We have developed software for the Apple IIe series of microcomputers for use in labs in an introductory astronomy course. This software emphasizes a toolkit approach to data analysis; it has been class tested with over 170 students and was a resounding success as a replacement for previously used graphical approximations. A unique feature of this software is the incorporation of image-processing techniques into a course designed for non-science majors.

The five software packages are:

1. (a) Datasheet - A six-column spreadsheet with columnwise operations, statistical functions, and double-high-resolution graphics.

2. (b) Image-Processor Program - Allows 37 × 27 pixel × 8 bit video captured images to be manipulated using standard image-processing techniques such as low pass/high pass filtering and histogram equalization.

3. (c) Picture-Processor Program - Allows 256 × 192 bilevel pictures to be manipulated and measured with functions that include calipers, odometer, planimeter, and protractor.

4. (d) Orrery Program - Simulates planet configurations along the ecliptic. A movable cursor allows selection of specific configurations. Since both relative times and angular positions are given, students can deduce the scale of the solar system using simple trigonometry.

5. (e) Plot Program - Allows orbital positions as observed from above the pole to be plotted on the screen. By entering trial values of elliptical orbit parameters, students obtain and the program plots the best fitting ellipse to the data. The sum of the squares of the residuals in the radial coordinate is given after each trial so that students can discover convergence more easily than by simple visual examination of a plot comparing the trial theoretical points with the raw data points.

Observations play an important role in the process of teaching astronomical knowledge. Practical observations of astronomical phenomena lead to analysis and explanation based on natural laws and so form the basis of cognitive processes in the education. Evidently the observations are an integral part of acquiring astronomical knowledge. Giving up observations, no matter what the reasons, is equivalent to losing quality in the educational process. It decreases the possible influence over the personal development of pupils and students. At the same time, observation and observational results are important for success in education.

Carefully planned observational time has a substantial influence on cognitive and educational processes. It leads to considerably more active participation in astronomy lectures.

Astronomy is the most popular and oldest of all sciences and it has had profound influence on human thought. Unfortunately, astronomy does not find an appropriate place in our school-college syllabi. This may be due to the fact that teaching of astronomy encounters a large number of problems with regard to visualization and practical experiments. Popularization of astronomy depends heavily on a large variety of astronomical events, such as the arrival of comets, eclipses, supernovae, etc. Visualization of dynamics in several directions, wide variance of time scales, concepts of space, etc., create problems in teaching/learning processes in astronomy. Our world of human experience is limited to within a narrow frame, whereas in astronomy we speak of size, time, and temperature in gigantic scales. To bring all these parameters onto the human level, one has to think of effective teaching aids and the right type of techniques. We have been using a large number of tools in teaching astronomy, including star charts, globes, models, photographs, slides, etc. Microcomputers act as an effective medium in teaching astronomy. They can even replace most of the above mentioned teaching aids (Hunt, 1986; Marx and Szucs, 1985; Sparkes, 1986). A microcomputer can also act as a textbook, a blackboard, or even a planetarium. The computer acts also as a mediator between the student and the model of some real-life situation. The process of building and using models, called simulation, helps us to investigate systems that would otherwise be inaccessible. We have developed a set of software to teach basic concepts in astronomy, such as the solar system, constellations, and the physics of stars. We have explored the possibilities of making the software interactive, using the observed data so that a real life situation can be experienced by the users, just as for practical experiments.

The basic idea of this project is to introduce a senior student to an astronomical phenomenon that he analyses carefully and simulates on the graphic screen of a personal computer. In a second step, this simulation serves as a demonstration for junior students.

Three examples are presented here: the retrograde motion of the planets, the Earth’s rotation, and the precession and the equilibrium figure of the Earth due to tides. Programs have been written on an IBM PC/AT.

It would be highly desirable to start an exchange program of material of didatic interest among the international astronomical community

About every other undergraduate student eventually takes the UCLA elementary astronomy class Astronomy 3, and the two of us have been teaching about 1,000 of them every year. We will not repeat complaints about their poor and patchy high-school preparation in science, but we must mention it as an important phenomenon in U.S. education. The European system appears to be preferable, in which mathematics, chemistry, physics, and biology are mandatory and taught every year, although only 3 hours per week. It prevents large memory gaps and the spiral-wise parallel development in all four subjects makes it possible to teach on a higher level every subsequent year.

The “Paperless Astronomy Classroom” was instituted at Edinboro University of Pennsylvania in the fall semester of the 1985–1986 academic year.

The goal of this endeavor was to teach an elementary and some advanced astronomy courses “on line” with the use of multiple terminals supported by a Digital VAX 11/785. Currently the system used is a clustered VAX system using two VAX 11/785’s and one VAX 8550.

The procedure of the “paperless classroom” eliminates the need for the transfer of paper between professor and students (homework, exams, supplementary handouts) in the first phase and eliminates the need for a textbook in the second phase.

An equally important goal is to provide additional enhancement for the student that may not be convenient or easily available from a textbook and the traditional classroom. Such an enhancement is series of large data bases, some of which can be the small data bases that traditionally appear in the appendices of textbooks. Another example might be a data base of graphs and charts (e.g., H-R diagrams, periodic table, abundance tables and graphs, binding energy curves, etc.).

At the turn of the century, astronomy was required of every senior in what is now the American University of Beirut, for the reason that “the heavens declare the glory of God”; this was especially appropriate for what was then the Syrian Protestant College. And in the late Middle Ages, astronomy was one of the seven liberal arts, a required part of every basic university education — for much the same reason. Thus, for many centuries, astronomy was considered essential for what every educated person should know. The organizers of this colloquium thought it would be informative to learn more about the historical background to our colloquium and asked if I would speak on the history of astronomy teaching over the ages. I demurred at such an overwhelming topic, which would require a major research program, and have offered instead something about the history of astronomy textbooks, because this subset provides answers to at least some of the broader questions of how astronomy has been taught.

A survey of 138 introductory-astronomy textbooks spanning 152 years reveals growing consensus regarding each topic’s proportion, with some clearly gaining space at the expense of others. The tables in the texts cite curious numbers, claim too many significant digits, neglect to note uncertainties, and are frequently inconsistent with, or badly behind, the research of the times. This study investigates apportionment of topics, planet and star data tables, and categorization of nebulae.

To probe the student/textbook interaction, I used one copy of each of 40 recent introductory textbooks when teaching astronomy in Fall 1986. Students swapped books each session. Texts’ treatments were surveyed in daily recitation as well as term papers comparing and contrasting them on specific topics. Most books sound much more positive than current data justify. There was lots of confusing phrasing, shoddy proofreading, and careless assembly of data tables. A few books are shamefully erroneous. There are numerous impressive examples of the imperfection and transience of “textbook learning.” The biggest and most pervasive sin was writing in the passive voice “Official Style” of interminable sentences laden with prepositional phrases. Illustrations, while important, are secondary to phrasing. Students need and use chapter summaries, glossaries, and indices. About half prefer paperbacks and half hardbacks. Students rated the books for appropriateness to their needs. The experience may stimulate others to develop controlled experiments to probe the student/textbook interaction.

I would like to address the issue of textbooks from a developing country’s point of view.

Firstly, I believe that in the developing countries a textbook should be written in the native language if it is to reach the very people whose awareness of astronomy needs to be raised. And when we talk about books in the vernacular, the problem is one of dearth: a dearth of writers and a dearth of resources.

The lack of writers comes about simply because in the developing nations there are inevitably very few astronomers and of these only one or two will be inclined to write books. If there exist writers, they are faced with several choices and problems. There are three types of books which can be written: a university text, a school text, and I shall include a book for the public. Each type of book targets a different kind of audience, so the writer must be attuned to the needs of the nation to know what the priority should be. If, for example, astronomy is about to be introduced into a school curriculum, then a school textbook should take the highest priority because it tackles astronomy education at the grass-roots level. Naturally, the final choice will depend on other factors as well, including promotion, fame, and pecuniary considerations.

Over the last dozen years, I have written textbooks on a variety of levels, starting with books for university students, proceeding to work with Naomi Pasachoff on books on the junior-high level, and, most recently, working with her and with others on an elementary-school series. I can testify that, in the United States, at least, the world of college and university texts is as different from the world of “el-hi” (elementary-high) texts as night is from day.

You might be somewhat surprised by the presentations [as delivered] so far, in that there has been relatively little discussion of pedagogical matters (e.g., what should be the content of a text and what should be its order and manner of presentation). It seems that rather personal factors are in the foreground of everyone’s thinking. But I think that is probably inevitable, because the process of writing a textbook is not only a huge undertaking that comes to dominate the life of the author, but it is also an endeavor that places the author directly at the interface between the idealistic world of education and the very practical world of economics as dictated by the realities of the publishing markets. In addition, a textbook has a strong effect on an astronomy class. It has been suggested that an important reason why so many educational research studies fail to come to a definite conclusion is that the textbook is such a dominant influence that it swamps all the other factors!

In astronomy, perhaps more than any other science, the cliché is true: A picture can be worth a thousand words. Unfortunately, with the illustrations in some astronomical textbooks, a picture can sometimes require a thousand words. And for beginning or inexperienced instructors, the worst thing can be that a picture may deserve a thousand words, but the instructor has only 50 words at his or her disposal.

Even for experienced instructors, unless the image happens to be in one’s own area of expertise, it can sometimes be difficult to appreciate or convey the full significance of a modern deep-sky photo, radiograph, or satellite multicolor composite image.

Many educators have found that models can add a lot to the understanding of astronomical concepts. Attractive commercial models of the solar system and celestial globes are readily available. Many models can be constructed of common materials — I found in my doctoral dissertation work that models made and manipulated by students increased retention of concepts of the celestial sphere and rotation, the seasons, lunar phases, and planet motions.

But there is another type of model which I have found very successful. I call it the “dynamic human model.” Actually, the concept is not new. I know that many good teachers have a favorite demonstration in which one or more students represent the Earth, sun, or moon. Also, the Elementary-School Science Project of the University of Illinois contained activities for student models to distinguish between Ptolemaic and Copernican systems. However, I do not think the idea has been extended as far as it should be. I would like to suggest ideas for dynamic human models beyond what I have seen elsewhere.

The teaching of astronomy in schools should start by explaining the most elementary phenomena, which are a part of everyone’s daily experience. Before proceeding to advanced topics, teachers of astronomy in school have to make sure that these very basic phenomena are fully understood. Since many programs have a gap at the elementary level, many people have foggy notions or disconcertingly wrong ideas of elementary matters. The seasons are a well-known case of a badly-understood phenomenon even for highly educated people. Still these people are honest and should not be laughed at. They do not understand the basic concepts of our contemporary scientific world, simply because these topics have not been taught properly. This problem raises a challenge for developing better ways of teaching astronomy. In order to show that there are specific new solutions to this challenge, I am presenting two innovative devices, which have been developed at the Universität Münster . The first example shows how the seasons may be successfully explained with a physical model that changes color when heated. The other example refers to the visibility of the stars and their disappearance in the daytime.

Many introductory astronomy students, when confronted with the idea of curved space-time in discussions of relativity and cosmology, don’t have a very good grasp of what this really means. They are told that the presence of mass “curves” space-time, but it is often not clear to them what is meant by that statement. We have developed a simple portable demonstration of what is meant by curved space-time, by using a two-dimensional analog. We have stretched a thin rubber sheet over a circular metal frame which is supported a few inches above a table top. By placing a heavy weight (about a kilogram) in the center of the sheet, we can mimic the effect of the curvature of space-time around a massive object on an orbiting body (such as a planet orbiting a star). We roll a small ball around the sheet, and the ball describes approximately elliptical orbits around the weight (see the photograph). The orbits aren’t exactly elliptical for two reasons: energy is dissipated by friction between the ball and the sheet, and the sheet doesn’t quite have the correct shape (it is shaped roughly like In r instead of 1/r: see this by solving Laplace’s equation in two dimensions with circular symmetry). We like to project this demonstration with a video camera placed directly above the sheet, so that the students can see the “orbit” without actually seeing the curvature of the sheet.

Except for two years, 1909 and 1910, the Observer’s Handbook of The Royal Astronomical Society of Canada has been published every year since 1907. It was founded by Clarence Augustus Chant, who also was responsible for the founding at the University of Toronto, of Canada’s first and largest department of astronomy, and who established the David Dunlap Observatory, which contains the largest optical telescope in Canada. In addition, Chant served as Editor of the Observer’s Handbook for 50 years, which is the main reason I am only the fourth editor since 1907. I should mention that John Percy, Chairman of the Scientific Organizing Committee of this Colloquium, was the third editor.

During the IAU Assembly in Prague (1967), Commission 46 on the Teaching of Astronomy decided to prepare a world-wide list of available material suitable for astronomy education at various levels and as in many languages as possible.

The first list was published in 1970 by E. Müller, under the title: “Astronomy Educational Material.” Since then, in order to keep the list up to date, an “Addendum” has been edited every three years.

Each Addendum is subdivided into three parts:

part A: material in the English language

part B: material in Slavic languages

part C: material in all languages with the exception of English and Slavic.

The Chinese proverb quoted above means more or less the same thing that our Rabelais did in the middle of the Renaissance, when his famous Gargantua made the statement: “well built brains are to be preferred to overfed brains.”

Indeed, when facing the fallacies that invade our modern life, and when facing the very quickly changing world in which we evolve, it seems that the only weapon we can give is a critical approach to science and life. We feel that anyone can assess at least the likelihood of any alleged fact, or, if he cannot, that he should be able to recognize openly his inability to do so.

Now let us consider the common fallacies of modern times. And you will excuse me if I come back several times to the same motto, from my old Rabelaisian education....