entities that are explicitly denied by the worldview. In contrast, theism provides the epistemic and metaphysical basis to fully account for our diverse knowledge. Liberal arts education is in a crisis due to the fragmentation of knowledge and loss of purpose caused by the combined action of pragmatic deconstruction and scientific reductionism Only by regaining a full appreciation of the depth and comprehension of the Christian worldview can we recapture the cohesive unity in diversity of a genuine liberal arts education.
In Search of America's Great Awakenings
Authors: Adie Douglas K. ,   Institute for Interdisciplinary Research
Published: January 2021

This essay re-examines Robert W, Fogel's thesis in The Fourth Great Awakening and the Future of Egalitarianim, which sees America's religious revivals as pivotal in the transformation of culture through the political process, ultimately producing greater equality. Fogel's work thus provides the context for examining the impact of evangelical Christianity on American culture. Curiously, Fogel's approach brackets the underlying spiritual reality beneath the conversion experience, and assumes the primacy of social, economic, arid political processes in U.S. history. Yet, the Puritan Awakening the nature of overlapping historical cycles leading to greater equality, and the increasing secularization of American society-all beg the question of interpreting U.S. history, and leave open the prospect of spiritual renewal which would characterize America's Fourth Great Awakening. Hence, the essay tries to regraft some of the spiritual roots onto Fogel's secular interpretation of historical events and the dynamics of American culture.
Wisdom Literature and Higher Education
Authors: Thomas Jesse J. ,   Institute for Interdisciplinary Research
Published: January 2021

The Biblical and Deuterocanonical Wisdom books have a great deal to contribute to contemporary higher education, which has been affected adversely by the secularization of the past centuries, most recently by postmodernism. This essay traces the development of the Wisdom literature from Proverbs to the Gospel of John and its implications for higher education in five areas: the integrative; ethical; personal; enjoyable; and transformational aspects of learning Higher education rooted in the Wisdom literature is uniquely capable of addressing each of these issues in a way that education cut off from traditional values cannot. Practical suggestions address such concerns as general education courses, classroom cheating and ethical and professional responsibilities of faculty. For example, some general education courses should be required of senior students in order to integrate courses that they have already completed. The conclusion follows that a balanced practice of the five areas can serve as an antidote to the ills of higher education without degenerating into the repressive educational environment feared by postmodernists.
The Chácobo Indians of the Amazon
Authors: Prost Gilbert R. ,   Institute for Interdisciplinary Research
Published: January 2021

This essay is about a life-affirming social revolution grounded in what theologians call Natural Law or the Orders of Creation, that innate universal Ground Plan within us which informs men everywhere how to live. It is about a social experiment in communicating a meta-culture of meaning and life to a dying monolingual, semi-nomadic Amazonian tribe living on the edge of extinction. As the Bolivian command culture slowly impinged on every aspect of the Chácobo lifestyle, this primitive, egalitarian, command-less, duty-based structured society, like so many other tribes before them, would eventualty disappear into the fabric of the dominant culture within a generation. The Chácobo would cease to exist as a tribal people. To prevent this, the society had to restructure itself from a defensive culture designed to reduce anxiety over existence in isolation to a pro-active culture designed to maximize human freedom within a universal moral order. Following the Plan of the Maker, Chácobo society, within a span of twenty-five years, moved from the edge of extinction to vigor and health, and from day-to-day existence to long-range planning while experiencing a five to six-fold irncrease in population growth.
The Intrinsic Worth of Persons
Authors: Colosi Peter J. ,   Institute for Interdisciplinary Research
Published: January 2021

This essay examines various sources of worth intrinsic to persons, and offers an overview of Peter Singer's ethical thought. Critics of Singer's ethical philosophy admit that there is a seemingly insurmountable obstacle to a definitive critique of his views. The "Singer Problem" is the notion that there are no facts intrinsic to persons capable of grounding their dignity and equality. Yet these are not so much critics as thinkers who do not like the conclusions that follow from unquestioned premises which they share with Singer: an overly rationalistic approach to reality, and the view that goodness is not an objective property of things. By exploring the uniqueness of persons, John Crosby shows a deep source of worth intrinsic to persons, which grounds dignity and equality. Based exclusively on traits common to all persons, Singer's notion of personhood excludes love from ethics; but love has a place in ethics.
Charles Darwin and Intelligent Design
Authors: Lamoureux Denis O. ,   Institute for Interdisciplinary Research
Published: January 2021

Many assume that Charles Darwin rejected outright the notion of intelligent design. As a consequence, the term "Darwinism" has evolved to become conflated with a dysteleological interpretation of evolution. The primary historical literature reveals that Darwin's conceptualization of design was cast within the categories of William Paley's natural theology, featuring static and perfect adaptability. Once Darwin discovered the mechanism of natural selection and the dynamic process of biological evolution, he rejected the "old argument from design in Nature" proposed by Paley. However, he was never able to ignore the powerful experience of the creation's revelatory activity. Darwin's encounter with the beauty and complexity of the world affirms a Biblical understanding of intelligent design and argues for the reality of a non-verbal revelation through nature. In a postmodern culture with epistemological fourmulations adrift, natural revelation provides a mooring for human felicity.
Science, Religion and a Culture of Life
Authors: Dilley Stephen C. ,   Institute for Interdisciplinary Research
Published: January 2021

For those who wish to affirm a culture that values human life, the relationship between science and religion continues to be of import. Some, like Edward O. Wilson, think that naturalistic science will eventually account for all phenomena, even religious experience itself. This essay considers Wilson's hypothesis by surveying three classic explanations of universal religious belief: Sigmund Freud's projection theory, Charles Darwin's evolutionarry paradigm, and John Calvin's sensus divinitatis. Both Freud's and Darwin's views suffer from self-referential and evidential problems. In contrast, Calvin's model handles well major objections of religious pluralism and atheism. Of these three, Calvin's view is superior. Religion may not be reducible to a naturalistic explanation, and those who wish to promote a culture of life ought to view the relations between science and religion in a non-Wilsonian fashion, eschewing reductionism.
Economic and Political Markets
Authors: Schansberg D. Eric ,   Institute for Interdisciplinary Research
Published: January 2021

Discussions about economics and politics often generate more heat than light. What do the dictates of Scripture and insights from the field of political economy bring to the table? Of greatest importance, in a world of sinful people, economic markets have the ability to constrain immoral behavior by connecting moral behavior with financial and social reward. Yet, freedom still allows the possibility of unjust actions in economic markets. Thus, some potential role for government obtains. From there, the tension is between the Utopian desire for government to constrain justly and the practical realities of government in a fallen world. At the end of the day, the Christian cannot be fully content with either economic or political markets. They are left with the clear Biblical call to act with righteousness and justice in their own spheres of influence and the possibility of defending the rights of others through politics in the limited occasions when government policy is an ethical, appropriate, and practical means to godly ends.
Moral Reflection and Markets
Authors: Halteman James ,   Institute for Interdisciplinary Research
Published: January 2021

The idea that the pursuit of self-interest in economic life would lead to social harmony had a positive effect on production, but it led many to assume that virtue arui moral reflection were no longer essential in socializing human passions. As specialization and trade extended markets, workers followed the jobs, leaving their social and moral moorings behind. The fragmenting of social capital made it difficult to foster social trust and cooperation. Neoclassical market theory does not interface well with other disciplines given its scientific approach of rational choice analysis. Non-egoistic motivations like values and beliefs are usually excluded from economic thinking so moral reflection is relegated to economic applications only. These factors reduce the impact of moral reflection in economic life. Yet self-regard, market flexibility, and a scientific approach to markets all have positive qualities for integrating economic and moral life.
Perspectives on Work in American Culture
Authors: Mizzoni John ,   Institute for Interdisciplinary Research
Published: January 2021

This essay compares five different conceptions of the nature of work: capitalist, Christian, Buddhist, republican, and environmentalist. The capitalist perspective on the nature of work profoundly affects our common conceptions about the nature of work as well as our experiences with work. Nevertheless, there are also non-economic conceptions of the nature of work that are effective, influential, and contribute to a moral marketplace. The four non-economic traditions suggest ideals of what work ought to be, and ways through which one may transform the experience of work while living in a democratic capitalist culture. Further, the fact that the four different non-economic traditions can agree in characterizing work as a calling gives credence to the notion that an interdisciplinary and interfaith conception about the ideals of work can be attained.
The wolf at the door—1957 style
Authors: Bernstein Allen L.
Published: January 2021

The facts of installment buying and repossession laws are explored in a consumer mathematics course.
Critical responsibilities in education today
Authors: Dodds B. L.
Published: January 2021

An educator looks at mathematics in the secondary schools and makes some observations concerning present day conditions.
Mathematics as a profession
Authors: Ettlinger H. J.
Published: January 2021

Why teach? You will find an answer in the remarks of an instructor who enjoys teaching.
Historically Speaking,— Using the history of mathematics in teaching on the secondary school level
Authors: Freitag Herta T. , Freitag Arthur H.
Published: January 2021

More than two thousand years ago, Pythagoras lectured on the power of number, meaning only integers and fractions. He reiterated again and again, “Number rules the universe; the essence of all things is number.” Then one day he evaluated the diagonal of a unit-sided square. Alas, there was no number as he understood number which gave an answer.
Robert Recorde's Whetstone of witte, 1557
Authors: Sanford Vera
Published: January 2021

There is little that is original in the content of Robert Recorde's Whetstone of witte. Yet this book contains the “pair of twin paralleles of one lengthe” which Recorde used to mean “is equalle to.” This was his own invention
A new approach to high school mathematics
Authors: Cogan E. J.
Published: January 2021

These are days in which many are seeking a new curriculum pattern in mathematics. In broad outline, this article proposes a new pattern for your consideration.
Testing Time: Testing the understanding of the concept of equation
Authors: Nichols Eugene D.
Published: January 2021

There are basically two types of tests used by teachers of mathematics: objective and subjective. In objective tests, the judgment of the scorer docs not affect the score; the objective test scored by a number of persons yields the same score on each scoring. Different scores on subjective tests frequently result not only when scored by different persons, but even when scored by the same person at different times.
The mathematics and science teacher of tomorrow
Authors: Zant James H.
Published: January 2021

How can we teach more and better mathematics?
Sequence and range of high school mathematics
Authors: Bruns Richard F. , Frazier Alexander
Published: January 2021

Here's a look at course offerings in large cities.
Teaching the etymology of mathematical terms
Authors: Mulcrone T. F.
Published: January 2021

Hints on how to make use of word origins and meanings in a mathematics class.
Tips for Beginners: An approach to solving word problems
Authors: Singleton Marilyn C.
Published: January 2021

Sometimes students become “answer conscious” when solving word problems. They feel that the main goal is to find some magic number they can call the answer. Many times the choice of the fundamental operation is a guessing game, depending to some extent on the size and position of the numbers in the problem.
The ancients versus the moderns, a new battle of the books
Authors: Kline Morris
Published: January 2021

Teachers of mathematics must face the issues pertaining to the reform of the high school curriculum. Morris Kline clearly and forcefully expresses one point of view. He has been kind enough to consent to an arrangement which enabled A. E. Meder, Jr., Rutgers University, to formulate a reply published on pages 428-433 of this issue.
Historically Speaking,— A history of computers, II
Authors: Larrivee Jules A.
Published: January 2021

The idea of using telephone relays as components of an automatic digital computer was first introduced by G. R. Stibitz, and a computer built along these lines was demonstrated in 1940. Since that time improvements have been made and several such computers built by Bell Telephone Laboratories are in daily use.
What is wrong with Euclid?
Authors: Meder A. E.
Published: January 2021

Euclid's achievement will always be remembered, but should our high school course in geometry be based on Euclid's postulates? Isn't it possible that with today's knowledge of mathematics a better set of postulates could be found?
Historically Speaking,—: Journey to Delos
Authors: Guggenbuhl Laura
Published: January 2021

In recent years, a number of delightful magazine articles [1]† have appeared telling about the beauties, the ancient history, and the friendliness of the Greek Islands. At what better time could one say that one of the most famous of the Greek Islands played host (even if only in name) to one of (he most famous of the mathematical problems of antiquity?
Historically Speaking,— Axioms in algebra—where did they come from?
Authors: Baumgart John K.
Published: January 2021

Today we hear a great deal about revision of the mathematics curriculum on both the high school and college levels. At the high school level some proposals involve the presentation of algebra from a more axiomatic viewpoint—in much the same way as geometry has been built logically from a set of axioms. It is interesting and instructive to trace the development of the axioms for algebra.
Computer programming for high schools and junior colleges
Authors: Littlefield Darrel G.
Published: January 2021

A proposed course in computer programming for secondary schools.
An application of the law of sines: How far must you lead a bird to shoot it on the wing?
Authors: Clifford Edward L.
Published: January 2021

Important experience in problem-solving where mathematics is applied to a practical problem, an experience not gained through textbook problems, is provided by problems of the type suggested here.
Optimal length of play for a binomial game
Authors: Mostbller Frederick
Published: January 2021

In a game where A plays against B, how many trials should A choose to play to maximize his chance of success?
Tips for Beginners: Building an electrical device for use in teaching logic
Authors: Giles Richard P.
Published: January 2021

In a mathematics course designed for prospective teachers at the University of Illinois, the students were required to design and build a project that could be used in a high-school classroom to illustrate or demonstrate some mathematical concept. Since earlier in the semester we had discussed the growing emphasis that is being given in high schools to the study of symbolic logic, I decided to build an electrical device that would graphically represent the truth table and the various operations which can be performed on propositions.
Historically Speaking,—: Two medieval methods for determining the obliquity of the ecliptic
Authors: Kennedy E. S. , Sharkas Haydar
Published: January 2021

The sun, in its daily trip overhead from the eastern horizon to the west, seems to travel along the arc of a circle on the celestial sphere. On the first day of spring, when the lengths of day and night are equal, the sun's path is a great circle, the celestial equator (Fig. 1). As the season advances, the sun moves slowly northward along the ecliptic, and its daily path is then, very nearly, one of the small circles which are parallel to the equator.
New trends in algebra and geometry
Authors: Meserve Bruce E.
Published: January 2021

It would be possible for us to discuss some new mathematics programs which have been spectacular succcHses. It would also be possible for us to discuss situat ions in which new programs haYe been dismal failures. By quoting the appropriate experts and by selecting the appropriate examples, we could appear to prove almost any point that we wished to endorse.
A nonmodular field: constructive approach
Authors: Ellis Wade
Published: January 2021

Some interesting and important ideas about groups and fields
Improving study habits in mathematics
Authors: Randall Karl
Published: January 2021

“The student may experience a few more difficulties and frustrations at first, but he should finish the course stronger if he hasn't been carried along throughout the year on the shoulders of the teacher.”
Five recommendations to school systems for improving secondary mathematics instruction
Authors: Mueller Francis J.
Published: January 2021

Five points for serious and constructive self-examination
III. The characteristic equation; minimal polynomials
Authors: Feldmann Richard W.
Published: January 2021

The characteristic equation of a matrix M is found by expanding the determinant of M − xI, where I is the identity matrix, and setting it equal to zero. The roots of this equation are the characteristic roots of M.
Jungle-Gym Geometry
Authors: Ranucci Ernest R.
Published: January 2021

DID you ever look at something you've looked at time and time again, something utterly familiar to you, something commonplace, and suddenly realize that you haven't the least idea of its construction? That's how I felt when I looked at a jungle gym, plaything of the younger set, and found that I hadn't the foggiest notion of its construction. I knew that it was made by joining lengths of pipes to special fittings, and that kids enjoyed playing on it, but that's about all.
A Visual Aid for an Elementary Applied Maximum Problem in Calculus
Authors: Viertel William K.
Published: January 2021

A SET of open-top rectangular boxes with square bases, made of transparent sheet plastic, has been found useful in dramatizing a typical applied maximum problem in calculus, and in convincing students that the methods of calculus really do give the dimensions for the box of maximum volume.
Historically Speaking– Debatable or Erroneous Statements Relating to the History of Mathematics
Authors: Read Cecil B.
Published: January 2021

The student or teacher who consults several references to obtain information about some historical point in the development of mathematics may, at first, be shocked to find definite discrepancies. Further study may reveal that while in certain cases the reference seems to be definitely in error, in other cases the point may be debatable. Sometimes the error seems clearly to be typographical; in other situations the author has been careless in drawing too-general conclusions; in still others the situation is simply one in which even competent research has not yet produced clear-cut evidence. Unfortunately, in some cases, reading of the references indicates an error caused by repeating an unchecked statement made by some previous author.
Classics in Mathematics Education: The Teaching of Mathematics
Authors: Young J. W. A.
Published: January 2021

In the study of the pedagogy of mathematics, the point of view is sometimes that of the manner in which the subject matter is arranged and developed; at others that of the manner in which it is presented to the pupils. To introduce this distinction into the nomenclature, the former has sometimes been called method and the latter mode.
International Mathematical Education: Some Recent Efforts for Improvement of School Mathematics in India
Authors: Kapur J. N.
Published: January 2021

Editor's Note.—The Mathematics Teacher (India) is a new journal in mathematics education directed mainly at secondary school teaching. With the September October 1966 issue it began its third year of publication.
An Interesting Observation Regarding the Sine Curve
Authors: Paisley David
Published: January 2021

I was having some difficulty with a transparency (Fig. 1) that I had made for my trigonometry class. The transparency had a tendency to curl and roll into a cylindrical shape. I then noticed that if the cylinder were twisted to a particular size, the sine curve wrapped around the cylinder in a shape that resembled an ellipse (Fig. 2). To obtain this particular size, the cylinder was twisted so that the points labeled K matched, and the points labeled O matched. The sine curve wrapped around the cylinder about three times on the particular model I had.
Door Spaces
Authors: McGehee Earl E.
Published: January 2021

It has been my experience that a student beginning the study of topology has a tendency to compare a subset of a topological space to a modern spring-operated door. If such a door is not open, it is closed; the student tends to attribute this same property to a subset of a topological space. That this is indeed not the case follows if one considers the interval [0, 1[, which is neither open nor closed when considered as a subset of the real numbers with the usual topology. But it is interesting to consider a topological space with this property. Such a space should obviously be called a door space. Hence we have the following definition.
Experimental Programs: A Study of the Ability of Secondary School Pupils to Perceive the Plane Sections of Selected Solid Figures
Authors: Boe Barbara L.
Published: January 2021

In the Child's Conception of space by Piaget and Inhelder1 one chapter is devoted to the topic of geometric sections and their place in the overall development of representational space. Based upon their observations of children, they have developed a theory concerning the conceptual development of representational space. Geometric sections provide the initial indication that Euclidean representational space concepts are beginning to emerge in the child's thinking.
Experimental Programs: Closed-Circuit Television Instruction in College Mathematics
Authors: Pethtel Richard D.
Published: January 2021

During the last decade or so, there has been a tremendous increase in the use of television in teaching courses at the college level. Although there have been well over four hundred studies on educational uses of television in teaching, very few of these have related to the teaching of college mathematics.
On Mathematical Structures in Some Problems of Politics
Authors: Saatv Thomas L.
Published: January 2021

In recent years there has been a remarkable surge of effort to develop quantitative foundations for the solution of political problems, both to increase understanding of the underlying structure and to improve predictions.
Experimental Programs Attitudes of College Freshmen Towards Mathematics
Authors: Roberts Fannie , Nichols Eugene D.
Published: January 2021

In the general education program mathematics is recognized as “an instrument to deal with the quantitative aspect of the environment.” 1 For this reason it, is generally included as a required course.
Using Programmed Learning in the Classroom: A Case History
Authors: Hennemann Willard W. , Geiselmann Harrison A.
Published: January 2021

Although computer-assisted instruction may eventually serve as the primary dispenser of factual information in the classroom, many educators and researcher feel that the currently available forms of programmed instruction are best suited for supplementation, enrichment, and remedial teaching. In this spirit, the authors have been experimenting with programmed learning as a means of supplementing and enriching a precalculus, introductory, college mathematics course. It is the purpose of this article to report the results of these experiments.
Classics in Mathematics Education: Intuition and Logic in Mathematics
Authors: Poincaré Henri
Published: January 2021

IT IS impossible to study the works of the great mathematicians, or even those of the lesser, without noticing and distinguishing two opposite tendencies, or rather two entirely different kind of minds. The one sort are above all preoccupied with logic; to read their works, one is tempted to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches against the place besieged, leaving nothing to chance. The other sort are guided by intuition and at the first stroke make quick but sometimes precarious conquests, like bold cavalrymen of the advance guard.
Classics in Mathematics Education: Mathematical Definitions and Teaching
Authors: Crosswhite F. Joe , Poincaré Henri
Published: January 2021

1. I should speak here of general definitions in mathematics; at least that is the title, but it will be impossible to confine myself to the subject as strictly as the rule of unity of action would require; I shall not be able to treat it without touching upon a few other related questions, and if thus I am forced from time to time to walk on the bordering flower-beds on the right or left, I pray you bear with me.
A Heuristic Approach to Pythagorean Triples
Authors: Wilson John
Published: January 2021

Formulas that generate Pythagorean triples were discovered many centuries ago, and they no longer hold much interest for the working mathematician. Unfortunately, it is often the case that they hold even less interest for the working mathematics student, who may be asked to prove that these formulas do, in fact, yield Pythagorean triples. Such a task doubtless provides practice in algebraic manipulation. This article will outline a problem-solving approach to the topic which not only affords ample opportunity for algebraic manipulation, but also indicates how the student might discover the formulas for himself.
Providing for Individual Rates of Learning in Mathematics
Authors: Noddings Nellie L.
Published: January 2021

Mathematics teachers are frequently amazed that the range of achieve ment in carefully grouped classes continues to be great. Even in the last two years of high school, where the range of ability is narrowed by selectivity, the range of achievement remains wide. In these years, the student's learning rate may be affected by increased interest in a special field, or in extracurricular activities, dating, a part-time job, or even in a vehicle.
Psychological Set in Relation to the Construction of Mathematics Tests
Authors: Jeffery Jay M.
Published: January 2021

A MATHEMATICS test intended to in dicate the amount of retention of new knowledge and the ability of students to apply new skills can yield biased results as a consequence of ignoring the effects of psychological set. Psychological set is defined here as the tendency of a person to behave in a mechanical way, repeating a process in situation after situation whether the process is applicable or not. A test biased in this way will often favor the student with an ability to resist set formation, and it will often work against those who tend to be more vulnerable to set formation.
Testing in the Mathematics Classroom
Authors: Swadener Marc , Wright D. Franklin
Published: January 2021

Is it possible to write a test in geometry without asking for a proof and yet test the students' knowledge of proof and of geometry? What are the procedures for making up a “good” test? What makes a “good” test? What are “fair” procedures for assigning grades? How often should you test? Do you understand the meaning and use of simple statistical procedures for improving tests? Why test at all?
The Magic of Manhattan
Authors: Arcidiacono Michael J.
Published: January 2021

It seems to be generally agreed that mathematics teaching should center on activities that (1) appeal to the intuition of the students, (2) actively involve them in the discovery of mathematical relationships, and (3) move from a concrete setting to an abstract one.
Chess in the Geometry Classroom
Authors: Whitman Nancy C.
Published: January 2021

The current interest in chess playing in this country prompts me to share a very effective technique I have used in introducing the study of formal geometry. Basically, it uses the chess game as an “advance organizer” of Euclidean geometry viewed as a deductive system. Of course, this is but one of several possible views of Euclidean geometry. For example, another view is that geometry is an abstraction of man's physical environment.
Patterns in Integers
Authors: Sicklick Francine P.
Published: January 2021

A method of discovery that is appealing to students is discovery via patterns. The teacher’s job is to arrange the series of tasks or problems so that certain results become obvious to the students. The teacher is the organizer; the students then discover the underlying patterns. To the students, it is like a puzzle solved or an actual discovery in which they take great delight.
Diagnosis: An Active Approach
Authors: Fremont Herbert
Published: January 2021

In recent attempts to individualize instruction and to develop programs for the reluctant learner at the junior high school level, we have become more aware than ever of the need for diagnosing student strengths and weaknesses. Much of the impetus for this has come from the movement to have us establish behaviorally stated objectives in order to clarify our goals and to be able to measure specific outcomes. Once a list of such objectives is formulated, the teacher is faced with the question, Which of these objectives do the students already know, and which of these do they need to master? The process of diagnosis is then employed so that the work may be geared to the needs of each student. Students need not waste time with skills and concepts that they have already mastered and may instead concentrate on those that they do not know.
Some Interesting Examples for Teaching Statistics
Authors: Joiner Brian L. , Campbell Cathy
Published: January 2021

How much statistics do you expose your students to? This article is “alive” with stimulating ideas and has an excellent list of sources for further reading.
A Chalkboard Group-Teaching Technique
Authors: Wernick William
Published: January 2021

Many oversimplified individualized programs deny opportunities for students to interact with each other and with the teacher. Here are some simple techniques that provide such opportunities.
A More Elegant Method of Deriving the Quadratic Formula
Authors: Hoehn Larry
Published: January 2021

Teachers of algebra should consider presenting this alternate method of deriving the quadratic formula to their students.
Results and Implications of the NAEP Mathematics Assessment: Secondary School
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: January 2021

During the 1972-73 academic year. the National Assessment of Educational Progress (NAEP) conducted its first assessment in mathematics. Representative national samples of 9-year-olds, 13-year-olds, 17-year-olds (including high school dropouts and early graduates), and adults between the ages of 26 and 35 were assessed to determine their levels of attainment in mathematical concepts and skills.
Testing in Mathematics— What Are We Really Measuring?
Authors: Crouse Richard , Jacobson Carl
Published: January 2021

A discussion of common faults in test items and ways of avoiding them.
Individualized Instruction: Thoughts, Pro and Con
Authors: McDonald Sam
Published: January 2021

“Individualization—Try It—You'll Like It!” We did, and we didn't. That is, we tried it—with mixed results.
Crossing Appellatia: A Nominal Recreation
Authors: Bowling J. Michael
Published: January 2021

Test your knowledge of the history of mathematics by trying this puzzle.
Mathematical Quotations for all Occasions
Authors: Curcic Barbara
Published: January 2021

Quotations can inspire, delight, and provoke much thought about the many roles and aspects of mathematics. Quotations have a wide range of uses in the mathematics classroom. For example, these “stimulators” can be placed on assignment sheets, tests, duplicated exercises, or even in a special corner of a chalkboard or bulletin board—daily, weekly, or as the need arises.
Applications of Calculators and Computers to Limits
Authors: Johnsonbaugh Richard
Published: January 2021

A Computer or calculator is sometimes regarded as a supplementary tool that affords an alternative and easier method of computation. For example, a student may use a computer to find numerical results to a problem without improving his theoretical grasp of the problem. There is, however, another point of view. If a student looks at how the computer interacts with the problem he may gain insight into the theoretical aspects of the problem. In this article I will give some examples from the elementary theory of limits to show how a computer or calculator can be used as a motivating, essential device, integrated with the theory.
The Mathematics of Color Mixing
Authors: Orton William R.
Published: January 2021

Algebraic properties can be simplified through the use of colors.
Wiggle Graphs and Signum Functions
Authors: Priest Dean B. , Wood Dianne D.
Published: January 2021

If you've wanted to introduce your students to “exotic” functions but have been reluctant because of the complications in graphing, here is an application of auxiliary graphs that should simplify visualization.
The Mean Value Theorem: Now You C It, Now You Don't
Authors: Goldberg Kenneth
Published: January 2021

Another look at a familiar theorem with a timely application to income tax tables.
Mathematics and Our Founding Fathers
Authors: Howard Frisinger H.
Published: January 2021

On july 4, 1776, fifty-six men signed the Declaration of Independence. This paper will discuss the contributions to mathematics or the interest in mathematics of four of these men. Two of these four, Benjamin Franklin and Thomas Jefferson, made significant contributions to the early development of mathematics in the United States. In addition to the mathematical contributions of Franklin and Jefferson, we shall briefly consider the mathematical interests of George Washington and John Adams.
Individualized Instruction in Mathematics: a Review of Research
Authors: Miller Richard L.
Published: January 2021

The purpose of this paper is to report the findings of an intensive review of research on individualized instruction in mathematics. It is hoped that the findings will aid classroom teachers who are considering an individualized approach. A secondary purpose is to identify questions that might be used as a focus for additional data-collection activities.
Another Way of Finding Prime Numbers
Authors: Cohen David B.
Published: January 2021

Locating very large primes by cleverly reducing the arithmetic!
NACOME: Implications for Curriculum Design
Authors: Kline Morris
Published: January 2021

The authors of the Nacome report are to be thanked for undertaking a massive task and congratulated for having done a comprehensive, conscientious, and fair survey of the recent educational movements in school mathematics. Though it does seem inclined toward defending the new math, the report has tried to do so with arguments that, if not acceptable to all, have some force and that perhaps, in a field such as education ahout which we all know so little, may be faultless. Moreover, it does not balk at leveling criticisms where it feels justified in doing so. The report not only describes what has happened but indicates the problems ahead now that we realize the promised millenium has not arrived. Its objectivity is in marked contrast to many of the one-sided reports that appeared in the 1960s.
NACOME: Implications for Teaching K—12
Authors: Taylor Ross
Published: January 2021

The National Advisory Committee on Mathematics Education (NACOME) has done the field of mathematics education a service by its preparation of the NACOME report, “Overview and Analysis of School Mathematics, Grades K–l2.” I feel that the Mathematics Teacher is also doing a service by publishing reactions to the NACOME report from the perspectives of three institutions concerned with school mathematics—elementary/secondary education. teacher education, and Morris Kline. From the viewpoint of a person who has responsibility for the mathematics program in a large school system, I feel that the information and recommendations contained in the report are very useful. I believe that my colleagues who are teachers and supervisors will find that the report tends to support many of their opinions about the current state of mathematics education. The report is particularly refreshing to me because it confirms and documents many of the convictions I had previously held.
A Rediscovered Test for Divisibility by Eleven
Authors: Engle Jessie Ann
Published: January 2021

With some encouragement, students can discover patterns and prove their conjectures.
Learning To Count In Geometry
Authors: Bright George W.
Published: January 2021

An example of how exploration and discovery can lead to some significant findings. Try it with your class!
Visualizing Mathematics With Rectangles And Rectangular Solids
Authors: Sharlow John F.
Published: January 2021

Mathematical patterns obtained by using rectangles and inductive reasoning should prove an interesting, worthwhile activity for junior and senior high school students.
The Surveyor and The Geoboard
Authors: Steffani Ronald R.
Published: January 2021

Polygons, areas, coordinates, determinants, vectors, surveying, and the geoboard are all tied together.
Developing Mathematics On A Pool Table
Authors: Hamel Thomas Ray , Woodward Ernest
Published: January 2021

A new look at pool tables, common divisors, and axiomatic systems combined into one exercise.