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Table of Contents

Martha Bedeaux                                                   99-01-01
Astronomical Patterns in Novels of Frank Waters, N. Scott Momaday, and Leslie Marmon Silko

Sean Callan                                                           99-01-02
Navajo Astronomy
An Understanding of the Cosmos
From Time of Creation to the High School Classroom

James Dudley                                                        99-01-03
Archaeoastronomy: Curriculum Unit on Trigonometry

Bill Glover                                                              99-01-04
Cultural Astronomy Curriculum Unit in the Highland High School Physics Curriculum

Blake Learmonth                                                  99-01-05
Naked Eye Astronomy for Middle School Students

Mary Ann Lee                                                     99-01-06
Cultural Archaeoastronomy:
A Study of Historical and Cultural Astronomy in the Southwest

Jennifer Murphy                                                   99-01-07
Research, Myth, and Memory

Roxanne Pacheco                                                99-01-08
Myths of Mesoamerican Cultures Reflect a Knowledge and Practice of Astronomy

Robert Squires                                                    99-01-09
Zuni, Acoma and Isleta: Three Pueblo cultures of New Mexico which are deeply rooted in naked eye observations of astronomical phenomena that provide the pivotal dates around which their lives are structured

Albuquerque Teachers' Institute Seminar, 1999                                                                                                                                                         

Archaeoastronomy, or Cultural Astronomy in the U. S. Southwest

Michael Zeilik
UNM Physics & Astronomy
800 Yale Blvd. NE, 87131
Phone: 505-277-4442 Fax: 505-277-1520

Seminar Description

Astronomy flourishes in New Mexico today, from the computer simulations at Los Alamos National Laboratory to the solar telescopes at Sunspot. Astronomy also has deep roots, revealed in the traditions of the Pueblo people. They perceive a cosmos in which nature functions with the active cooperation of humankind, who must perform the proper ceremony at the proper time to assure the continuity of the cosmos. The proper times were guided by astronomical observations that were the responsibility of religious officials, who kept the Pueblo sky watch for calendric purposes. We can use these practices as lenses on the past to, reconstruct the use of astronomy the prehistoric Pueblo wold. This seminar will focus on the astronomy of the historic and ancient Pueblos to learn how the flow of ceremonies connects to the cycles of the sky. These practices involve a ritual sequence that unites myriad aspects of Pueblo life and touches diverse points of Pueblo culture

Content Sequence

Session 1: Why? What? How? Crossing Cultures
Session 2: Naked-Eye Astronomy: Sun
Session 3: Naked-Eye Astronomy: Moon
Session 4: Naked-Eye Astronomy: Planets
Session 5: Naked-Eye Astronomy: Stars
Session 6: Southwestern Ethnoastronomy
Session 7: Southwestern Cosmovision
Session 8: Southwestern Prehistory
Session 9: Practical Aspects of Fieldwork
Session 10: Intersecting Disciplines
Session 11: Beyond the Southwest
Session 12: Speculations

Field Trips

We will at least go to Coronado State Monument and Petroglyph Park National Monument. Other sites (Chaco, for instance) subject to discussion.

Observations
Every Fellow will be expected to complete one observational project during the Institute. These activities may be carried out individually or in small teams. A project may embody fieldwork at a prehistoric site.

Readings
You will be given a diverse set of articles that will form the core of the seminar content.

Bibliography

                    Farrer, Claire R. Living Life's Circle. Albuquerque: University of New Mexico Press, 1991

                    Williamson, Ray A. Archaeoastronomy in the Americas. Ballena Press, 1981                                                                                        

Martha D. Bedeaux

How an individual relates to the cosmos is a compelling theme in Native American literature. Native American cosmologies often refer to the interaction of various parts of nature in order to create the world. The animals, the plants, and the dome of the sky all are intertwined in traditional native stories. An individual who does not walk in harmony with all these forces must find a way to restore the balance. The traditional practices of sun, moon, and star watching are external evidence of the search for this internal harmony with the universe. Three modern novels, The Man Who Killed the Deer, House Made of Dawn, and Ceremony, all show an alienated hero trying to regain his sense of place in the cosmos. An awareness of traditional astronomy and its role in Native cultures can help students to see the pattern of reintegration as well as the links between heaven and earth in these novels. Besides enriching the students’ reading, this unit links literature and science to show that all learning is connected.

Traditional Astronomy of the Southwest: Sun, Moon, Stars

There is ample historical evidence that the pueblo people watched the sun, the moon, and the stars and that these practices continue today. The agricultural peoples watched the sky to determine the times of planting, of harvest, and to predict the coming of rainfall. In winter, the night sky provided evidence of the people’s history written in the stars. Ceremonies to ensure the proper balance of life were timed according to the appearance of the sun and/or the moon and/or the stars. Thus, the purpose of this watching was/is both practical and religious--to predict planting times and to participate in the order of the universe. Separating these two purposes may be an artificial distinction that accommodates the Western way of examining behaviors.

The ethnographic evidence suggests that the very act of living is both a religious and practical act--or should be. One example of how close traditional peoples live to the cosmos is the kiva. The kiva is a sacred building in pueblo architecture. Emulating the dome of the sky, kivas are typically round, sunken into the earth, with significant markers for the four directions inside. The center of a kiva often contains an emergence place or sipapu as a reminder that the native people emerged from the world below. Some kivas may have a window in the side or roof situated so that the sun shines through on a particular day, such as the solstice, and marks a specific place on the wall. Some literature indicates that the stars are observed through the opening at the top of a kiva. In essence, the kiva is a kind of microcosm: the sunken room represents the womb of Mother Earth with the dome of the ceiling representing the dome of Father Sky. Emerging from the kiva is akin to being reborn.

Sun Watching

As the sun moves through the year, its rising and setting points move along the horizon, towards the northeast approaching the summer solstice and returning to the southeast for the winter solstice, moving relatively quickly through much of the year and slowing as the solstices approach. The observation of the sun’s rising and setting points can provide a good indication of these two turning points of the year.

At the summer solstice the sun rises at its far northern boundary. From our earthbound perspective the sun’s rising and setting swing along the eastern horizon like a huge pendulum from south to north and back again. For a few days at the end of each "swing" the sun appears to stop its movement, staying still on the northeastern horizon or southeastern horizons before returning. The winter and summer solstices mark the turning points of the year. At the spring and autumn equinoxes the sun is halfway through its northerly or southerly movement when it rises and sets on the celestial equator--that is, due east and west.

The observations common to multiple pueblo peoples share some fundamental

methodologies (Zeilik, "Anticipation in Ceremony" ): a sun priest is responsible for watching the sun, observations take place most often at sunrise in a place in or near the pueblo, horizon markers are commonly employed, the solstices are significant times of the year, the priest announces the impending date in advance to allow time for preparation, and both anticipatory observations and confirmations are done in the same way. It is important to understand that all members of the community would likely greet the dawn with offerings to Father Sun. The agricultural basis of the community ties everyone to the cycle of the sun.

The timing of ceremonies has been influenced by the overlaying of Catholic holidays onto traditional Native culture. Hence, Christmas celebrations also include winter solstice ceremonies and dances. In modern times, the elders may also move the celebration to a time convenient for tribal members who work outside the tribe or who must travel. For example, summer solstice ceremonies may take place on a weekend near the date, or even on July 4.

Moon Watching                                                                                                                                                                                                        

Most pueblos used the phases of the moon to determine ceremonies. Both the Hopi and the Zuni have records of lunar calendar sticks which were likely used to anticipate the proper phase of the moon. Ceremonies based on the solar calendar were often adjusted to coincide with a certain phase of the moon. Planting may have occurred during a full moon, to gain the power of both sun and moon for the growth of new life.

Like the sun, the moon goes through a regular cycle, though the moon’s movement is faster and apparently more erratic than the sun’s. Not only does the appearance of the moon change, the moon’s pendulum-like swing is not as regular as the sun’s ecliptic. In a month the moon travels the same distance on the horizon as the sun does in a year, and its path moves above and below the sun’s ecliptic.

While from our perspective, both the stars and the moon move westward through the sky, the moon moves eastward in relation to the stars. The moon’s movement from full (rising at sunset) to full takes about 29.5 days. It is the cycle of the moon through its illuminated phases that accounts for our monthly divisions of the year. The moon goes through a full cycle twelve times during the solar year--with about eleven days left over. So, if a ceremonial needs to fall at a particular time of the year, the people may also wait for a particular phase of the moon in order to maintain the balance of the two celestial bodies.

Each moon of the year has a particular name--often one identifying the ceremony or activity that occurs during that time. For example, for the Havasupai, the February moon is called "Midiig ymaya" or "bean dance." The Hopi also have a Bean Dance in February. November’s moon, to the Eskimo, is the "time of drumming," and for the Potawatomi November is the "month of the turkey and feast" (Native Moons, online). Some moons are named for events tied to the seasons: for the Navajo February’s moon is named for the "birth of baby eagles," while the Lakota call it the "moon of popping trees." Some native peoples have a "no name" moon (Zuni’s November), possibly to allow flexibility in integrating the lunar and solar cycles (Native Moons, online). The Zuni appear to make an effort to have the winter solstice coincide with a full moon (weak sun, strong moon) and the summer solstice close to a crescent moon (strong sun, weak moon) (Tedlock, qtd. in Zeilik 1986). This adjustment reflects the duality inherent in the Pueblo belief system.

The moon, like the sun, reaches a time of "staying still." These lunar standstills occur when the moon rises and sets at approximately the same position on the horizon for about five days. The standstill cycle takes 18.61 years. The sun moves along the horizon and back within a 60 degree range over the course of a year. The moon’s monthly pendulum-like movement in its rising and setting gradually increases from a minimum swing of 45 degrees (inside the sun’s ecliptic) to a maximum swing of 72 degrees (outside the sun’s ecliptic). During the time that the moon’s rising and setting falls within the 45 degree range the moon appears to rise and set in the same place for several days--a minor standstill. About 9.3 years later the rise and set at 72 degrees results in a major lunar standstill. Perhaps not many peoples kept track of this long period of time in a formal way, but there is potential evidence at Chimney Rock Pueblo in Colorado that some peoples did.

Star Watching                                                                                                                                                                                                        

The stars also provide a calendar. Certain constellations appear to rise at different times throughout the year. For example, the Pleiades rise just before dawn in June and are high in the sky on October nights. Orion is clear in the night sky during the winter months. Some groups may use the rising and setting of particular stars or constellations to time ceremonies, but primarily the stars are a pattern that records the history of the people. While the sun and the moon regulate the seasons and the ceremonies, the constellations provide the stories that help us on our way. In the constellations of native peoples we can see the impact of geography, what is needed for survival, what is common to the region, and hence the formative elements of the culture.

Petroglyphs made by prehistoric peoples seem to correspond to star patterns in the area. Navajo star lore is particularly rich. Canyon de Chelly in Arizona is reputed to have many Navajo star paintings. Navajo stories and ceremonies make reference to stars, and there are star patterns on some ceremonial items. The creation story of the Navajo further illustrates the importance of the stars to the culture. In this story, Black God was placing the stars in arrangements to represent each animal on earth, but Coyote comes along and spills the contents of Black God’s bag. The Milky Way appears in other stories from other cultures, often as the "starry path" or as the "starry river." Other star patterns that frequently appear in a variety of Native cultures are those of Orion (Long Sash or First Slender One), the Pleaides (the Deer), and the Big Dipper (Revolving Male, Bear). Morning Star and Evening Star, the twin sons of the sun, likely correspond to Venus and/or to Mars. In Tewa stories, Grandmother Spider, who makes the world, lives in the sky beyond the Milky Way. Clearly, the history and beliefs of the Native peoples are illustrated in the sky, one more example of how the dome of the sky and the earth are linked.

Three Novels: Waters, Momaday, Silko

The Man Who Killed the Deer--Frank Waters

Biographical Information

Frank Waters was born in Colorado Springs, Colorado, in 1902 and died in 1995. He studied engineering at Colorado College for three years but left without taking a degree. His Book of the Hopi is a respected work of ethnology, while Woman at Otowi Crossing takes on the making of the atomic bomb. Waters felt a close bond with the Natives he lived so near and was somewhat of a mystic in his view of nature. Out of respect for the peoples portrayed in his book, Waters submitted the manuscript of The Man Who Killed the Deer for review by tribal elders before publication. See the following web site for more information about Frank Waters: http://www.unm.edu/~wrtgsw/.

Summary

Martiniano returns to his pueblo after being sent to "away school" by the government. He kills a deer out of season and without the proper sacrifice, thus breaking the code of two cultures. His estrangement and disharmony with the universe influences his own peace of mind, his relationship with his wife, his relationship with his tribe and the tribe’s relationship with the United States government. As Martiniano struggles to find his place, the tribe struggles to regain their rights to the sacred Dawn Lake. Martiniano is haunted by the deer he killed, having visions of it on several occasions. Gradually, Martiniano accepts his role in the pueblo, but not before having his individual pride and desire for success suppressed by several failures. In contrast to Martiniano’s individualism, his friend Palemon provides an example of a life in harmony with the tribe and the world. After about a year and a half of struggle, Martiniano’s reintegration to the tribe is signaled by four events: his own agreement to participate in the dances, the birth of his son, the emergence of Palemon’s son from kiva training, and the pueblo’s victory in regaining the use of Dawn Lake for their most sacred ceremonies.

Reflections of the Cosmos in The Man Who Killed the Deer(See chart of Sun/Moon/Star references)                                                                

Frank Waters’s The Man Who Killed the Deer follows Martiniano through the course of almost two years, from October through two winter solstices to the next August. He begins the story as an outsider, caught between two worlds. Gradually, in accordance with the yearly cycle, Martiniano is reintegrated psychically and culturally.

Significant events occur at the changing of each season. During the first winter Martiniano’s literal and figurative alienation is shown by the fact that he does not come inside the pueblo for the "time of staying still." During the following spring, Martiniano has followed and left the "peyote road" in his search for a faith. He watches the Spring Corn Dances, but as a spectator alongside the white trader Byers.

A major transition in Martiniano’s position occurs around the summer solstice. By June, Martiniano begins to accept his duties within the pueblo, claiming his blanket and receiving a whipping, but also discovering that his wife is pregnant. When the autumn equinox comes, Martiniano’s damaging pride is finally defeated when he fails to climb the ceremonial pole. At the winter solstice, when the ceremonial dances are held, Martiniano’s wife takes the role of the Deer Mother in the Deer Dance. Following the dances, Martiniano’s growing inner harmony is affirmed when he finds Palemon’s wounded son, Napaita, in the snow and delivers the boy to the kiva.

Martiniano’s rebirth is revealed by the multiple new beginnings in the spring. In March, the month of the spring equinox, Martiniano’s son is born. Napaita also emerges from his kiva training. In May Martiniano participates in the dawn races and by June, the month of the summer solstice when the sun’s power is at its peak, Dawn Lake has been restored to the tribe. The book ends with Martiniano listening to the great August ceremonials taking place at Dawn Lake. Martiniano’s return to his place and his people follows the solar and ceremonial year.

House Made of Dawn--N. Scott Momaday

Biographical Information

N. Scott Momaday was born in 1934 in Oklahoma. He is a Kiowa who nevertheless spent much of his boyhood in Jemez Pueblo, where House Made of Dawn is set. His parents were both well educated and integrated into Anglo-American life. Momaday’s writing reflects a deeply bicultural heritage. He attended the University of New Mexico and received his doctorate from Stanford University in 1963. Momaday has written poetry as well as prose, and he also paints. He currently teaches at the University of Arizona in Tucson. House Made of Dawn won the Pulitzer Prize in 1969. His most recent book is The Man Made Of Words: Essays, Stories, Passages (St. Martin's Press, 1997). See the following web sites for more information about Momaday: http://www.angstgrrl.com/intelligensia/authors/momaday/momaday.html
http://www.ipl.org/cgi/ref/native/browse.pl/A50                                                                                                                                                        

Summary

A prologue describes a young man running into the dawn. The story proper begins when Abel returns to his pueblo, Walatowa (Jemez) at the end of his wartime service. He tries to fit back into the pueblo way of life, but is unable to make a smooth transition, partly because he was not at peace with himself when he left. Abel’s mother died when he was small as did his brother Vidal. He was raised by his grandfather, Francisco, the son of a priest who served at the pueblo in the 1870s. Abel meets a pregnant woman, Angela St. John, and has a brief alliance with her. Several days after the Feast of Santiago, where an albino man wins the "rooster pull" and flails Abel with the dead rooster, apparently as part of the game, Abel kills "the white man" outside a bar where they both had been drinking.

The next section of the novel takes place in Los Angeles in 1952 on the night that Abel receives a horrible beating. As Abel drifts in and out of consciousness we learn about the past six years of his life, his time in prison, his relocation to California, his affair with a social worker named Milly, and his friendship with Benally, a Navajo. Superimposed on Abel’s delirious state is the sermon and peyote ceremony led by J.B.B. Tosamah, Priest of the Sun.

The third segment of the book takes place a month later and is told by Benally who provides even more information about Abel’s uneasy relocation to Los Angeles. While Abel was in the hospital, Angela came to visit him. Benally says that he and Abel had plans to go back home together.

Abel goes home to Walatowa in February and watches over the death bed of his grandfather. Each morning for six mornings the old man wakes and speaks. On the seventh morning he dies. Abel performs the appropriate ceremony for his grandfather and then goes out to participate in the traditional dawn race with the sun, demonstrating that he has found his place at last.

House Made of Dawn is a complex novel that embraces and interlaces multiple views of the cosmos to reveal Abel's psychological, physical, and spiritual disintegration and reintegration. Momaday overlays Kiowa, Jemez, and Navajo traditions in the telling of Abel’s story in House Made of Dawn. The solar calendar so important to the agricultural life of the pueblo mixes with the fierce sun of the plains and the story-telling power of the Navajo herdsmen’s night sky. During his childhood, Abel is raised in the traditions of his pueblo; he is in tune with life and death just as he knows the "motion of the sun and the seasons" (11). (There are indications that Abel is not in complete harmony with his world even before he goes to war). In his dark night of the soul, when he lies beaten near death on the beach in Los Angeles, Abel remembers the story of the Kiowa Sun Dance --how it was destroyed by the government but the people found a way to survive. Finally, the title of the story refers to the Navajo name for the cosmos, and the healing Night Chant performed by Benally is also Navajo in origin.

More so than The Man Who Killed the Deer or Ceremony, House Made of Dawn includes references to the lunar cycle to point to the ongoing cycle of death and rebirth. The moon images are concentrated in the portion of the book where Abel lies beaten, drifting in and out of the present. At one point Abel realizes that the moon controls both sea and land (joining the struggling fishes on the beach with the beautiful flying geese he saw with Vidal). The cycle of the moon gives a kind of permanence to the world as we see in Tosamah’s description of the cricket framed by the moon where "its small definition [is] whole and eternal." Such visions and memories not only reflect how Abel pulls himself up, they seem actually help him to accomplish the rebirth. Indeed, a major theme in this novel is the creative power of the word.

Two star stories are also deeply embedded in the structure of Momaday’s book. Several critics have noted that Abel and his brother Vidal are like the Stricken Twins of the Navajo. The twins also appear in Pueblo culture as Masawe and Oyuyuwe, the Morning and Evening Star that follows the moon so closely. Their separation from one another reflects Abel’s imbalance and disharmony in the world. Gradually, Abel is reintegrated, helped by Benally’s Night Chant and the sense of relatedness he feels with Benally.

The second star story important to the novel is the Kiowa story of how Devil’s Tower was created when six sisters climbed to the top of a tree that grew to the sky to escape their brother who had become a bear. They became the stars of the Big Dipper. Abel’s recollection of Tosamah’s story serves as a reminder that he has "kinsmen in the night sky." The bear image appears in the story that Angela tells when she visits Abel in the hospital. Benally also tells a bear story. On his death bed, Francisco, Abel’s grandfather, remembers the good bear hunt of his youth. The killing accomplished with the appropriate ceremonies shows the harmony and unity of heaven and earth, humans and animals, in the "house made of dawn."

When considering the book through an astronomical lens, it seems significant that the story begins in July when the sun has already turned toward its winter place and ends in February when the winter solstice is past and the sun is moving again towards spring. In the Prologue the dawn runner seems to be in stasis; one might even argue that he has reached a time of solstice: "Against the winter sky and the long, light landscape of the valley at dawn, he seemed almost to be standing still, very little and alone" (2). Abel’s run at the end is marked by motion, as though, like the sun, he has begun his journey back towards life: "All of his being was concentrated in the sheer motion of running on" (212). By the end of the book, Abel is ready to perform the appropriate ceremony for his grandfather’s death and to pick up the unbroken beat of the drums by running into the dawn, to draw power from the sun and to lend his power to the sun for the continuation of the eternal race.                                                                                                                                                                                                            
                                                                                                                                                                                                        

Ceremony--Leslie Marmon Silko

Biographical Information

Leslie Marmon Silko is of mixed ancestry: Laguna, Mexican and white. She studied at the University of New Mexico and taught there for a time. She received a MacArthur Foundation grant to pursue her writing. He writing incorporates prose and poetry, folklore and modern issues. Her most recent work is Gardens in the Dunes (Simon & Schuster, 1999). See the following web site for excellent links to more information about Silko: http://omni.cc.purdue.edu/~njpete/Silko.

Summary

Tayo, a mixed-blood character who was raised in his aunt’s house, returns to his pueblo from World War II mentally and physically ill. His cousin, Rocky, was killed in the war and Josiah, his uncle died while he was away. Tayo feels responsible for both deaths. He spends a lot of time drinking with his buddies and telling war stories. One war buddy, Emo, is particularly twisted, and he and Tayo had a run-in soon after they returned. An old medicine man, Ko’oosh treats Tayo, but suspects that there is more wrong than he can cure. Tayo offers to begin helping out his Uncle Robert with the ranch work and they plan to get back the spotted cattle that were stolen from Josiah during the war.

Robert takes him to Gallup where he meets Betonie, a mixed-blood medicine man. Betonie makes a sand painting and tells Tayo he must find a woman, a mountain, the cattle, and the pattern of stars in the painting to complete the ceremony. When Tayo goes up the mountain to round up the stolen cattle, he sees the star pattern in the sky. He discovers that a woman has corralled the cattle for him. Later on, when Tayo returns to the ranch, he finds the woman has already set up camp there. They spend the summer together, she collecting plants, he tending the cattle. Finally, Robert arrives and tells Tayo that Emo has started rumors about him, that it is time to go back home.

On the way home, Tayo is met on the road by his friends Leroy and Harley. Thinking that the "witchery" must not extend to friends, he goes with them, getting so drunk he passes out. When he wakes, he realizes he is in danger, and he begins to run with the sun. He rests at an abandoned uranium mine and recognizes that everything is connected: the uranium from this mine went into the bomb that killed the Japanese that killed Rocky. Fearful of discovery, Tayo hides in a culvert. His friends arrive and Emo proceeds to torture Harley gruesomely. Tayo uses all his newfound understanding to resist the impulse to participate in the hatred by killing Emo. He heads for home, crossing the river at sunrise on the day of the autumn equinox.

Tayo tells his story to the men in the kiva. Harley and Leroy are found dead in the wrecked truck. Pinkie is killed by Emo, who is banished. Grandma comments that she thinks she’s heard these stories before. The witchery is "dead for now," and the sun rises, greeted by a prayer.

Reflections of the Cosmos (See chart of Sun/Moon/Star references)

As Momaday does in House Made of Dawn, Silko weaves together the Pueblo solar calendar with the star lore of the Navajo in Ceremony. Like Abel, Tayo comes home from the war alienated, suffering from "war sickness." Also like Abel, the completion of a ceremony indicates his reintegration to his society. Like House Made of Dawn, Ceremony begins and ends with a sunrise and emphasizes the creative power of the word. Silko, however, suggests that the ceremonies must change in order for the people to survive. The culture must not become stagnant.

Tayo’s connection with the solar calendar is absolutely clear in the context of the story. Tayo returns home in "late February" and the story begins in "late May" as the pueblo is experiencing a drought (11). The books ends at the next year’s autumn equinox when "a transition was about to be completed: the sun was crossing the zenith to a winter place in the sky" (247). The traditional story of how the animal people work together to break the bad magic and bring the rains back to the land mirrors Tayo’s own story of breaking the power of the bad magic over himself. Tayo’s meeting with Old Betonie, a mixed-blood medicine man, sets him on a quest to find the spotted cattle, a woman, a particular pattern of stars, and a mountain. The star pattern appears later on an old shield Tayo discovers in the woman’s cabin and the cabin is on the mountain where he finds the missing cattle. The star pattern Betonie draws includes the Pleiades. According to Peggy Beck in The Sacred, "The Pleiades star group occurs on some Navajo rattles used in various curing of-the-ill ceremonies" (87).

Embedded in Tayo’s story is the traditional story of The Gambler who has captured Orion and the Pleiades and is keeping them in a bag. Spider Woman gives her son, Sun Man, the secret for setting the stars free. These are the stars Tayo sees in late September, the stars that provide "the pattern of the ceremony" and "the constellation [that] formed a map of the mountains in the directions he had gone for the ceremony" (247). To complete the ceremony, Tayo goes to the kiva and tells the story of his return. In this sense, Tayo’s return follows the archetypal pattern of the hero who not only travels to the underworld, but who shares his knowledge for the good of his people when he returns. This reinforces Silko’s point about the need for ceremonies to be able to change in order not to lose their power. The circle of Tayo’s healing journey is closed with a sunrise song.
                                                                                                                                                                                                                    
Teaching the Unit

Essential Question (Students will be expected to answer this question at the end of the unit.)
How does our relationship with the physical world reflect or impact the structures of our lives?
Target group
This unit is designed to be part of an American literature course at the junior level in high school. Students will be members of an Advanced Placement English class, but the unit could be adapted to fit any ability level, possibly by reducing the number of readings or changing the pace.
Time Frame
This unit will take approximately three weeks of classroom time to complete. Students will need at least three weeks to read outside of class. They will receive their assigned text at least two weeks before instruction begins. Astronomy lessons will take one week. One week will be devoted to collaborative in-depth study of the novel and preparation to present information and insights to the whole class. The last week will be used to share and synthesize the reading experiences.

Objectives

• Students will read traditional stories of Native Americans.
• Students will consider the role of astronomy in the cultures discussed.
• Students will demonstrate an understanding of the cycles and movement of the sun, moon, and stars.
• Students will be able to identify the following constellations on a star chart and provide evidence of having observed them in the night sky: Orion, the Pleiades, the Big Dipper, the Little Dipper.
• Students will read a novel focused on pueblo life through the lens of cultural awareness, including references to the sun, moon, and stars.
• Students will examine ways in which the structures of these novels reflect the Native world view.

Procedure
Unit Overview

Students will choose one of three books to read: The Man Who Killed the Deer, House Made of Dawn, Ceremony. They will read their chosen text independently, keeping a dialectical journal as they read. They will be instructed to look for astronomical references in the text and to comment on their possible significance and potential connection to the cultures we are exploring in class.

In class, we will read stories of various peoples that reflect their concern with the sun, moon, and stars. We will document what we know about the movement of the sun, moon, and stars. Students will receive instruction regarding the sun-watching practices of the Anasazi. The astronomy lessons will be discussed in terms of the stories and poems from the oral tradition.

Upon completion of the reading, students will meet with the others who read the book, have an in-depth discussion of the structural elements they perceived, and determine what they wish to share with the rest of the class about their text. Students will receive guidelines for their presentations.

Students will prepare a multimedia presentation about their findings. Each group will have one class period in which to share with and instruct the rest of the students. Time will be saved at the end of each of these periods to make connections with the other novels and their patterns, structures and links to astronomy.

The following day(s) will be used to debrief the presentations, to synthesize information and to prepare for a writing assignment which springs from the evidence and information the students present.
                                                                                                                                                                                                                         
Materials Required

• Student copies of House Made of Dawn, Ceremony, The Man Who Killed the Deer.
• Star chart(s)
• markers and newsprint or other large paper for recording group responses
• Selected stories for illustrating astronomical aspects of native cultures (see student resources in bibliography).

Lesson Plans

Two to three weeks in advance:

Hand out copies of the selected texts. Student may choose or be assigned one of the three books. Ideally, there will be no more than eight students reading a particular book.

Assign eight dialectical journal entries (see sample at end)--six of these entries should relate to a passage that seems to have astronomical significance. The reading and the journal entries should be done before beginning the unit. Students may need some additional guidance with their reading, especially with Ceremony and House Made of Dawn since the treatment of time in these texts is nonlinear and can be confusing.

Beginning the Unit
Day 1: Introduction and Sun Watching                                                                                                                                                                

Ask students to do a timed writing (five minutes) in their journals commenting on the possible significance of astronomical elements in the novel they read. Encourage them to write down questions they may have about the references they encountered.

Follow up with a brief discussion of students’ observations and comments. Use this discussion as a springboard to introduce the concept of horizon calendars and the solstices.

Students should be able to approximate the position of the sun on an imaginary horizon through the course of a solar year (Refer to Zeilik’s Interactive Lesson Guide for Astronomy, "Sunrise Points" 27-28).

Closure: Read "Dawn House Song" in The Earth Under Sky Bear’s Feet and one of these others: "How the People Came to the Middle Place" in American Indian Mythology, "How the Sun Came," or "First Tale" from Spider Woman Stories.

Homework: Watch the sunset and be able to describe the current appearance of the moon (noting the location of the moon in the sky and the time you made your observation) when you come to class tomorrow.

Day 2: Moon Watching

Allow students to compare their observations of the sunset and moon. Use this discussion to introduce the motion and cycle of the moon. In pairs, students should be able to physically demonstrate the movement of the moon around the earth and its position in relation to the sun at each phase of its cycle.

Closure: Read "The Emergence" of the Tewa of Arizona in Tewa Tales (Parsons) or "Moon and His Sister" in Star Tales (Mayo).

Homework: Look up at the stars tonight. Stand facing the north and see if you can find the Big Dipper. Find a parent or someone else to help you if you don’t have a clue where or what this constellation is.

Day 3: Stars

Using a star chart (three to four poster sized charts would be nice), have students work in teams to find the following constellations and transfer the patterns to their journals (they should try to keep the relative positions intact when they transfer the patterns): The Big Dipper, the Little Dipper, the Pleiades, Orion’s belt, the Milky Way.

Closure: Read the "gambler poem" from Ceremony (pp. 170-176).

Homework: Explain that in The Man Who Killed the Deer the constellation referred to as the Deer includes the Pleiades. Ask students to see if they can first find the Pleiades and then add to their journal diagram (in another color) the stars they observe that might complete the constellation. For extra credit they can transfer this sketch to a separate page show the stars clearly and create an artistic rendering of the Deer showing where the stars they’ve plotted appear on the Deer’s body.

Day 4-5: Sky Stories and the Oral Tradition                                                                                                                                                

In groups of four or five, students will read a "sky story," a tale from a native culture that includes references to the sun, moon or stars. In this first group, they will need to learn the story well enough to be able to tell the basic events from memory to a new group the next day. The selection of stories listed in the student resources section should be readily available at your public library. The next day, students will be regrouped so that a member from all the other groups is in the new group (expert jigsaw). Students will take turns telling their tales to the new group members.

Closure: As time permits, have students comment on similarities and differences among the stories.

Homework: Think about how all the things we’ve done this week may or may not apply to your novel. Come prepared to discuss the importance of the astronomical elements in your novel.

Day 6-9: Expert Groups

Students will meet with others who read the same novel as they. They will receive a worksheet of questions to guide their discussion (see attached). Students should complete two items on the worksheet each day. By Day 9 students should be able to synthesize their conversation to complete the statements at the end of the worksheet.

Day 10-11 Planning the Presentation to the Class

Still meeting with their now expert group, students will decide what they think the rest of the class ought to know about this novel. They must present as much of the information they have accumulated as possible in a creative and fun way. Each group will have one class period to present. The presentation should include a focus activity, the presentation of information (the 400 word summary of the novel is required), a class-involvement activity, and a review of key points. Depth of knowledge, efficiency and interest of presentation, and creativity will be considered in evaluation. Students may create handouts, posters, visual aids, demonstrations. It will help the students if the teacher prepares a simple checklist or matrix rubric of required elements of the presentations so that students can prepare well.

Students will also prepare for a Protagonist Panel where the main characters from each of the novels will meet to share their experiences. The groups will submit four questions for the other protagonists on index cards by the end of the period on Day 10.

Day 12: Protagonist Panel                                                                                                                                                                                        

The students chosen to impersonate their main character will be seated on a panel, but they may receive help from their groupmates when the discussion begins. The teacher or another student will present the questions (twelve in all), rotating which protagonist answers first. (Tayo will answer question 1 first, Martiniano will answer question 2 first, and so on). A time keeper will limit responses to one minute for each question. Debrief at end of period as time allows.

Day 13-15: Assessment

Group presentations: Students in the audience may be given a copy of the teacher-made evaluation rubric to complete at the end of each period for the group who presented. Students will be asked to comment on the performance of other students in their group.

Final Assessment: Students will write an essay on their novel using one of the following prompts. The essay may be assigned as an in-class essay on Day 16 or as a homework assignment due the following week.

Essay prompts: (These will be evaluated using a version of the Advanced Placement nine point scoring guide).

1. Consider how the essential question applies to the main character of the novel your read: How does his relationship with the physical world reflect or impact the structures of his life?
2. A common theme in literature is the reintegration of an alienated hero. Discuss how this theme appears in the novel you read. Provide beautiful sentences and persuasive specific evidence.
3. Some critics argue that a book is a work of art that should be able to stand on its own. Others say that context is everything. How important is it to have some understanding of the culture(s) that produced this novel? What might you have missed? What needed no cultural context to have an impact on you?
4. How is this novel like or unlike other works you have read? Choose a book you know well and consider the kinds of similarities or differences between that book and this one (structure, character, plot, setting, and so forth).

Other Activities

1. Have students begin a horizon calendar well in advance of the unit Use these calendars for the opening discussion on the solar cycle.
2. Name that constellation (students will find their own pattern in the stars, name the constellation and write a brief story/myth to account for how/why that pattern is in the sky). These writing could be examined in terms of revealing what the writer values, where he/she lives, the essentials of survival, and so forth.
3. Create a pictograph for each significant event in the text or in the student’s own life.
4. Students might be asked to write a comparative paper drawing on the myths and poetry to compare themes and elements to the text they have read in depth.
5. Students may be given a formal reading quiz and/or final test over their particular text.

Sun/ Moon/Star References in the Novels
Sun/Solar Year References in The Man Who Killed the Deer                                                                                                                                   

Moon References in The Man Who Killed the Deer

Star References in The Man Who Killed the Deer                                                                                                                                                    

Sun/Solar Year References in House Made of Dawn                                                                                                                                            

Moon References in House Made of Dawn                                                                                                                                                                 

Star References in House Made of Dawn                                                                                                                                                          

Sun/Solar Year References in Ceremony                                                                                                                                               

Moon References in Ceremony                                                                                                                                                                      

Star References in Ceremony

Sample Dialectic                                                                                                                                                                                            

Directions: Choose a passage that you find interesting, beautiful, or challenging. Copy the passage (no more than two or three sentences) onto the left side of your paper. Then record your thoughts on the right side. Try to give evidence of at least three of the five habits of good readers: questioning, clarifying, connecting, predicting, evaluating.

Guided Discussion Worksheet for (title)___________________________                                                                                                    

Group Members: ______________________________________________

As you meet with each other this week, work through the items on this page, keeping an accurate record of your discussion. These items should NOT be parceled out and done by a single individual--every member must be able to adequately justify the group’s choices. We are all one in this effort.

1. Write a 400 word summary of the novel. Be as concise and compact in your final product as you can be.
2. Select four or six significant passages from your novel (use your dialectics) that contain references to the sun, the moon, or the stars. Briefly explain why they are significant.
3. Does it appear that the author was aware of the traditional astronomy of his/her people?
4. Find four examples of things that are said or done in groups of four.
5. Discuss the character of your protagonist. What are his problems, hopes, desires, dreams? How does he go about solving his problems? What is his worst/best moment? How does he fit into the community? Choose one of your group to impersonate your main character in a panel discussion. You may use notes.
6. Examine the patterns and movement in the novel. Is there repetition? Is the movement linear or cyclical? Give examples.
7. Choose one of the patterns below (or make your own) that best applies to your novel. (See Page 27) Label the parts in a way that makes sense to you and that you can explain readily to someone who has not read the book.
8. Complete (and justify your manner of completion) the following sentences:

1. This novel is about ____________________________________.
2. The author wants us to understand __(what about what)__________________.
3. The four most significant events in the novel are _____________. (Be prepared to justify).
4. This novel reflects Native American culture in these ways: (name at least two)____________________. You will use these materials to prepare a presentation for the class.
                                                                                                                                                                                                

Bibliography and Resources

Student Resources

Archaeoastronomy                                                                                                                                                                                  

N. Scott Momaday                                                                                                                                                                               

Leslie Silko                                                                                                                                                                                            

Frank Waters

                                                                                                       Navajo Astronomy                                                                                                          

An Understanding of the Cosmos

The purpose of this research is to explore Navajo Astronomy, and then a unit plan / lesson plan will be developed. This curriculum will then be made available to the Albuquerque Public Schools (APS) Indian Education Unit (IEU). It will add to the developing Native American Studies (NAS) curriculum guide. The NAS curriculum is designed to address esteem, literacy, and math components of the District Core Curriculum Scope and Sequence (DCCSS).

My purpose is for students to relate to the constellations and the cosmos from an intimate or personal experience through the teachings many of the Native American students may have been exposed to from extended family members or elders. Intergenerational learning is a typical Native American method of traditional teaching. By validating traditional teaching we are validating the Native American student. Meaningful learning is often more effective if the student can relate to it from an identifiable cultural context.

Background                                                                                                                                                                                                               

Granted, we will have only scratched at the Navajo understanding of the universe. This project could potentially be an ongoing effort to flesh out and incorporate Native American scientific perspective and its relationship to the dominant Western scientific rule. It is my belief and understanding that all societies may benefit from each other through the sharing of cultural and common knowledge.

Navajo Creation of Earth, Solar System and Universe                                                                                                                           

At this time the Holy Ones realized the universe needed light. They also realized there was no order, direction or sense of time or measurement. The Holy Ones again collaborated to address this need.

The Navajo perceive an order to their universe and the actions of the people are to be deliberate to maintain harmony and balance. When harmony and balance are interfered with, ceremonies are held to reestablish that order. Taboos are used to educate and inform people of their roles and responsibilities to affect Hozho, or balance and harmony.

Morning and Evening Star                                                                                                                                                                               

However, these stars are equal to all other stars. Many stars have their own ceremonies. These ceremonies focus on restoring balance and harmony for the people on earth. The Evening Star travels first and the Morning Star follows. Male songs and prayers are said and sung first and female follows.

Science, Myth and Constellations                                                                                                                                                               

The Big Star Ceremony is the spiritual basis that provides the purpose, understanding and role of these constellations, this was the intention of the Holy People. The individual strengths of these constellations will be discussed in the following sections. I will give a brief scientific explanation for these constellations, but will forego Greek interpretation as those can be found in any science book.

The Male and Female Revolver (Ursa Major and Minor) and the Central Fire                                                                                            

There are four stars surrounding the fire guarded by the Revolvers. They extend to the four cardinal directions. The guarded fire is referred to as the central fire. From this the people are blessed with children and grandchildren. The teaching is "If you are man or woman enough to keep the fire burning strong and always keep it safe, for this is the fire for your coming generations" (Scott 1992).

The Planter (Pleiades)                                                                                                                                                                                   

The Planter is often called upon for winter ceremonies such as the Night Way. Griffen-Pierce explains how the Planter is depicted in sand paintings and other ceremonial objects (Griffen-Pierce 1992). Special songs and prayers are used for the nine-night ceremony that begins generally at the end of October. Medicinemen use the position of the Planter in the sky to determine the time of night. This is often done during a ceremony in order to complete the doings with an appropriate song or prayer at dawn.

The First Slender One (Orion)                                                                                                                                                                    

Other times First Slim One is female and is paired with First Big One (Scorpius) who is the male counterpart. Europeans have a similar belief and understanding of this constellation. This is an interesting duality that reflects the need for balance and shared qualities in Navajo philosophy. All stars are really Holy People and communicate with each other and earth people. This too is an intention of the Deities.

Man With Legs Ajar (Corvus)                                                                                                                                                                   

The story goes that when a cane is needed an offering of corn meal must be placed in the tree for use of one of its branches before the branch is cut. It must be remembered in preparing a cane that the part used for the bottom must be the end that was nearest the roots of the tree. The tip where the leaves grew must be the handle. In this way the cane remains standing, just as when the branch was growing on the tree. The elders’ teachings say this is so because life must continue to grow in the direction it was originally set out.

Rabbit Tracks (Tail of Scorpius)                                                                                                                                                               

The Tracks are also symbolic to the paths we all must walk in our life. Everything and everyone has their own tracks. All constellations have their own tracks or footprints. In certain ceremonies on earth corn pollen and yellow corn meal is used to make footprints on the ground. This act of making symbolic footprints is to make certain that the order of creation, with all its purpose and significance is maintained. It must be kept sacred, so the people will lead a blessed life and will follow them as their guide.

One That Awaits Dawn (Milky Way)                                                                                                                                               

East is adorned with White Shell, its color is White and associates with Dawn and Spring. The sacred color of the South is Turquoise / Blue and the Turquoise stone is used to symbolize this; it is associated with the Midday and Summer season. Abalone is the stone for the South whose color is Yellow and is associated with Sunset and Autumn / Fall time frame. The North has Black Jet stone whose color is Black and associated with the Darkness of night and the season of Winter.

Summation                                                                                                                                                                                               

I hope that this study can be shared and explored in the classroom. The references in the bibliography are filled with detailed explanations and understanding of Navajo acceptance of the cosmos and their role in it. In the following pages please find a student-centered rubric, unit or lesson plan ideas, and an extensive bibliography that includes music, video and suggested student readings. In a good way, it has been shared.

Resources: Tribal and Community Members & Elders as guest speakers and Storytellers, see Bibliography for other sources

Aims, Goals and Objectives

Evaluation                                                                                                                                                                                       

*Review of current theoretical literature on curriculum, culture and cognition, epistemological of learning in Native American (Dine’) culture (s)
Society / Culture                                                                                                                                                                                                        

• general cultural right brain orientation

*Image thinking vs. Word thinking

Learning Theory                                                                                                                                                                                               

Yazzie, Ethelou Navajo History Volume 1 Navajo Curriculum Center Rough Rock Demonstartion School Rough Rock, AZ1971

Archaeoastronomy

Curriculum Unit on Trigonometry

Background

Trigonometry as it is used and taught today has little relationship to the cultural context in which it originated. In order to undertake sea voyages to distant shores, fifteenth century navigators needed maps. Getting accurate maps and charts required better ways of calculating angles and distances. Trigonometry emerged -- together with advances in technology and the desire for evangelization and trade -- from the emerging capitalist spirit in small Mediterranean kingdoms in the 1400s.

The trigonometry developed at that time allowed anyone with tables of the sine, cosine, and tangent functions and an accurate way to measure angle and distance to calculate unreachable angles, distances, and areas. It enabled Columbus to track his position and movement well enough to sail the 3500 miles west from Cadiz, in Spain, to Hispaniola, in the Americas. All this was done by the "right triangle trig" now usually given little emphasis in mathematics textbooks. (This is the trig where the sine of an angle in a right triangle is defined as the ratio of the side opposite that angle to the hypotenuse of the right triangle. The cosine ratio for that angle is side adjacent to hypotenuse, and the tangent's ratio is side opposite to side adjacent.)

In the late 20th century, however, map making depends upon aerial photography rather than trigonometry. And modern applications of trigonometry have moved on to modeling periodic motion, angular velocity and momentum, and solids of rotation.

In order to demonstrate the power of trigonometry to high school students, most teachers still use examples of historical, or "cultural" trigonometry. The class goes outdoors to calculate the height of a flagpole or a distance across an imaginary river. Or a surveyor tells the class how trig is used (or could be used) in triangulation. Meanwhile the meat of the course continues with graphing trig functions, solving trig equations, verifying identities, and analyzing relationship between the six trigonometric functions. The visual anchor no longer is the simple right triangle with its hypotenuse, opposite, and adjacent sides. In most high school math texts, the preferred visual model is a circle with its center at the origin of a coordinate (x-y) plane and with each point on the circle defined by an x- and a y-coordinate and r, the radius of the circle.

It appears that the archaeoastronomy of the U.S. Southwest implies connections with modern trigonometry that European historical trigonometry misses. Rather than angles and distances on earth for their own sake, the ancient Pueblo people concerned themselves with the movement of heavenly bodies across the sky, especially of the sun and the moon and especially with their rising in the east and setting in the west. In the living pueblos today, a religious leader has the important job of tracking sunrise or sunset points along the horizon in order to predict winter and summer solstices. There is ample evidence at sites in and around Chaco Canyon that their Anasazi predecessors did too. (Zeilik, 1997 and Malville, 1993)

This unit focuses upon the recording of horizon line sunrises (or sunsets) and the relation of that periodic motion to the cosine function. While doing that, the unit also invites students to examine the purpose and methodology of angular measurement as well as historical and ethnographic implications of geocentric and heliocentric conceptions of space.

A person who observes exactly where the sun rises notices that during most of the winter and spring the rising point moves northward every day, and during most of the summer and fall it moves southward. At the time of the solstices, however, the rising point of the sun doesn't appear to move at all for several days. In fact, the rate of change of the sunrise points varies throughout its cycle, moving fastest near the equinoxes and slowest (or not at all) near the solstices. Winter solstice is crucial to hunters and gatherers and agriculturalists living in mid-northern latitudes because it means that the sun ceases rising and setting further and further south (causing shorter and shorter days) and will begin moving northward again. Pueblo societies wanted to be able to predict this "turning around" of the sun, and they assigned this task to a sun priest.

For a sun priest in pueblo societies today (and presumably for the Anasazi of the 1200s), the goal is not only to determine when the solstices occur but also to be able to predict them far enough in advance so that preparations can be made for the ceremonies. There is no indication that Pueblo astronomers used any day counts greater than around fifty days. In other words, they don't predict the winter solstice by counting 365 days from the last winter solstice. What they do is to establish, over a period of a few years, a horizon mark for a date some time prior to the solstice. Then they are able to announce to their village, say eight days beforehand, when the solstice will occur, and preparations can begin for its observance. The entire procedure would be something like trying to locate the exact maximum of a sine wave, which can only be done with reference to the lesser values symmetrically located on either side of the maximum point. (See Suina, 1992, for cautions about interpreting Pueblo religious observances.)

Another method sometimes employed by Pueblo astronomers, especially when no adequate horizon line exists, is to use an opening in a building that casts a beam of sunrise against a wall opposite. Successive sunrises then appear to move (in reverse direction) across the wall. Turning points -- solstices -- can be marked with turquoise, shell, or bone, as can anticipatory dates a certain number of days prior to each solstice. The advantage of this kind of sun reckoning to archaeologists is that they may survive in the ruins of ancient buildings, whereas horizon marking leaves only occasionally some trace of the station from which the horizon was viewed. The caution regarding the verification of a prehistoric sunlight aperture for wall casting is that it may appear by chance in a reconstructed ruin when it may never have had any astronomical meaning to the original inhabitants.

For many people now in the teaching profession, the idea that Columbus "discovered" the New World is linked to the view that on his first voyage he set out (with sailors fearful of falling off the edge) to disprove the notion of a flat earth. And that when he reached the "Indies," even though he'd miscalculated his position by some 8,000 miles, he had forever demolished the Medieval theory of the flat earth and its geocentric underpinnings.

We expect now that students learn something about the fallacies inherent in the above paragraph. That Columbus happened upon a "new world," previously unknown to Europeans, that was rapidly moving from tribal to national social and political systems and which soon would be ravaged by diseases imported from Eurasia. That Columbus set sail, sponsored by Italian merchants eager to maintain commercial ties to China and India, in a time when the notion of a flat earth for practical purposes had long since been abandoned. And that the reason he has been portrayed as a bold, scientific discoverer, rather than as an oppressor and plunderer, has very much to do with the desire of Americans to feature the peaceful rather than the conquistorial nature of the European penetration of the Americas. (See Bigelow, Krupp, and Sanchez for extended discussion on the persistence of colonial perspectives on native thought and practice.)

It is also widely understood that the work of Copernicus (1473-1543) and Kepler (1571-1630) made possible the more sophisticated Western conception of the (heliocentric) solar system and its place among galaxies of distant stars. What may not be as widely understood is that the geocentric universe (sun, moon, planets, and stars revolving around the earth), supposedly consigned by Columbus to reliquaries of the Middle Ages, is actually the one modern astronomers use much of the time to track celestial bodies and events. Rising and setting, azimuth, zenith, angular size and displacement, scientific phrases all, still descend from a geocentric model as well suited for a modern astronomer as for the ancient Anasazi skywatcher.

The modern school year, just as the ancient Pueblo year, centers on the winter solstice. For a high school trig class this means that by the time the winter solstice arrives, there has been ample time to establish a horizon line and begin recording sunrise or sunset points along that line. It also means that if recordings are begun soon after school starts in September, students can learn and refine recording procedures during a time when daily intervals are at their maximum lengths. In many pre-calculus courses, little actual trigonometry is done during the fall semester; but horizon line recordings would be done then, and later analyzed during the more specifically trig sections of the course during the spring semester. (See "Beginning Activities" numbers 3 and 4 on pp 12-13.)

Even though the sine function may be more commonly understood, for consistency with students learning trigonometry the cosine works better. The cosine wave is identical to the sine wave except for being shifted 90 degrees to the left. But the cosine depends upon x values (horizontal values), and better models movement along a horizon line. In the activities that follow, the horizon line is treated as the x-axis. Angle values of zero and 180 degrees represent the winter and summer solstices, respectively, while 90 and 270 degrees represent the vernal and autumnal equinoxes. (See Figure 1.)

Wall castings follow a similar model, with the directions reversed. (See Figure 2 and "Beginning Activity" #5.) Basic instructions for classroom applications include: 1) cutting a slit (about a quarter inch wide and one inch high) in a piece of cardboard; 2) taping the cardboard to a window that faces the eastern horizon; and 3) setting a piece of masonite (or another cardboard) parallel to the window and a convenient distance inside the room. At a distance of four feet, the masonite will need to be at least 5 feet long to accomodate the extremes of the winter and summer solstices. At sunrise at the equinoxes, the slit in the window cardboard will project a rectangle of light directly opposite on the masonite. As the sun moves toward a solstice, the sunrise light moves north or south along the masonite until it approaches a standstill. The light projection loses its rectangular shape but still travels a measureable distance each day, except within a few days of the solstice. (Five feet divided by the 180-day half-year works out to an average daily change of one-third of an inch.) Just as for horizon marks, the record of daily changes on the masonite can be modeled by the cosine function, with fast movement at the equinoxes (90 and 270 degrees) and barely perceptible change at the solstices (zero degrees for the winter solstice, 180 for the summer).

Given the basic mathematical correspondence -- the cosine function that reduces circular motion to the x-axis, the sun's movement around the circle of the ecliptic reduced to movement along a horizon line -- there remain crucial practical considerations. Establishing a horizon line can be tricky. A preference between the views to the east and west may determine whether sunrises or sunsets will be recorded. A featureless horizon will serve no purpose for horizon line recording. Neither will a too distant, or a too near horizon. Because of perspective, distant sizes seem smaller than near ones. Distant movement is less perceptible than near movement; and features (peaks, notches, etc.) which would distinguish a nearer horizon become less distinct with distance. In order to be able to record the change in each morning's sunrise location, an observer must be able to perceive some change in location, but not so much that slight movements of the head or body may affect the results. The ideal of a horizon line that has a resolving power of from 4 to 8 minutes of arc three weeks before the solstice implies an ideal horizon of from 2 to 10 miles distant.

For summer solstice calculations, it happens that the Four Corners area, a region of heavy settlement by ancient Pueblo people where the modern states of New Mexico, Colorado, Utah, and Arizona meet, normally experiences exceptionally dry and clear weather preceeding the summer solstice and lasting for a week or two after it. (The summer rains often begin in early July.) This means that in doing the observations for a new pueblo in a new site, a sun priest might have about three weeks to verify that an early June rising point matched an early July reading, to establish the summer solstice exactly in between. In future years, the observer would know that the solstice would occur exactly half the total number of days between the two identical readings after the early June reading.

For an interior light casting, however, a flat horizon becomes ideal, for this reason: especially near the summer solstice, the sun rises at a sharply slanting angle; and this slant can be amplified by distant peaks and valleys to distort the true direction of the sun's rising point. Also for wall castings, the observer must strike a balance. The greater the distance between the slit that admits the sunlight and the recording wall, the more day-to-day movement there is to observe, but also the fuzzier the image becomes. An average of one cm of change per day seems ideal, and this implies an ideal distance of about one meter between the spot where light enters the room and the wall upon which daily changes are recorded.

Another difficulty in recording observations, of course, stems from the fact that sunrises and sunsets normally occur outside the typical school day. So the students are doing a new and strange activity at an often unusual time of day. However, students can practice sketching a horizon line at any time of day and from any location (someplace on the school grounds, perhaps) which affords a clear view of a horizon. In order to keep the drawing to scale, students can learn a basic sighting method which depends upon another application of "modern" trigonometry, that of radian measure. The outstretched fist has long been used by skywatchers to estimate the size of objects in the sky, angular distances between stars, and degrees of arc along the horizon. The basic calculation involves dividing the length of an arc by the length of its radius. This is the same relationship defined by angle measure in radians in the formula

0 = s/r

(where 0 is the angle, s the arc length, and r the radius).

The procedure is personal: (See Mini-project #7.)

1) Divide the width of your outstretched fist by the distance from your eye to your fist.

[This gives the angle, in radians, across your fist.]

2) Then multiply that result by 57.

[That converts radian measure to degree measure, since there are approximately 57 degrees to one radian.]

Once the degrees of the fist have been calculated, say 8 degrees, then students can impose that scale upon the horizon. Beginning at due east, they can divide the horizon into six to eight 8-degree segments. This results in a sweep of the horizon from about 30 degrees north to about 30 degrees south of due east.

Beginning Activities: Mapping, observing, and recording

Objectives:

1) students calculate the angular distance of their own outstretched fist

2) students apply radian measure to the calculation of angular distance

3) students locate and sketch a horizon profile appropriate for tracking sunrise (or sunset) points

4) students gain experience recording sunrise (or sunset) points along their horizon profile

5) students experiment with the trigonometry of light casting, and record daily changes to estimate solstices and equinoxes.

Carrying out the Beginning Activities

1. Students practice approximating angular measurements using their outstretched fist. They measure the distance s, across their knuckles and the distance r, from their eye to their fist. Dividing s by r gives the angle 0 in radians. Multiplying 0 by 57 gives an approximation of the degrees swept in the sky by their outstretched fist.

2. An alternative procedure uses the astronomers' formula

s = .018Ad

for approximating distances and diameters in space. Here s stands for a diameter or the distance between two celestial bodies, d stands for their distance from the observer, A the angle in degrees between the bodies, and .018 represents the conversion factor 1/57 that relates radians to degrees.

3. Students select a horizon line near their home and sketch it to scale using angular measurements of their outstretched fist.

Several considerations must be taken into account. Does the horizon have enough relief to show short distances? Is it visible winter and summer (with leaves on the trees)? Does it extend far enough north and south for the particular latitude? Even though it probably would not be used for sunrises or sunsets because of the time of day students are at school, a class project constructing a horizon line near the school is recommended so that students become familiar with procedures they may never have used before.

4. Students begin recording sunrise or sunset points and dates.

5. Students in the classroom experiment casting a small beam of sunlight upon a surface. In a morning class, students can simulate an actual sunrise by establishing a false horizon in a nearby roof or by taping a piece of cardboard partway up an east facing window. They then place two pieces of cardboard inside the classroom and parallel to the window. The first, nearest the window, has a small opening for projecting the sunlight. The second piece of cardboard is used for recording "sunrises" every day. Students begin experimenting with various distances between the pieces of cardboard to see which "length of throw" of the light produces the best results in tracking daily changes in sunrise points.

An optimal length of throw is one that reveals day to day change in sunrise locations with a sharp and easy-to-trace image. Once optimal procedures are established, students continue to record sunrise points throughout the semester.

Mini-Projects

Mini-projects are intended to give students the chance to figure out a problem and to explain how they did it. At the teacher's discretion, they are intended for teamwork or for students working individually. They may be written or presented orally (or some combination of the two). The basic components of any mini-project are:

1) Tell briefly and succinctly what the project is.

2) Show the steps you used to solve the problem. Include figures, diagrams, charts, and graphs as appropriate.

3) Explain what the answer means. Explain what you did to get it.

Mini-projects are assessed according to how well the above three basic components are done AND upon the accuracy of the answer. Mini-projects can be done together as part of the regular class assignment OR they can procede independently of other classwork. If they are presented orally to the class, then presentation skills (clarity, eye contact, quality of visuals, coordination among presenters) can be assessed additionally by students in the audience.

1. Circular Movement [See Figure 1.]

Objective: student correlates movement around a circle to movement across its diameter.

Materials needed: compass and protractor, horizon profile marked with sunrise points.

Procedures: Draw a large circle with a horizontal diameter. Beginning at the right end of the diameter, mark 15 degree intervals on the circle all around the circle. Drop perpendiculars from each point on the circle to the diameter. Describe how the perpendiculars move along the diameter. Compare that movement to the movement of sunset marks along a horizon line.

2. Cosine Values on a Number Line [See Figure 3.]

Objectives: students visualize change in cosine values

Materials Needed: ruler, calculator for cosine values

Procedures: Draw a long number line, labeled by tenths, with zero at the center, -1 at the left end and 1 at the right end. Calculate the cosines of all the angles at 15 degree intervals from 0 to 360 degrees. Plot those cosine values on the number line. Explain the connection to the sunset marks on a horizon line. Why is the cosine function used? What angle interval would be used to model the sunset marks every day?

3. Using TI-83 LIST options to Model sunrise points

Objective: Students see how the cosine function models a reflection of circular motion.

Materials Needed: TI-83 graphing calculator

Procedures: Use a TI-83 graphing calculator to mimic the movement of the sunset marks and to calculate the intervals between successive marks.

Set up Lists 1, 2, and 3.

STAT 5 then type L ,L ,L

Store 5-degree angle intervals to List 1.

seq(5X,X,1,72,1) L [seq is in 2nd LIST 5, is STO ]

Store the cosines of the values in List 1 to List 2.

[STAT 1:Edit place cursor on L and type cos (2nd L )]

How are the standstills modeled in List 2? What about the equinoxes?

Calculate the intervals between points in List 2 and store them as List 3.

[place cursor on L and type 2nd LIST OPS 7 2nd L ]

Questions: What do the intervals in List 3 have to do with the day-to-day change in sunset marks throughout the year?

What do they have to do with the slope at various points along the cosine curve? With maxima and minima?

Mini-projects 4, 5, and 6 extend concepts from #1, #2, and #3

4. What would happen if the daily sunset horizon marks were plotted on a number line as in mini-project #2 and the inverse cosine values were calculated? What would you expect as the interval between those inverse cosine values? Why?

5. Mini-project #1 models sunset marks on a horizon line without any reference to trigonometry, but only to a circle. How do you think that could relate to ancient Pueblo thinking, especially as compared to miniprojects #2 and #3?

6. If a student wouldn't tell you her birthday, but located it on a horizon line, to what accuracy could you predict her birthday?

Mini-projects 7, 8, and 9: Using your Fist and fingers

Objective: student learns to use his/her hand and fingers to measure celestial distances

Materials Needed: tape measure or ruler

7. Calculate the diameter-to-distance ratio of your outstretched fist. (See p. 9) Of your little finger. Of your thumb. Convert each ratio to an angular diameter using the formula

s/d = A/57 (or s/r = 0).

8. Use the angular diameter of your little finger to estimate the angular diameter of the daytime moon. If you know that the moon is about 2,000 miles in diameter, can you estimate its distance from the earth? (See also Zeilik, 1998, Interactive Lesson Guide for Astronomy. The first four "Focused Discussions, pp 11-18, all deal with angular sizes and distances.)

9. (During Balloon Festival) Compare the angular diameter of a balloon to the moon's. Estimate the distance to the balloon using 20 meters as an average diameter for a balloon.

[Use the formula r = s/0]

Mini-projects 10, 11, and 12: Thought Questions on the connections between Trigonometry and Astronomy.

10. Calculate the error involved in using angular diameter to approximate an actual diameter. On a graphing calculator:

y = x/180 gives angular diameter

y = sin x / sin .5(180-x) (from the Law of Sines) gives the linear diameter

Use the TABLE function to compare the two diameters for small values of x. Calculate the percent error at 5 degrees.

11. Why do you think astronomers, who do cutting edge scientific research, use degrees instead of radians?

12. Is the horizon a line or an arc? What difference does it make in calculating sunrise points?

         
Figure 1                                  Figure 2                                            Figure 3

Bibliography

                    Zeilik, Michael: Astronomy: The Evolving Universe, 1997

Cultural Astronomy Curriculum Unit

Academic Setting:

Highland High School is the most ethnically and culturally diverse public high school in New Mexico. Our student population includes Anglos, Hispanics, African-Americans, Native Americans, Vietnamese, Chinese, Cambodians, Indians (east) and Arabs. Next year Catholic Relief Services plans to relocate a number of Bosnian families in the Highland district. Indeed the Highland school district seems to be quite popular with new immigrant communities. Highland High School also has a relatively large Native-American student population.

The objective of this unit is to provide an historical and cultural context for the study of physics. I would like the students to understand that the modern worldview has evolved from and is linked to the beginnings of civilization, and in particular, to the ancient’s study of astronomy.

This Curriculum Unit is intended for a Physics I class. Physics students at Highland are usually high achievers, with very good academic skills. The students who take Physics also reflect the ethnic diversity of the school. For the coming school year, we have 80 students enrolled in three sections of physics.

Introduction

Being an amateur historian, I like to put the development of science and math in a historical and cultural context. It appears to me that the development of a system of astronomy is one of the first things that a civilization produces. Astronomy is integral to the development of culture. When I discuss the earliest developments of math and science with my students, I usually take examples from the ancient civilizations of Babylon and Egypt. The development of math and astronomy appear to be closely linked to the development of organized agriculture and the need to plan planting and harvesting (astronomy), and to tax agricultural production (math). Astronomy is the first discipline to develop a really rigorous system of observation and data recording, followed shortly by the keeping of records of land ownership and taxation. Astronomy is also closely linked to a civilization's religious and cultural development. Thus in my classes, I like to talk about why a civilization would develop a system of mathematics or find patterns in the heavens and how these developments relate to our current civilization and culture.

Pueblo culture is an important and interesting part of New Mexico's culture and history. Also, Highland High School has a relatively large Native-American student population. The first civilizations of Babylon and Egypt are both temporally and spatially distant from my students, while Pueblos surround Albuquerque. The Pueblo culture is something we can witness today. As it happens, however, I know a lot more about the ancient Near East than I do about Pueblo culture. I would like to be able to share with my students facts about the development of astronomy by our own native cultures. Math and science come alive when we can see how and why they were developed, and better yet if we can go and look at nearby examples.

In this curriculum unit I will discuss the approach to astronomy of a number of ancient or traditional cultures and where possible relate those approaches to the modern world and how we do science now. I will also discuss some of the key cultural differences, and emphasize how our cultural context influences (if not dominates) our view of physical reality.

Cultural Background:

Astronomy and the Beginning of Civilization

Observational astronomy is considered to be the oldest science. Ancient astronomers used the motions of the Sun, Moon, stars, and planets to provide them with the first clocks and calendars. By observing the yearly motions of objects in the sky, they were able to determine when to plant and harvest their crops and when to prepare for the cold weather and the coming of spring. While our reasons for observing the sky have changed over the centuries, our awe of its wonders remains as strong. Many cultures throughout history have contributed to our knowledge of the universe.

Early civilizations along the Tigris and Euphrates rivers and along the Nile river, as well as the Anasazi watched the stars for religious and agricultural purposes. According to Will Durant, science, like civilization, in general began with agriculture. Geometry began as the measurement of the soil. Predictions of planting and the harvest, the cycle of the seasons and the development of a calendar may have evolved into astronomy. New civilizations seem to have stargazing linked to the development of organized agriculture.

In some civilizations, like ancient Egypt, and Babylon, astronomers began to incorporate mathematics into their observations; the Anasazi however did not. In the seventeenth century BC, the Mesopotamian (hereafter referred to as Babylonians) accurately observed Venus, the Moon, planets, eclipses, solstices and equinoxes; the Greeks contributed modeling, geometry, and logic; the Egyptians, observations; the empire of Islam, instrumentation, constellations patterns, and star names. Astronomy, initially a tool of religion and agriculture also became the basis for scientific observation, data collection and a good bit of the mathematics of geometry and trigonometry.

Much of the ancient culture is with us today. For the traditional people of the modern Pueblos, the astronomy of the Anasazi is still an integral element of their cultural and spiritual lives.

Mesopotamia and Egypt

Religion was an important aspect of astronomy for the Babylonians. They believed that the motion of the heavens could predict the future. The Babylonians thought of each planet as a god, and every movement of the sun, moon and stars foretold some earthly event. The Babylonians began charting the stars around 2000 BC. Their priest-astronomers plotted the motion of the sun and moon and could predict their eclipses and conjunctions. They divided the ecliptic into the twelve signs of the Zodiac, and developed a calendric system to fix the dates of the equinoxes and solstices. To manage this, they observed and recorded astronomical data for centuries. The Babylonians gave us the 360-degree circle, the sixty-minute degree and the sixty-second minute. These probably result from their sexagesimal counting system (and I have no idea why they used a base 60 number system). They even solved quadratic equations. They gave us the year of twelve lunar months and from time to time added a thirteenth month to keep time in kilter. They also divided the day into twelve hours.

The Egyptians were less skilled at astronomy than the Babylonians. But they were good enough to predict solstices and equinoxes. Most importantly they could use astronomy to predict the flooding of the Nile. The Egyptians were more agriculturally oriented than the Babylonians in their Astronomy. (Our Oriental Heritage, Will Durant, Simon and Schuster, New York, 1954). The Babylonians possibly knew already that the rotation of the stellar constellations was subject to change, but Hipparchus was, in the 2nd century BC, the first astronomer who gave a description of this phenomenon

The Greeks

Greeks were odd by ancient standards. They often studied things just because they were curious. They were also unusually eager to share their wisdom with anyone who would listen. So for the Greeks the religious aspects of astronomy were much less important than for other cultures.

Three prominent figures in Greek astronomy are Hipparchus, Ptolemy and Aristotle. Little is known of Hipparchus's life, but he is known to have worked in Nicaea, Rhodes and Alexandria. He worked on trigonometry. He introduced the division of a circle into 360 degrees into Greece and produced a table of chords, an early example of trig tables. He also gave methods for solving spherical triangles and advocated the use of latitude and longitude for position on the Earth. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. Hipparchus's value of 46" for the annual precession is good compared with the modern value of 50.26" and much better than the 36" Ptolemy was to obtain nearly 300 years later. His star catalog, containing about 850 stars, lists magnitude with a six-point scale similar to that used today. His star catalogue, completed in 129 BC, was used by Ptolemy and its quality was such that it was even used by Halley.

Ptolemy (AKA Claudius Ptolemaeus) lived in Alexandria (in Egypt) from approx. 87 -150 AD. Very little is known about his personal life. He was an astronomer, mathematician and geographer. He codified the Greek geocentric view of the universe, and rationalized the apparent motions of the planets, as they were known in his time. Ptolemy synthesized and extended Hipparchus's system of epicycles and eccentric circles to explain his geocentric theory of the solar system. He believed the planets and sun to orbit the Earth in the order Mercury, Venus, Sun, Mars, Jupiter, and Saturn.

This system became known as the Ptolemaic system. It predicts the positions of the planets accurately enough for naked-eye observations. This is described in the book Mathematical Syntaxis (widely called the Almagest), a thirteen book mathematical treatment of the phenomena of astronomy. It contains a myriad of information ranging from earth conceptions to sun, moon, and star movement as well as eclipses and a breakdown on the length of months. The Almagest also included a star catalog containing 48 constellations, using the names we still use today.

In addition to his well-known works in astronomy, Ptolemy made very important contributions in geography and cartography. Ptolemy, of course, knew that the Earth is a sphere. Ptolemy's map of earth is the first known projection of the sphere onto a plane. His

Geography remained the principal work on the subject until the time of Columbus. But he had Asia extending much too far east, which may have been a factor in Columbus's decision to sail west for the Indies.

The Ptolemaic explanation of the motions of the planets remained the accepted wisdom until the Polish scholar Copernicus proposed a heliocentric view in 1543. It should be noted, too, that Ptolemy's system is actually more accurate than is Copernicus's. The heliocentric formulation does not improve on Ptolemy's until Kepler's Laws are also added to take into account that the planetary orbits are elliptical.

In addition to formalizing the law of formal logic, Aristotle chiefly contributed a flawed theory of the universe that posited a geocentric universe, where all celestial motion was circular. The Church viewed the theories of Aristotle as though they were divinely inspired. Galileo, Copernicus and Kepler finally put an end to the Aristotelian View of the universe.

The Mayans

The Maya were quite accomplished astronomers. They seemed to use astronomy more for religious purposes than for agriculture. Their primary interest, in contrast to "western" astronomers, were Zenial Passages when the Sun crossed over the Maya latitudes. On an annual basis the sun travels to its summer solstice point, or the latitude of 23-1/3 degrees north. Most of the Maya cities were located south of this latitude, meaning that they could observe the sun directly overhead during the time that the sun was passing over their latitude. This happened twice a year, evenly spaced around the day of solstice. The Maya could easily determine these dates, because at local noon, they cast no shadow. Zenial passage observations are possible only in the Tropics and were quite unknown to the Spanish conquistadors who descended upon the Yucatan peninsula in the 16th century.

The Maya had a god to represent this position of the Sun called the Diving God. The Maya evidently thought quite a bit about the Sun and they watched it trace out a path along the ecliptic. They followed it year round, presumably following its path along the horizon. At Chichen Itza, during sunset a sun serpent rises up the side of the stairway of the pyramid called El Castillo on the day of spring and Autumn Equinox. It tells us that the Maya noted not only the extremes of the Sun at the Solstices, but also the Equinoxes when the Sun appeared to rise due East or due west. In addition to the Zenial Passages mentioned earlier, ecliptic observations must have been a major portion of Maya solar observing.

The Maya had a lunar component to their calendric inscriptions. After giving the pertinent information on the date according to the Maya calendar the typical Maya inscriptions contain a lunar reckoning. The lunar count was counted as 29 or 30 days, alternating. The lunar synodic period is close to 29.5 days, so by alternating their count between these two numbers the moon was carefully meshed into the calendric sequence as well. Their lunar knowledge was impressive for they also made eclipse predictions. An almanac for predicting them is contained in the Dresden Codex.

The Maya Kings timed their accession rituals in tune with the stars and the Milky Way. They celebrated a feast called k'atun approximately every twenty years. At the end of the 20-year k'atun period, Maya rulers regularly erected a stela, called a stone tree, to commemorate the event. On stone stela they depicted themselves at the time of these ceremonies dressed in costumes that contained the symbols that were associated with the World Tree. By wearing the costume elements of the World Tree the Maya ruler linked himself to the sky, the gods and that essential ingredient, life. In addition, it has been found that when the k'atun ending coincided with certain planetary positions the Maya went to war to obtain captives for sacrifice.

Anasazi and Pueblos

Indian tribes in what becomes the southwestern United States paid close attention to the sun, moon and stars. These elements were seen as powerful religious figures, and most tribes paid homage to them. The Anasazi, who are thought to be the ancestors of the modern Pueblo tribes, left numerous sites of astronomical/religious significance in the areas of Chaco Canyon and Mesa Verde. The Anasazi paid especially close attention to the winter and summer solstices.

Anasazi, and later the Pueblos’ prayers and ceremonies were dedicated to the sun in order to keep the world in harmony. The changes of the season were mostly determined by sun watching. The single most powerful and highly respected symbol in Pueblo life is the sun. According to Ray A. Williamson, "The Sun and its power dominates the Southwest."

Most of Pueblo astronomy can be linked directly to the sun. Extensive observations of the sun led to the development of an advanced sun-based religion among the Pueblo cultures. Each pueblo consists of a tight organizational structure headed by a priesthood, which controls the social, political and religious aspects of daily life. The primary function of the priesthood in Pueblo society is to perform ceremonials for the good of the people by keeping them in harmony with nature. The purposes of the ceremonials are to control the weather and the movements of the sun, and to promote fertility in all living things. In addition, a common outlook exists between the Pueblos, which probably resulted as a response to how successful their crops were.

Since the Sun is such an important factor for the health of the pueblo and for the individual, Pueblo astronomy is different from astronomy in the traditional sense; it focuses more on the daytime sky, rather than the stars and other features of the night sky. The Pueblo people have put much emphasis on the sun for practical purposes. Solar calendrical devices were made to indicate proper times for ceremonials and other important events. In particular, the solstices were regarded as special occasions and many of the calendrical markers were geared to indicate precisely when a solstice would occur. At Hovenweep Castle, an ancient Anasazi ruin, a room acts as a solar calendar. Several "ports" or holes cut into the walls of this room align with the rays of the sun at particular times and indicate the summer and winter solstices and the spring and fall equinoxes. Other ruins have indicated similar findings. Of course, planting and harvesting are tied to the equinoxes.

At Chaco Canyon, the Casa Rinconada site appears to have astronomical functions. The Anasazi built Casa Rinconada in nearly a perfect circle. The four main supporting posts in the ancient kiva were located in the corners, which also indicate the four cardinal directions: northwest, southwest, southeast, and northeast. The portholes found in the ruins were likely used for predicting the equinoxes.

Relevance to Modern Science

So what is the relevance of ancient or traditional astronomy to modern science? Although astronomy predates the scientific method, the methodology of the ancient astronomers sets the groundwork. The scientific method entails observation, hypothesis, and the testing of that hypothesis to determine if it is an accurate predictor. The ancients observed the motion of the sun and moon and stars. They noticed that eclipses occurred from time to time. They looked for patterns in the motion of the celestial bodies. They developed hypotheses about when the next eclipse would occur. They tested those predications and eventually developed an accurate methodology for eclipse prediction. To do such predictions, the ancient Chinese and Babylonians developed the idea of systematic observation and data records.

The regular and predictable nature of the motion of sun and moon becomes the basis for measuring the passage of time. Perhaps it is the basis for the pre-relativity concept of the passage of time as regular, constant and immutable. I have heard arguments that the way Native Americans view the nature of space and time is more in tune with Einstein's view of an integrated space-time. This is a big divergence in the view of nature from the ancient civilizations of Asia and the Anasazi/Pueblo tradition.

In Babylon and Egypt and later in Greece the astronomer/priests developed geometry and the rudiments of algebra to help them with their celestial calculations. The early mathematics also facilitated property records and taxation. The Native Americans of the Southwest did not develop a system of math; they also appear to have had a less hierarchiacal social structure with less emphasis on ownership of property and no record of taxation.

Further, in order to do predictive astronomy, one needs a frame of reference for observations and measurements. Ancient people thought that the Earth was the center of the universe. Ptolemy developed a complete (or as complete as one can be without a telescope) and accurate model of celestial motions, with the Earth at the center of the universe. The heliocentric model gained acceptance in the 17th century. As we began to grasp the size of the universe, it was no longer clear that we could find its center. In the 17th and 18th century, with the development of the laws of motion and the mathematical tools to describe them, one could do calculations from any frame of reference.

Astronomical Background

What can we all observe in the sky without the aid of instruments- the sun, the moon and the stars (some of them anyway)? After observing the sun rise daily for a number of years, even the most casual primitive observer might notice a pattern. Seeing a pattern in day following night, our observer might begin to look for patterns elsewhere. Pretty soon early civilizations find that agricultural cycles can be tied to the motions of the sun and moon. So a cottage industry of sun and moon gazing springs up in conjunction with developing civilizations increasing dependence on a successful agricultural system. The dawn of astronomy, perhaps the dawn of all science.

Some basic things the early astronomical observer will note are the seasons, the phases of the moon, the variable length of the day as follows:

The Earth is in an elliptical orbit around our Sun. In Earth's case, its orbit is nearly circular, so that the difference between Earth's farthest point from the Sun and its closest point is very small. Earth's orbit defines a two-dimensional plane which we call the ecliptic . It takes roughly 365 days for the Earth to go around the Sun once. The time it takes for the Earth to go around the Sun one full time is what we call a year. The combined effect of the Earth's orbital motion and the tilt of its rotation axis result in the seasons

As the Earth travels around the Sun, it remains tipped over in the same direction, towards the star Polaris. This means that sometimes the northern half of the Earth is pointing towards the Sun (summer ), and sometimes it is pointing away (winter). These points in the Earth's orbit are called solstices. When the northern hemisphere is tilted towards the Sun, the southern hemisphere is tilted away. This is why people in places north of the equator have the opposite season of people south of the equator.

Halfway in between the solstices, the Earth is neither tilted directly towards nor directly away from the Sun. At these times, called the equinoxes, both hemispheres receive equal amounts of sunlight. Equinoxes mark the seasons of autumn and spring and are a transition between the two more extreme seasons, summer and winter.

The Moon has an elliptical orbit which is nearly circular. Its average distance from the Earth is 384,400 km. The combination of the Moon's size and its distance from the Earth causes the Moon to appear the same size in the sky as the Sun, which is one reason we can have total solar eclipses. It takes the Moon 27.322 days to go around the Earth once. The changing position of the Moon with respect to the Sun leads to lunar phases . The same side of the moon always faces the Earth. It takes the Moon the same amount of time to rotate around once as it does for the Moon to go around the Earth once. Therefore, Earth-bound observers can never see the 'far-side' of the Moon

c. 30000 BC Bone carving interpreted as record of lunar phase cycle (France)

c. 7000 BC Rock paintings interpreted as tally of lunar-month days (Spain)

4000 BC Evidence of specific labeled constellations (Euphrates Valley)

2800 BC Beginning of Stonehenge construction (England)

2608 BC Observatory built (China)

2500--2000 BC Equinoxes and solstices determined, gnomon invented, observations of Pleiades, comets, solar eclipses (China)

2000--1501 BC Geometry used as basis for astronomical measurement signs of the zodiac known (Babylonia)

1750 BC Temple Wood observatory built (Scotland)

1500 BC Oldest known sundial (Egypt)

165 BC Spot on Sun reported (China)

140 BC Construction of armillary sphere (China)

129 BC Hipparchus catalogued 1080 stars divided into 6 magnitudes positions were given in latitude longitude as referred to the ecliptic

500 AD Written commentary on astrolabe (Egypt)

850 AD Astrolabe perfected by Arabs

1600--1609 AD Telescopes invented perfected (Netherlands), Galileo constructs a telescope, Kepler's laws of planetary motions, and Simon Marius observes Jupiter's moons

1610 AD Galileo observes Jupiter's moons, Harriott discovers sunspots,
Peresc discovers Orion Nebula

1665 AD Cassini determines rotations of Jupiter Mars Venus

1666--1668 AD Newton measures the Moon's orbit; constructs reflecting telescope

1705 AD Halley predicts return (1758) of comet seen in 1682

1750 AD Expedition to Cape of Good Hope to determine solar lunar parallax

1781 AD Herschel discovers Uranus

1800 AD Herschel discovers existence of infrared solar rays

1846 AD Adams/Leverrier discover Neptune

1930 AD Tombaugh discovers Pluto

1989 AD Magellan and Galileo spacecraft launched

1990 AD Hubble Space Telescope placed in orbit

1992 AD Mars Observer launched

Vocabulary

Altitude- the angle of elevation from the horizontal plane to a point above the horizon. Altitudes range from 0 (on the horizon) to 90 (straight up).

Annular eclipse - a solar eclipse in which a ring of sunlight can be seen around the edge of the moon.

Ascending lunar node - the intersection of the moon's orbital plane and the ecliptic where the latitude coordinate is increasing.

Autumnal equinox - one of the two points on the celestial sphere where the ecliptic intersects with the celestial equator.

Azimuth- the angular measure from a particular point on the horizon to another point also on the horizon. Traditionally the starting point of the azimuth is the northern most point on the horizon. Azimuth angles are then measured positively from the north (0°) through (90°), south (180°) and west (270°).

Central eclipse- a solar eclipse in which the axis of the moon's shadow cone crosses the surface of the earth.

Descending node- the intersection of the moon's orbital plane and the ecliptic where the latitude coordinate is decreasing.

Ecliptic- the sun's apparent annual path or orbit as seen from the earth. Against the background stars, the sun appears to traverse the ecliptic in the course of one year. From the point of view of the sun, the ecliptic is the path of the earth about the sun. The word ecliptic is also used to define the plane that contains the orbit of the earth about the sun.

Equinox - either of the two days when the periods of daylight and darkness are of equal length. The one in March is vernal equinox and the one in the fall is called the autumnal equinox.

Gregorian Calendar a reformation of the Julian Calendar which changed the way intercalary days (leap years) were calculated. For example: the year 2000 is a leap year, but 1900 and 2100 are not. Similarly, 1996 is a leap year, but 1997 is not. This reform approximates the tropical year to within about one day in 2500 years.

Horizontal coordinates these use azimuth and altitude to measure a location in the sky. They are referred to the plane of the observer's horizon.

Julian Calendar Day- A day in the calendar created by Julius Caesar. That calendar was a solar calendar that had twelve months each of a fixed length. An intercalary day, or leap year, was added every fourth year, so the average solar year was 365.25 days. This calendar was instituted in 46 BC and was replaced by the Gregorian Calendar in 1582.

Latitude - angular measure on the celestial sphere measured north or south of the ecliptic along the great circle that includes the poles.

Latitude- angular distance on the earth measured north or south of the equator along a great circle that includes the poles.

Longitude- an angular measure on the celestial sphere along the ecliptic starting from the vernal equinox (0°) and continuing positively to the east.

Longitude- angular distance measured along the earth's equator starting from Greenwich, England and continuing positive to the east.

Node- the intersection of a great circle on the celestial sphere with a plane that contains the origin results in two points called nodes. For example, the moon's orbit intersects the ecliptic plane at the ascending node and the descending node.

Season - one of the four divisions of the astronomical solar year, either solstice or equinox.

Solar eclipse- the partial or total apparent darkening of the sun when the moon come between it and the earth. The Sun appears in the sky either partially or totally covered by the Moon.

Solstice the day when the sun's longitude is either 90° (summer solstice) or 270° (winter solstice). At those times noontime Sun is either highest in the sky (summer solstice) or lowest in the sky (winter solstice).

Synodic month- the time from one full moon to the next (29.530588 days).

Presentation of the Unit

This unit will be presented at the beginning of the term. Highland is on a block schedule; each class session is 85 minutes long. I anticipate presentation, along with the demonstrations to take about three class sessions. On the first day we will discuss the motion of sun and moon. Lecture and discussion will last about an hour followed by the "Revolution and Rotation" activity described below.

 

On the second day we will discuss the astronomy of the four cultures discussed in the cultural background. We will do the demonstration " the Lunar Month" described below.

 

On the third day we will discuss the relevance of the work done by the ancients to our world. We will do the " Day on Earth" activity.

 

The demonstrations of rotational motion will be used to present the most difficult concepts of the unit. The motions of spinning bodies orbiting other moving bodies should be the most challenging portion of the unit.

 

Unit Objectives:

Students will: 1) become familiar with the motion of the earth relative to the sun and the rotation of the moon relative to the earth, 2) understand the cultural origins of the science of astronomy, 3) gain an appreciation of how the past is relevant to the present, 4) gain an understanding of how one’s culture affects one’s understanding of the world.

Outcome/Evaluation:

 

The degree to which students achieve the unit objectives may be measured in a number of ways. Since we will not be focusing on computational methods or physical theories, the traditional problem and short answer based physics test format is not appropriate. A long essay or an essay test which addresses the key ideas and concepts of the unit is the most obvious method of assessment. A group project where students collaborate to prepare a presentation to the class of new, but related, material is also a reasonable method of assessment.

The first time the unit is presented, student understanding of the unit will be evaluated by an essay test. I will try the group presentation the next time and determine which works better for my classes. A term paper is also required for the course, and topics presented in this unit may be used as the subject of the required paper.

Demonstrations:

Rotation and Revolution: The Moon

Have a student stand in front of the class facing the back of the room. Have him slowly turn counterclockwise a full 360 degrees. Have him describe what he sees as he turns: the back of the room, the left side (as viewed from the front of the room), the front, the right side, and then the back again). Explain that the student has just rotated once and as the student turned he saw, in turn, all sides of the room. This is rotation.

Now have another student stand in front of the class, facing the back of the room, toward the class. Have the first student move in a circle, counterclockwise, around the second student, always facing the back of the room. The first student starts out in back of the second student, then to their right, then in front, then to their left, and then back in back of them. This is revolution.

Now ask the students whether or not the first student rotated while revolving around the second student: No, they always faced the back of the room. Now, have the first student revolve around the second student, but this time always facing the second student. As they move around the second student, have them describe what part of the room they are seeing: first the back, then the left side, then the front, then the back again --- they rotated once as they revolved around the second student!

The Lunar Month

We can now discuss the Moon as it goes around the Earth. Since we always see the same side of the Moon, this implies that the Moon rotates once as it revolves around the Earth Student 1 = Sun. student 2 = Earth, student 3 =Moon. Have student 3 revolve and rotate around student 2 once (2 motionless). This is how long it takes for the Moon to go once around the Earth, 27 1/3 days. However, in reality, the Earth is revolving around the Sun. In 27 1/3 day, it has one nearly 1/12 of the way around the Sun. Have student 2 demonstrate this by having them move a little counterclockwise around student 1, the Sun.

Now, bring back student 3. Line up the students Sun, Earth, and Moon (1, 2, and 3) with the Moon student 3) facing the Sun and the back of the room. As seen from the Earth, this is full Moon. Now, as student 3 rotates and revolves around the Earth, have the Earth revolve slowly around the Sun. Have the Moon revolve and rotate once, so they are facing the back of the room again --- as can be seen in Figure 1, the three students are no longer in a straight line, it is not full Moon. The Moon must continue to revolve and rotate about 1/12 of an orbit until the Sun, Earth, and Moon are aligned again. This is defined as one month, the time from full Moon to full Moon, 29 1/2 days.

Have student 2 rotate once counterclockwise, begin facing the Sun and rotate until they are facing the Sun again --- they have rotated once. For the Earth this is 23 hours 56 min 4 sec. Now have student 2 do the same thing, but have them revolve slowly around the Sun at the same time.

In order for them to end up facing the Sun again, they have to rotate a little bit more than once. Therefore, the time from noon to noon, when the Sun is overhead (24 hours or one day), is slightly more than the time it takes the Earth to rotate on its axis. This is why we see different stars at different times of the year. The stars are like seeing different parts of the room as we rotate on our axis and revolve around the Sun.

Bibliography

                    Our Oriental Heritage, Will Durant, Simon and Schuster, New York, 1954

Internet Resources

http://www.astro.uva.nl/home2.html

http://seds.lpl.arizona.edu/nineplanets/psc/theman.html

http://idt.net/~craigi19/archaeoastronomy/DEFINED.HTM

http://ethel.as.arizona.edu/~collins/astro/subjects/observation3.html

http://www.ukans.edu/history/index/europe/ancient_rome/E/Gazetteer

Suggested Reading

Star Names: Their Lore and Meaning, by Richard Hinckley Allen. ISBN 0-486-21079-0. 1963, Dover Publications.

Native American Astronomy edited by Anthony F. Aveni. ISBN 0-292-75511-2. 1977, University of Texas Press

Archaeoastronomy in Pre-Columbian America, edited by Anthony F. Aveni. ISBN 0-292-70310-4. 1975, University of Texas Press.

Astronomy of the Ancients, edited by Kenneth Brecher and Michael Feirtag. ISBN 0-262-52070-2. 1981, MIT Press.

When Stars Came Down To Earth, by Von Del Chamberlain. ISBN 0-97919-098-1. 1982, Ballena Press.

Echoes of Ancient Skies: The Astronomy of Lost Civilizations, by E.C. Krupp. ISBN 0-452-00679-1. 1983, Harper & Row Publishers..

In Search of Ancient Astronomies, edited by Ed Krupp. ISBN 0-07-035556-8, 1978, McGraw-Hill Publishers. Star Tales, by Gretchen Will Mayo. ISBN 0-8027-6672-2. 1987, Walker & Co., New York.

Living The Sky: The Cosmos of the American Indian, by Ray A. Williamson. ISBN 0-395-35414-5. 1984, Houghton Mifflin Co. Boston.

Naked Eye Astronomy for Middle School Students

Blake Learmonth

Background and Rationale

Ask middle school students about Astronomy, and most will describe a science with telescopes, planets, stars and distant galaxies, a modern high tech science. Most would be surprised to find out that Astronomy is probably the oldest of the sciences, possibly the origin of observational science, and that in many societies it predates written history by thousands of years.¹ Equally surprising, would be the concept that Astronomy can be done with simple instruments (or none at all) and that it has very down to earth, practical applications. Fewer still would be aware of astronomy’s deeply spiritual connections.

Modern urban people seem out of touch with the natural world and the cosmos around them. At some level, that is not too strange. If a person buys food at a grocery store that imports off- season fruits and vegetables from the other hemisphere, travels from an air-conditioned house to an air-conditioned office in an air-conditioned car, the natural cycles around him have little effect on his daily routines. In today’s light-polluted world it takes a well-publicized event like an eclipse or a comet’s appearance to get people to look up, and then, in urban areas at least, they don’t see much.

Students in my classes, 6th and 8th graders, are at least as out of touch as their adult contemporaries. As part of a mapping unit that my students were working on last spring, students were required to know their cardinal directions and place them with reasonable accuracy on a map of our school. While the maps were being created I was frequently asked for help identifying directions. I would prefer that my students work things out rather than just tricking me into just giving them the answer, so I often answer questions with questions. My first reaction question to their direction question was, "Where does the Sun come up?" Several of them gave the right verbal response, "east," and some could draw the compass rose with the directions in the right relation to each other, but very few could point the right direction. I should mention that this took place in Albuquerque, New Mexico, a city with frequent clear weather, where the sun rises over a 10,000-ft mountain range. The view of the mountains is seldom obscured by dense vegetation or tall buildings. In the winter months, at least, these students are often traveling to school while the Sun is rising over the mountains; it is part of their daily experience.

In addition to lack of knowledge, Middle school kids harbor some serious misconceptions about some pretty basic astronomical ideas.² Snider cites an Israeli study from the late 1970s, replicated in San Francisco in the 1980s which indicated that the majority of elementary students and 25% of eighth graders were unclear as to what it meant when people said the Earth was "round." Many who agreed that the Earth had a spherical shape believed that we lived on a flat spot either on or in the sphere. The misconceptions that the phases of the Moon are caused by the shadow of the Earth and that seasons are caused by being closer to or farther from the sun, persist into adulthood. As teachers, we have to watch out for the belief that some ideas are so basic that "everybody knows" them. In teaching an American history lesson to eighth graders, during my first year as a teacher, I was pleased that most of them could state that a "Tory" was someone loyal to the British king. My bubble was burst however when my teaching partner discovered that most of them had no concept of what "loyal" meant.

Some concepts important to studying astronomy are very difficult for children who have not mastered abstract thought. Being able to think in three dimensions, for example, is hard for many adults. Many astronomy lessons require the student to change back and forth between a standing-on-Earth point of view and an out-in-space or "God’s eye" view, which is simply beyond the capability of most 11-14 year olds. The solution seems to be to involve students in first hand observation. (See lesson recommendations below.)

Unit Goals

One of the goals of this teaching unit is to make students aware of the astronomical phenomena that take place around them on a daily or seasonal basis. This awareness will be encouraged through both casual and formal observation. Since careful observation is at the root of all science, this practice can be justified on several levels: Experiencing the kind of observation that led to the science of astronomy, establishing a connection with the natural world by experiencing cycles first hand, and establishing or reinforcing a connection with Southwestern Native culture by emphasizing the long history of naked eye astronomy in this region. Studying ancient astronomy will also provide an opportunity for students to compare and contrast ancient and modern astronomy as well as notice the similarities and differences between the early astronomy of variety of cultures.

Additionally, activities should provide concrete role playing type opportunities where students can act out astronomical situations that are difficult to conceptualize, as well as the opportunity to build tools for making scientific astronomical observations.

Why Study Astronomy?

Ignorance may be bliss, but knowledge is power. An ignorant individual is totally at the mercy of apparently unknowable forces around him. Such an individual is also at the mercy of less ignorant individuals. For ancient people ignorance and survival were mutually exclusive. A person living in the natural world is confronted by astronomy; ignorance is very hard to maintain. The Sun, the Moon, the visible planet, and the stars rise and set everyday. Long before any kind of systematic study of the heavens existed, people had to notice day-to-day changes. Since natural phenomena like seasons affect all living things, members of even the most primitive societies benefit from being able to predict natural cycles. There is a right time to hunt for certain animals, a right time to gather certain plants. In agricultural societies timing becomes even more important. Conveniently, the sky provides the clocks and calendars to help people know the best time and, possibly more importantly, to anticipate or predict the best time. All that is required is careful observation.

To the ignorant, prediction has a magical, supernatural aspect, and those with the ability to predict are relatively more powerful than those who live from surprise to surprise. The job of Astronomer seems to have evolved from groups valuing individuals who could predict celestial cycles and events. According to John North in The Norton History of Astronomy and Cosmology, "Astronomy has always been allied with religion--in the first place, one suspects, because both were concerned with the same objects. The Sun, moon, and stars were divinities in many societies."³ I question the "always" in North’s statement. It seems that science and religion have had an adversarial relationship in western society for the last 500 years or so, but recent European history aside, astronomy has been valued by a wide variety of societies for its ability to predict natural occurrences and thereby schedule human activities in spiritual or practical harmony with natural cycles. For me it has been important to keep in mind that the disconnect between science and religion, spiritual and practical is a modern European phenomenon. To this day, in Southwest Pueblo societies, the pueblo astronomer is a religious figure, a "priest," who assures that his people, "perform the proper ceremony at the proper time."⁴ The observations that the priest makes are no less systematic or "scientific" than the observations made by people thought of as scientists by the non-Pueblo society. An activity like planting crops has both a spiritual "proper time" and a practical "proper time" that coincide and can be determined from astronomical observation. Getting the time right has, for many societies, both practical and religious implications.

Archaeoastronomy, Ancient Astronomy

If there is any idea that is consistent about ancient people and astronomy, it is that all ancient people were aware of sky, both the day sky and the night sky. They created rock art all over the world, they built structures that were either shrines or actual observatories, they created stories to explain celestial events, and they deified celestial objects. However, once the basic similarities are established, the details lead in a thousand directions. Additionally, while many of the astronomical practices which will be described below have contributed to, or evolved into, modern astronomy, others, like past and present Southwestern, Native American astronomy, exist actively independent of any interaction with non-native astronomy.

Ancient Europeans: the "Henge Builders"

The debate about the meaning of various British henges, Stonehenge, Woodhenge, and many others constructed over 2 or 3 millennia, all over the British Isles, fills literally hundreds of volumes, not to mention dozens of Internet sites. The debate itself brings up a very important aspect of Archaeoastronomy, the tendency to project modern ideas onto ancient cultures. Historian Stuart Piggott put it this way:

Scientists studying the various stone, earth and wood circles of Britain have been obsessed with alignments of various stones or posts with various astronomic events. Scientists have descended on these, and other, sites with video cameras, surveying equipment, and computers, none of which ancient astronomers would have had at their disposal. All of the technology applied to Stonehenge has not led to agreement among scientists about how it worked, though most seem to agree that the henge sites do function at some level as either observatories or shrines. To add to the confusion many of the sites have been rebuilt, not by modern archaeologists, but by a long succession of ancient people who used the sites. Their purpose may have evolved as well. "There were really several Stonehenges. Like a cathedral, it was built and rebuilt on the same spot over a span of two thousand years," using different building materials. "Successive construction work...destroyed much evidence that would allow us to trace astronomical alignments with confidence."⁶

Whether the alignments work or not, the high banked ditches and lentil topped stones (found only in the later versions at Stonehenge) form an artificial horizon that could have been useful in predicting events as common as solstices or as rare as solar eclipses.⁷

Egyptians and Babylonians

The Egyptians and Babylonians were sky watchers too. Having written languages and systems of numbers, they developed systems for recording events in the skies. Both developed calendars, and kept track of days, and divided the day into hours. The 365-day year is an Egyptian creation as is the 24-hour day. Dividing the hours into 60 minutes and again into 60 seconds comes from the Babylonians. Egyptians used star observations to determine their seasons, which were not solstice based. Egyptians had only three seasons, ‘flood’, ‘emergence’, and ‘low water’ or, ‘harvest,’ based on the flooding of the Nile and indicated by the helical rising of Sirius. (the first sighting of Sirius on the eastern horizon after its winter period of invisibility, in mid July) ⁸ The Ancient Egyptians also had three ten-day weeks in each month, which has no astronomical connection. In text books, Egyptians are often given credit for being great astronomers in the modern sense of the word, but:

Roman records considered any one living in Egypt to be Egyptian, so Greeks like Ptolomy, "the greatest astronomer of antiquity,"¹⁰ who lived in Alexandria, are referred to as Egyptians. Roman records also credit Egyptians with having invented things that were really borrowed from other cultures. The zodiac, for example, with several of the same constellations we use today, is found in Egyptian temples, but also in earlier Babylonian records.

Babylonian/Mesopotamian astronomical records span several centuries before and around the BC/AD transition. Modern astronomers relate to the Mesopotamians because they far exceeded the Egyptians in using mathematics. "All those sciences in the modern world that make use of mathematical methods are indebted to the astronomers of Babylon, from the last five or six centuries before the Christian era."¹¹ Among their accomplishments was the development of the sexagesimal, base 60, number system, which forms the basis for our time keeping and angle measuring systems today. Their oldest literature, the Gilgamesh epic "Has hints of ritual observing of the Sun, moon, and planets over distant peaks,"¹² a practice which seems to be the basis for observational astronomy in many cultures.

Over centuries of observation and recording events Babylonians began to see patterns in the recurrence of celestial events, and became able to predict events such as eclipses. Many of their predictions came directly from the data and a fairly accurate calendar. If an event happened over and over at a given interval, it was reasonable to predict that it is going to happen again at the same interval. There was no need to understand the why. Some Mesopotamian religions thought that certain numbers were important and meaningful, so it is possible that the numbers were seen as the actual cause of an event. Babylonian religion also connected astronomical events with earthly events. With huge astronomic records and huge historical records, Babylonians produced lists of omens, 7000 all together, many of them relating to the planet Venus, which predicted all manner of events. These omens were not exactly astrology, which was really a later Greek development. Babylonians had fallen into a very popular logical fallacy, post hoc, ergo propter hoc -- after this, therefore caused by this. And they had the records to prove it.

In a trend appreciated by modern scientists as a breakthrough, Babylonians made the transition between just observing events, and developing mathematical rules that exactly predicted the results. They had, for example, rules for calculating the rising and setting time of the moon in relation to its phase. Between the use of long record keeping and sophisticated mathematics, Babylonians became very good at predicting astronomical events.

Mesoamerican

Like the Babylonians and the Egyptians, The Mayans had written language, a system of numbers and mathematics. They kept extensive records of both historical and astronomical events. Unfortunately, most of these records were destroyed by the Spanish in the early 16th century, in the clash of religions that inevitably followed European invasion of Native American cultures. Although the loss of the majority of Mesoamerican written records to religious chauvinism has certainly limited, and possibly skewed, our knowledge of their society, continuing progress has been made in interpreting the surviving documents. As well as surviving documents, there are surviving people, descendants of the Maya, from whom ethnographic information may be gleaned.

We know, for example, that Mayans produced a variety of calendars, and that the calendars were based on astronomy. From studying Mayan documents and monuments:

There were basically three Mayan calendars. One roughly equivalent to our 365 day solar calendar, one referred to as the "vague" calendar with 360 days, and a religious calendar of 260 days, which is referred to as an almanac because it also contains records and predictions of eclipses and other astronomical events. These included some that could not possibly have been observed by the Mayans or any of their neighbors, but that could have been predicted mathematically.

There are Mayan records of horizon watching, and when the horizon was obscured by jungle, the Mayans built structures to observe solar events at least. At Uaxactún in what is now Guatemala a pyramid faces east, providing a view of three small temples that form an artificial eastern horizon. An observer standing on the center of the steps of the pyramid at sunrise on the day of the summer solstice sees the sunrise aligned with the left temple. If the procedure is repeated at either equinox the sun rises centered in the middle temple. At winter solstice the sun aligns with the right temple.

Mayans also observed, recorded and predicted the behavior of the visible planets and stars; they particularly focused on the movements of Venus which are said to have dictated the time for ritual warfare.

Southwestern Native Astronomy

In contrast to the Maya, the Southwestern Pueblo People, both modern and prehistoric, have not kept written records (Until very recently their languages have not been written.) There is no indication that they use(d) mathematics, or even arithmetic, beyond relatively short counts.¹⁴ Despite these facts, Pueblo people have a long tradition of observing and using astronomical events. For Pueblo people the spiritual world and the world of astronomy coincide. The reasons for doing astronomy are spiritual. It might be reasonable to say that all actions in the Pueblo world are spiritual. When one combines this idea with a view of the cosmos as interactive, the job of astronomer takes on a very different character from the job of astronomers in the outside world. Westerners study astronomy to try to understand the cosmos, pueblo people already understand the cosmos and do astronomy to stay in harmony with the order of the universe.

Staying in harmony has requirements. "Nature functions with the active cooperation of mankind, who must perform the proper ceremony at the proper time to ensure the regulation of order."¹⁵ Furthermore, the method for knowing the proper time and the proper ceremony must also be correct. For example, most Pueblo groups do sun watching in order to anticipate ceremonies around the winter and summer solstices; the responsibility usually falls on a "Sun Priest," who could just get out an almanac and look up the exact time of the solstice and announce it to the people in time for them to prepare for the ceremony. To an outsider this would seem fine, but for order to be maintained, the Sun Priest must obtain the information in the proper way. The proper way is to observe the sunrise or sunset from a certain spot, possibly marking your observations in some way, until the moment is right to announce the ceremony. It seems that the process is critically important. In a Zuni story recorded in the 1960s , a woman tries to seduce Pequin, the Zuni sun priest.

Later in the story, the woman kills the Sun Priest, and he is proven right when the Sun doesn’t come up until a new Pequin is found.

The idea that astronomical rituals are performed to assure the continuation of life as it has been, is not unique to the Zuni. When asked why ancient Britons would build Stonehenge, Alison Jolly replied, "Anyone who has lived through an English winter can see the point; to make the sun come back."¹⁷ For the Chumash of California, "The winter solstice was the most critical moment of all because of the possibility (If the people did not take the correct ceremonial actions) that he sun might choose not to come back."¹⁸

Careful observation of the Sun, Moon, and stars also reinforces the Pueblo view of a cosmic duality. The Hopi universe, for example, is made up of two worlds, an upper and a lower. The two worlds are balancing opposites. When it is day in the upper world, it is night in the lower world; as stars set in our world they rise in the other, summer is winter...¹⁹ Ceremonies help insure that the Sun, which is personified and deified along with other celestial objects, will make harmonious transitions to and from the other world at the proper time.

The Mechanics of Pueblo Astronomy (Sunwatching and some basic astronomy)

Since pueblo astronomy is tied up with ceremonial schedules, celestial objects, which exhibit repeating cycles throughout the year, are most commonly observed. Since instruments are not commonly used, these cycles must be observable with the naked eye. From an earthbound point of view, the Sun, the Moon, and the stars all go around the Earth rising in the east and setting in the west. (Caused by the eastward spin of the Earth) Days are counted by the rising or setting of the sun, which is pretty hard to miss. But, unless one is paying attention, some of the other celestial motions are not so hard to miss. Still from an earthbound point of view, the point of sunrise (or sunset) on the horizon changes from day to day with the seasons. At the spring (vernal) equinox, when day and night are of equal length, the sun rises to the east (March.21). From that day until the summer solstice, June 21, the day gets longer, the night shorter, and the sun rise moves north along the horizon. At first the movement north is quite rapid, easily visible. As the year progresses toward the summer solstice, the day to day movement of sunrise slows to the point of being imperceptible. The sun seems to stand still, which is what solstice means, "sun stands still." With practice and careful observation, a sun watcher can both mark and anticipate the solstice. No fancy equipment is needed. World wide, ancient and modern people use the two methods used by Pueblo Sun Priests. The first is horizon watching. Sun priests selected a spot, usually near the pueblo, with a good view of the eastern horizon. It is important that the horizon is not smooth; there must be details for reference points. (See figure 1) From his watching point, the sun priest watches for the first gleam of sunlight every morning, noting its location relative to features on the horizon. At first, all the sun priest would be able to do would be to note the solstice having passed. He would notice that the Sun’s northward movement had stopped, seeming to stand still for a few days. The Sun would then be seen to move south, at which point the Sun priest could announce that the solstice had passed. As the sun moves south along the horizon, it passes the same points as it did on its way north. If a count had been kept, tying knots in a cord or scratching lines on a calendar stick, the priest would know how many days it had taken for the sun to make the round trip from a particular landmark to the " Sun’s Summer House" and back (let’s say 20 days, for example). The natural assumption would be that it took half of the days each way, so the solstice would be the middle day in the count. The next year, with a good memory or some sort of record, the Sun priest would know that when the sun passed the horizon marker, solstice would be in 10 days. Assuming the sun priest has chosen a good place from which to watch, the same procedure works for winter solstice, only the directions are reversed. Similarly, sunset also works, but is much harder to view, since the observer is blinded by the sun right up to the moment that the last gleam needs to be observed. Topography often dictates the choice of the sun watching procedure.( See Figure 1)

In the Zuni oral tradition, the story is that it took the first Pequin eight years to get the solstice right, Which may or may not be intended to be taken literally. It may just indicate that it was important to get it right and that it took a long time. Eight and other multiples of four are important ritual numbers for Pueblo people.²⁰ The second method for Sun watching involves using features of either natural or man made structures to project sunlight on a wall so that the approach of the solstice can be anticipated and then confirmed. For this to work, placement of the opening and the distance to the wall have to be within certain limits. The alignment to the Sun also has to be right (but there are several different alignments that work). The ideal situation is to have a small opening in a wall that has an unobstructed view of the rising or setting Sun and an inside wall one or two meters from that opening onto which light can be projected. The sunbeam entering the opening acts like a lever, projecting a spot of light on the opposite wall which pivots on the fulcrum of the opening as the Sun moves. The position of the spot of light at sunrise (or sunset) can be marked on the wall. Unfortunately, there are two aspects of the light projection system that work against each other. If the opening in the outside wall and the wall onto which the light is projected are very close, the spot of light will have very crisp edges, which is good for accurate observations. However, the shorter lever arm of the sunbeam means that the spot will move only a very short distance, too short for daily changes to be apparent. Light projected on a more distant wall will have more apparent movement, but the resolution deteriorates, the edges of the spot become fuzzy. For naked eye observation, the projected spot needs to move at least .5 cm per day in the period about two weeks before the solstice. If the site meets these criteria it can be used to predict the solstices within a day.

Apparent alignments of buildings used by prehistoric pueblo people have led to the inference that, like their descendants, early residents of the southwest used structures for astronomical purposes. There are many sites in the Chaco Canyon area of New Mexico and elsewhere in the Four Corners area where interesting things happen at important astronomical times. There are certainly places that could have been astronomic observatories.

One particularly interesting prehistoric pueblo site is Pueblo Bonito in Chaco Canyon, which has features that make both types of sun watching possible. Pueblo Bonito is a large multi-story structure with several hundred rooms and many round ceremonial Kiva spaces. It also contains several corner windows or doors, which are uncommon in ancient Pueblo architecture. For winter solstice anticipation, one of these openings in particular, gives a good view of the southeastern horizon which has features allowing for good sunrise watching until the end of October. At that time the sun starts to move on to a relatively featureless part of the horizon. About the same time as horizon watching becomes difficult, the opening projects a beam of light into the room which moves noticeably northward as the solstice approaches. The light patch moves an average of 3 cm per day; with wall markers, the beam’s horizontal motion could be used to anticipate the winter solstice within a day.²¹ The beam continues across the wall until the winter solstice when, "the sunbeam neatly throws a square patch of light into the corner of the room.²² (I should mention that a small west facing window in my house projects a rectangular patch of light onto the opposite wall of my living room, which aligns very nicely with the corner of the room at summer solstice sunset. Until very recently my living room had not functioned as an observatory.)

Moon Watching

Pueblo people observe the moon, particularly the phases of the moon, in order to schedule ceremonial and agricultural activities, (See "Moon Phases" below) and to establish a measurable length of time shorter than a season but longer than a day. The "moon" = "month" concept is certainly in line with the origin of the word "month" in English. Pueblo "months" also come from lunar phase cycles.(The Jewish and Islamic calendars are similarly lunar cycle based.) "For most pueblos, the month usually begins at the first sighting of the first visible crescent -- the observable "new" moon,"²³ which sets the length of pueblo months at about 30 days. Ten months per year is most common, but numbers of months from 6 to 14 are historically reported.²⁴ There are two important concepts that contribute to the controversy. Because of the Pueblo concept of duality, the names of the first five or six months of the year are sometimes recycled for the second half. Also, and this is a problem for all calendars, the 29.5 day lunar phase cycle doesn’t fit evenly into the 365.25 day solar year. The discrepancy leads to the need to create intercalation, "leap" periods, to compensate. It would be very easy for an outsider to confuse the intercalation periods with real months.

Moon Phases

The daily change in appearance of the Moon from fully lit to completely dark and all of the steps in between, are the "phases" of the Moon. Contrary to very commonly held misconceptions, the shadow of the Earth on the Moon has nothing to do with the phases. Because the Moon’s orbit around the Earth is tilted about 5 degrees from the Earth’s orbit around the Sun, the Moon very seldom passes through the Earth’s shadow. Phases are caused by the Sun’s light hitting the Moon from the side from our point of view. Imagine someone sitting next to a lamp in a dark room. If you are facing them, the half of their face toward the lamp will be brightly lit; the other side will be shadowed. Observe the "first quarter" Moon about two weeks after the new Moon. It will be in the southern sky at sunset. If you face the Moon, the right side of your head and the right side of the Moon will be lit by the Sun. A person facing you would see half of your face lit by the Sun in just the same way that you see half of the Moon’s face lit by the Sun. At full Moon, the Moon rises at sunset and its entire face is lit by the Sun (it always is fully lit, but you are observing at a different angle each day, so the fully lit part faces a different direction from your point of view.) Again, a person standing between you and the Sun sees you the same way you see the Moon, one "face" in full sunlight. The "third quarter" Moon is high in the southern sky at sunrise. As you face the Moon, its left side will be lit and a person facing you will see your face lit on the left side. In both cases the side toward the Sun is lit. Lastly, at the new Moon you probably won’t be able to see the Moon at all, since the Moon is more or less between you and the Sun all day. Both the brightness of the Sun and the fact that the shadow side of the Moon is facing you make the moon nearly impossible to see. A few days after the new Moon, just after sunset in the western sky, something really interesting occurs; the Moon, still lit mostly on the side away from you, appears dark, although a glimmer of sunlight may be showing on the right edge, but the dark side of the Moon is lit by Earth glow, the Sun’s light reflected off of the Earth. Someone standing on the dark side of the Moon would experience a "full Earth." None of the previous words, even if I had stated them perfectly, would be a thousandth as effective for making this concept clear as really doing the observation. You may also be surprised, as I was, how often the Moon is visible during the day. (See Moon phase activities below.)

Observational Methods and "Tools"

As various cultures carried out astronomical observations, they developed methods and tools to make the process easier. The earliest "tools" were natural; as indicated above, many people used--and still use-- horizon landmarks to mark the position of the sun, moon, and stars. The Moon’s phases were, and are, also observed. The information obtained was and is used to track and predict celestial events and to time ceremonial and practical events. Tools that followed seem to fall into two groups: time measuring tools, and position measuring tools. Time measuring tools included calendars and sundials,( as well as other shadow clocks). Position measuring devices were used both to locate objects in the sky and to use objects in the sky to locate one’s self on the Earth.

If one pounds a stick or pole into the ground, a shadow will be cast. The shadow casting pole is called a gnomon. Observing the shadow will allow a person to notice several things. Hourly (continuously), the shadow will change direction and length. From day to day, the sunrise and sunset angle of the shadow will change, as will the length of the shadow at mid day. Gnomons were used by many ancient people and are still used in modern sundials. Observing seasonal changes in a gnomon’s shadow allows solstice prediction and also establishes a yearly calendar.

Gnomons can also be used to establish directions.²⁵ (See gnomon activity below.) In the simplest use, the shadow of a vertical gnomon points north at noon (when its shadow is shortest.) for latitudes north of the Tropic of Cancer. The east-west line can be established by connecting the end points of equal length shadows. Malville and Putnam suggest that the prehistoric pueblo people may have used gnomons to precisely align their buildings.²⁶

Astrolabes

Any instrument used to measure altitudes above the horizon can be called an astrolabe. Planispheric astrolabes combine the ability to measure angles with star charts for specific locations, which allow the time to be determined as well as allowing a number of other observations to be made. There is an excellent web site devoted to astrolabes that can be found at: http://myhouse.com/mc/planet/astrodir/astrolab.htm. Many navigational instruments, including sextants and quadrants evolved from astrolabes which were developed thousands of years ago by Greek and Islamic scholars. The astrolabes that students will construct will be simple sighting and angle measuring tools. (See astrolabe lesson below, and figure 3.)

Lesson and Activity Suggestions

Target grades: 6-8

Sun and Moon Watching:

Focusing Activity:

Talk with students about the historical precedence for making basic astronomical observations. Emphasize whichever cultural history or histories are appropriate to your locale. In any case, students should know that people have been observing the sky for millennia. They might enjoy a challenge, "Most kids a thousand years ago, with no telescopes, computers or television, knew more about what was happening in the sky than you do."

Each period will keep a Moon and Sun watching log, including the local rising and setting time, the phase of the Moon (by description and drawing), and the position of the first glimmer of sunlight on the Eastern horizon. The teacher will create forms for posting the information, and find a suitable location for sun watching. The instructions should include dire warnings in as many languages as necessary, instructing students not to look directly at the sun! After Astrolabe lesson has been done (See below) students can also record the azimuth, the number of degrees along the horizon, of the rising sun, as well as its altitude at noon.

University Of Texas, Austin McDonald Observatory’s Star Date Radio Report:

Students will be required to listen to University Of Texas, Austin, McDonald Observatory’s Star Date radio report on National Public Radio (7:00 PM daily in Albuquerque) or access their web site, http://stardate.utexas.edu/radio/s_

radioscript.html, to post in their science journals and report back to their classes. All of these responsibilities will be rotated among the students, so that every student won’t have to watch the sun and moon or report on Star Date every day.

Regular Lessons:

Lesson One: Introduction to Astronomy Through Children’s Books

Goals:

Use low reading level, high interest children’s books to introduce the subject of astronomy and to introduce astronomy vocabulary. To encourage peer teaching.

Objectives:

In groups of four, students will review children's books on astronomy. Students will report to the class what they liked and didn’t like about the books they reviewed as well as three pieces of information that they think were important. Each group will also add 5 astronomy words to a class vocabulary list (which will be combined with lists from the other 5 classes).

With teacher guidance, students should acquire basic information about the structure of the solar system, particularly the Sun-Earth-Moon system. They should become comfortable with the idea that their universe extends far beyond the solar system. They may acquire some information on different cultural outlooks on astronomy.

Background:

I was astounded at the number of children's books on astronomy in my local branch library. Most are graphically vivid and exciting, and as far as I could tell most were free of obvious misinformation. If this is typical, it should be fairly easy to assemble a fairly large collection of books to be reviewed. If books on local Native American astronomy or ancient astronomy are in the collection, try to get them as a contrast to modern "Western" astronomy.

This class is the anticipatory set for the unit, and as such has no anticipatory set of its own. My guess is that with a pile of Astronomy books on a table the problem will be to get the kids to stop looking at the books long enough to give instructions.

Instruction:

Students should be placed in groups of 3-5, using whatever group selection and role assignment scheme is typical in your classroom. Let the students know that they are starting a unit on astronomy and that you would like them to look at the books on the tables for about 5 minutes. After 5 minutes have students brainstorm what they think astronomy will be about. Use a web or list on the board to record their ideas. Pass out or describe the following assignment:

Compile the vocabulary list from all classes and distribute to students. Use crosswords, word searches, and other vocabulary games to increase vocabulary knowledge.

Materials:

25-35 children’s astronomy books, some duplicates would be okay. (In the Southwest, Native American astronomy stories can be included for cultural reference.)

Lesson Two, Angles:

(Could be a cooperative lesson taught with the math teacher if students are in "teams" or "families.")

Goals:

To make students aware of angles. To acquaint students with tools for measuring angles.

Objectives:

Students will observe and measure angles. They will be able to identify 45^o, 90^o angles, and 360^o of a circle.

Background:

Babylonians came up with the idea of dividing the year and the circle into 360 parts. The degrees of the circle correspond closely to days of the Earth’s orbit around the Sun. Like time, Babylonians with their number system based on 60, divided each degree into 60 minutes and each minute into 60 seconds for very precise measurements of angles on very big circles.

Focusing Activity:

Students should have protractors. Distribute several cut out shapes to each table group. Shapes should include triangles, squares, rectangles, polygons, and circles. Let students manipulate them for five minutes. Suggest that students might "measure" them with their protractors, but don’t explain what "measure" means. After 5 minutes, ask what students think that an angle is. Allow the discussion to go on until a reasonable answer is obtained.

Instruction: Measuring Angles

Talk briefly about Babylonians. (See background above.) Ask if any of your students are skateboarders, dancers, or ice skaters. If so, ask what a "360" is, a full circle spin. Explain that the name comes from the 360^o in a circle. Have students look at their protractors, most will have half circle 180^o protractors. Using either a giant protractor on the board or a clear one and an overhead projector, demonstrate measuring some angles. You may want to talk about acute, sharp angles less than 90^o and obtuse, open angles greater than 90^o. Be sure that you measure some 90^o angles and some 45^o angles. (90o angles are important in astronomy, 90^o separate the cardinal directions, the equator and the poles, and the horizon to the zenith, and 45^o angles are common in everyday activities.)

Practice:

Create or acquire a work sheet on measuring angles; or use the shapes from earlier in the activities. Have the students measure a variety of angles using their protractors.

Assessment:

Within the groups, have students exchange and correct the papers. Let them know not to be too picky, that the idea is to get within a few degrees of the correct angle. Precision will become more important as they practice and measure real angles in astronomy. The mission of the group is to make sure everyone at their table knows how to measure angles.

Lesson Three: Shadows and Gnomons

Goals:

To allow students to experience the way shadows are cast and see what the shadows can tell us about the movement of the light source or the shadow casting object.

Objectives:

Students will construct small shadow casting instruments and experiment with positioning them relative to light sources.

Materials:

Per student, one piece of Per table, either a flashlight or a foam core, table lamp with no shade
0 cm x 10cm x 5mm
one toothpick
protractors

Shadow Activities: (See figure 2.)

Here are two activities that can run simultaneously so that only half as many lamps and flashlights will be needed, and a third separate activity.

Activity One:

Students construct squares with cardinal directions indicated on them as pictured in figure 2. A tooth pick should be stuck in the center as close to vertical as possible.

Students will experiment with aiming a flashlight at the toothpick gnomon from different angles, changing both vertical and horizontal position, and recording how the shadow changes as the light source moves. The observations can be very freeform, or students can be provided with a list of angles of the light, and be required to record shadow length and angle for each.

Extension:

Have students prop up the north edge of the gnomon platform about 20^o_. Observe the changes in the shadows.

Activity Two:

In this version the light source, a small table lamp with no shade stays still and the gnomon platform moves around it. It is important that the platform continues to be pointed in the same direction while it moves around the light.

Extension:

At first, the gnomon platform should remain flat on the table as it "orbits" the lamp. Once the effects have been observed in one plane, students can try raising and tilting the platform.

Activity Three:

Find a large unshaded area outside. Have students bring in poles, broomsticks dowels, 2x4s, pipes, rebar, pretty much any thing tall and straight will work. Place the poles vertically, scattered around the area. Visit the area frequently with students to observe shadows. Use the gnomon shadows to establish the cardinal directions.

Lesson Four: Astrolabes

Background:

Both the Project ASTRO Universe at Your Fingertips, (sec J. page 9-19), and Astronomy For All Ages, (pages 35-38) have excellent plans and activities to make and experiment with astrolabes. A web search on "making an Astrolabe" will also yield reproducible patterns for making simple angle measuring astrolabes.

(http://myhouse.com/mc/planet/astrodir/astrolab.htm) is an excellent site for astrolabe history and for information on a variety of types of astrolabes. The site creator also offers fairly sophisticated astrolabes custom made for your location.

Goals:

To acquaint students with an ancient astronomical instrument, the astrolabe and its usefulness for measuring angles to objects both on the earth and in the sky. Also to introduce safe solar observation techniques. To create a tool that can be used in later activities.

Objectives:

Students will construct simple astrolabes from easily obtainable materials. Students will use their astrolabes to make a number of horizontal and vertical angle measurements. Students will use their astrolabes to measure angular heights and angular separations of various objects around the school and on the horizon.

Materials:

Either: copied or printed astrolabe protractor from one of the sources mentioned above and a stiff material like card stock, cardboard, thin plywood, or foam core, and suitable glue for mounting reproduced protractor

Or: a plastic student protractor

And: a smooth plastic straw, tape or glue to attach the straw to the protractor, strong thread or thin string, a washer, nut or fishing weight, and an 1/8 inch or smaller drill bit (for putting a hole in the plastic protractor).(see figure 3)

Activities:

Use the astrolabes outside of the classroom to measure the angular height of a variety of objects. Sight through the straw and read the angle off of the protractor.

To measure the angle of the Sun, aim the astrolabe straw at the Sun without looking at the Sun. Put your hand or a paper in the shadow of the astrolabe and adjust the angle until there is a small round dot of sunlight passing through the straw and hitting your hand or the paper. Read the angle off of the protractor.

Evaluation:

Check as students are doing their observations or give a specific list of objects to measure

Lesson Five:

Using the Astrolabe to Prove that the Earth’s Surface is Curved

Goals:

To allow students to experience the curvature of the Earth directly, using the astrolabes that they created in the previous lesson as a tool. Students should convince themselves and each other that their observations indicate that at least the part of the Earth around Albuquerque, NM is not flat.

Objectives:

On a field trip, students will measure the vertical angle of the sight line from the top of Sandia Peak, east of Albuquerque New Mexico to the top of Mt. Taylor, about 110 km away, using an astrolabe. They may also just get a feel for the curvature of the Earth from the way the horizon looks from a high mountain point of view. Students will brainstorm possible implications of the angle that they observe. Hopefully students can reach a consensus about the shape of the Earth.

Background:

Middle school students still have problems rationalizing the conflict between their daily observation that the world around them is more or less flat, with being told over and over by their teachers that it is "round." The word "round" may well be part of the problem. I try very hard to use the word "spherical," but find that neither my sixth nor eighth grade students are really comfortable with the word "spherical." I usually end up saying, "round, like a ball." This field trip will help students experience the sphericalness of the Earth directly.

Activity:

Aside from physically transporting the students to the top of the mountain, this is really a very straight forward lesson. Students will be shown a western horizon profile as seen from Sandia Peak (10,400ft, 3800 m.); Mt. Taylor (11,300 ft, 4130 m) is a very prominent, cone shaped volcano, and is hard to miss.

Their assignment is to sight the top of Mt. Taylor through the straw of their astrolabes and record the angle compared to the ground, which is the sight line when the weighted string passes by the 0^o mark on the astrolabe’s protractor. (This may take some explanation if you are using a plastic protractor for the degree scale of your astrolabe, since straight down is 0^o on an astrolabe, but is 90^o on most protractors. Subtracting 90 from the number on the protractor will give the degrees of altitude relative to the horizon) What should stimulate controversy among the students is that while Mt. Taylor is higher in altitude than Sandia Peak the sighting angle will actually be negative, down several degrees below the place where the horizon would be if the Earth were flat. Students with quarter circle astrolabes will have to flip them around backwards, looking through them opposite direction they use sighting stars, which will again emphasize the downward angle of their sighting.

At the next class opportunity encourage, the discussion as to why Mt. Taylor seems "down" from Sandia Peak. Get students to diagram their explanations. Possibly a debate format would work if the class seems to be dividing up into a "flat Earth" group and a "curved Earth" group.

Lesson Five: Acting Out a Year in the Life of the Earth:

Goals:

By modeling the actions of the Sun-Earth-Moon system students can get a feel for how the seasons work, what causes the phases of the Moon, and why we see different stars at different times of year.

Objectives:

Students will create a room sized map of the constellations on a large roll of black bulletin board paper, create papier-mâché Earth and Moon "heads," and act out a year of the Earth orbiting the Sun. The system will be stopped at various points for a tour guide style narration of the sights. (and for the actors to get aligned correctly to simulate the Earth’s tilt on its axis)

Focusing Activity:

In class reading of Sun and Moon stories from a variety of cultures.

Materials: large roll of Black paper
white chalk
very large balloons for Earth and Moon forms (globes would of course work too.
papier-mâché supplies: water, wheat paste, and newspaper.
very bright light source
darkened room

Activities:

Each period will create a section of the zodiac equal to two months of calendar time.
Earth and Moon heads will be created or Earth and Moon globes located.
Earth and Moon actors will be elected
Several "tour guides" will be selected. and given their scripts. These scripts could also be generated by students researching a particular section of the zodiac as a research project.

The completed zodiac will be attached to the outer walls of the classroom at about table height.

A very bright light source will be pointed at the "Earth" and "Moon" as they orbit.

The "tour guides" will narrate at least the following events:

The Summer and Winter Solstices. At Summer Solstice the North Pole tips toward the light source about 23^o. At Winter Solstice the North Pole tips away from the light source about 23^o. The Vernal Equinox, 90^o counter clockwise from the Winter Solstice, the Earth Tilts back toward the Winter Solstice point. The Autumnal Equinox, 90^o past the Summer Solstice the Earth still tilts toward the Winter Solstice point. At any point, the Moon’s phases can be demonstrated. Remember, the Moon’s orbit is very slow compared to the Earth’s spin, about 1/27 as fast.

Lesson sketches:

Sundial Activity: Use gnomon activities with the "field of poles" to spin off into building sundials. There are good patterns in The Universe at Your Fingertips and Astronomy for All Ages.

Field Trip to an Observatory: On Friday evenings, during the school year, the University of New Mexico observatory is open to the public. There are several telescopes set up and usually several friendly helpful UNM astronomy students to guide kids. I’ve taken as many as 100 students, but smaller groups on successive weeks works better.

Field Trip to an Ancient Native American Archeological Site where Astronomers and Archaeologists believe astronomical observations were made. Chaco Canyon is a great place to visit but it is a long way from almost anywhere.

Bring a Planetarium to School: Most cities have museums or organizations with inflatable mobile planetariums. If you teach middle school, make sure they know that you need them to do their activity 6 times in a row.

Start a Sun and Moon Watching Tradition: Set up a location for making sunrise observations. Have kids design a structure to help with observations. The gnomon field might give them some ideas. Have kids write a secular ceremony to welcome the Sun. Consult with religious people to avoid stepping on any one’s traditions. Maybe a "Sunrise Club."

Notes

1John North, The Norton History of Astronomy and Cosmology, (London: W.W. Norton & Co., 1995) xxii.