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A Note to Science Teachers: Copy the Students Manual below for your students, not the background materials which follow it!

In this exercise, you will observe, generalize, explain the generalizations with a hypothesis, and then use this hypothesis to make predictions. This four-step process is typical of many scientific discoveries. For example, after observing the action of many suction pumps, I might come to the generalization that suction pumps at sea level cannot lift water above 34 feet. I might then explain this generalization with the hypothesis that the Earth is surrounded by an atmosphere and that the weight of this atmosphere can only lift water to 34 feet. From this I might predict that the Earth's atmosphere will only be able to lift mercury (which is 14 times more dense than water) 2.5 feet or so.

Before you begin, you need to know three things: (1) the apparent shapes of illuminated spheres; (2) how to estimate the angles between two distant objects; and (3) the causes of eclipses of the Sun and Moon.

Lighted Spheres. The following observations can be carried out in class or at home. Make the room you are in as dark as possible. Shine a strong, focused light (flashlight or overhead light) on a small, opaque, raised ball (a softball will do) placed about 15 inches away (see figure 2). Adjust the distance so that only the half of the ball facing you is illuminated. Slowly walk around the ball and light source at a distance of about 6 feet and record the apparent shape of the ball. How does it appear when you are directly behind the light+when you, the light source, and the ball (in that order), are in a straight line? How does the ball appear as you move along to either side? Or when the light source, the ball, and you form a straight line?

Angles. Later in this exercise, you will be asked to determine the angle between the Moon and the Sun. To do this, you will need to point one straight stick at the Moon and another at the Sun (see figure 3). This can be most conveniently done around sunrise or sunset, or when both Sun and Moon are visible in daytime. A given angle can be estimated roughly, as shown in figure 4.

moon4.JPG (53447 bytes)

Eclipses. Figure 5 (above) depicts lunar and solar eclipses. During a solar eclipse, the Moon blocks our view of the Sun; during a lunar eclipse, the Earth casts a shadow over the Moon. Both types of eclipse occur because the Moon orbits the Earth.

For this portion of the activity, make observations every seventy-two hours and record information on (1) the approximate size of the Moon in its new, crescent, half, three-quarters, and full phases and (2) the angle between the Moon and the Sun. Record your data in the log below and summarize them with a drawing. For illustrative purposes, the log includes a sample entry for one observation. Before you begin, keep in mind the following points:

2. It will be hardest to catch the new and crescent Moons, which occur about two weeks after the full Moon, so make more frequent observations 12-18 days after a full Moon.

3. Skip observations during cloudy conditions; if cloudiness persists, extend the observation period.

4. Continue your observations until you know the angle at full Moon, half Moon, and new or crescent Moon.

You may have noticed the existence of a pattern+ that is, the phase of the Moon seems to have a constant relationship to the Moon/Sun angle. Can you express this pattern in your own words?

Such a regular pattern can hardly be a mere coincidence. We know, for instance, why water in a suction pump rises to no more than 34 feet at sea level. Likewise, there might be a reason for the link between the Moon's phases and the Moon's angular separation from the Sun. What might be the reason?

Once your hypothesis has been discussed in class, you will have enough information to make two predictions. To succeed, you only need imagination, curiosity, and persistence:

Prediction #1. What will be the phase of the Moon when the next lunar eclipse occurs?

Prediction #2. What will be the phase of the Moon when the next solar eclipse occurs?

Besides telling you something interesting about sunlight, moonlight, and eclipses, and besides enhancing your reputation as the neighborhood sleepwalker, your outdoor explorations illustrate the process of scientific discovery. What generalizations about this process can be drawn from your experiences?

Almost everyone knows that the Moon shines as a result of reflected light, but few know how we know this. According to Arnold Arons, "very few people have ever watched the Moon in its changing phases and taken the intellectual step of noting the simultaneous location of the Sun" (1990). In the introductory nature-of-science class in the Interdisciplinary Studies Program at Wayne State University, we have adapted Arons' approach into an activity that is more concerned with illustrating the process of scientific discovery than with astronomy. The manual for this activity is reprinted below, so I will provide here only a brief summary and a few teaching tips.

This activity was created especially for nonscience majors taking a required class in the physical sciences. This activity requires no special equipment and can be performed, at no cost, in the students' home and in the ordinary classroom. Students should be provided with just enough background information and assistance to complete the activity on their own. The written manual below can be used with few or no changes in introductory astronomy and nature-of-science classes in college and high school. We begin the activity by providing background information on the apparent shape of a moving illuminated sphere (Arons 1977), on measuring angles, and on the causes of lunar and solar eclipses. Students observe on their own the phase of the Moon as well as the Moon's angle of separation from the Sun every third night for approximately a month. At the end of the observation period, students submit a lab report that includes their logs (see p. 0), a generalized pattern of the relationship between Moon phases and Moon/Sun angle of separation, and a hypothetical explanation of this pattern. They then combine this explanation with the earlier background information to predict Moon phases during solar and lunar eclipses. In the ensuing class discussion, we use a diagram such as that in figure 1 to help them visualize the observed relationship. The activity concludes with a second lab report in which students extrapolate from their personal experiences to the process of scientific discovery as a whole.

Although this activity is more time-consuming than traditional laboratory exercises, it is probably more effective at overcoming students' misconceptions about astronomy and the nature of science (Lightman and Sadler 1993). In our experiences with guided discovery exercises, the most serious problem is not foreknowledge but the occasional student, who, despite repeated pleas to the contrary, finds out the answers from textbooks or friends instead of deriving them independently. Inaccessibility of the answer is helpful; the text we use says nothing about the phases of the Moon. But it is even more important to encourage students to go it alone and to assure them that they are not expected to come up with a "correct" answer and that they only need to honestly observe and explain things on their own. Students need to be reassured, as well, that the two lab reports will be graded on the basis of effort alone, or (for those instructors who insist on more meaningful performance criteria) that they will be graded on the basis of effort, intellectual coherence, and creativity. Either way, the instructor should stress that the students not look up the answers, that doing so will take the fun out of the activity, and that knowing the answers, in this particular activity, is neither expected nor rewarded.

(Note: In certain locations and during certain seasons+for example, in Oregon's Willamette Valley from October to April+this activity is probably impractical).

This activity has been adapted from Arnold Arons' The Various Language (1977). It has greatly benefited from his, Donna M. Hoefler-Nissani's, and Claire M. Wilson's, critical comments. Any errors and oversights that remain, however, are mine.

Lightman, A., and P. Sadler. 1993. Teacher predictions versus actual student gains. The Physics Teacher, 31: 162-167. Spencer, H. 1864. Quoted in G. DeBoer, 1991. A history of ideas in science education. New York: Teachers College.

M. Nissani is an associate professor, Interdisciplinary Studies Program, Wayne State University, Detroit, Michigan 48202. He is the author of Lives in the Balance (Carson City, NV: Dowser, 1992) and of science education articles in The Journal of College Science Teaching, The Physics Teacher, and The Science Teacher.