mindset mathematics visualizing and investigating big ideas grade 4

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Mindset Mathematics Visualizing And Investigating Big Ideas Grade 6

Author : Jo Boaler
ISBN : 9781119358831
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Mindset Mathematics Visualizing And Investigating Big Ideas Grade 5

Author : Jo Boaler
ISBN : 9781119358787
Genre : Education
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fifth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual mathematics tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Mindset Mathematics Visualizing And Investigating Big Ideas Grade 3

Author : Jo Boaler
ISBN : 9781119358794
Genre : Education
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Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the third-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Mindset Math Grade K

Author : Boaler
ISBN : 1119357608
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Proceedings

Author : American Society for Engineering Education. Conference
ISBN : UCSD:31822006825749
Genre : Engineering
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An Encyclopedia Of Cosmologies And Myth Ancient Astronomy Clive Ruggles 2005

Author : ABC-CLIO, Inc
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Genre : Body, Mind & Spirit
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The Wonder of the Skies The sight of a truly dark night sky is simply breathtaking. In the modern world it is denied to all but those who still live, or might occasionally venture, well beyond the glare of city lights and the effects of atmospheric pollution. For people in the past, though, the panoply of thousands of stars was a familiar sight. Some twinkled particularly brightly; others hovered on the borderline of visibility. A few were tinted orange or blue. They formed distinct patterns that moved around but never changed. The Milky Way was a familiar sight to all, snaking across the heavens with its light and dark patches forming recognizable shapes. The sky also contained numerous isolated faint and fuzzy objects (nebulae), fixed among the stars, as well as bright wandering stars (planets), and of course the moon, dominating the night sky, lighting the way by night, and rendering many of its fainter companions temporarily invisible. Added to all this was the occasional appearance of something rare or totally unexpected: a shower of meteors (shooting stars), a lunar eclipse, an aurora (at high latitudes), or—more seldom still—a comet (often perceived as a tailed or plumed star) or a new star (nova). The exact appearance of the heavenly vault differed from place to place and time to time. Whether it was visible on a particular night was dependent, of course, upon local weather conditions. However, the visual impact of the sky on a clear night was always stunning, and even in the cloudiest and wettest of places there were a good many clear periods. As a result, human communities the world over, and for many thousands of years, have recognized familiar patterns and cycles of change in the skies, as well as unexpected sights and events, and struggled to make sense of them. The inhabitants of the night sky—whether perceived as animals, fantastical creatures, legendary characters, ancestors, or other entities— were ever present. The cycles of their appearance and disappearance provided the basis for, and reinforced, countless creation stories and cultural myths. The lack of opportunity to experience the true night sky is, for a great many people in the modern Western world, something beyond their control. The same cannot be said, though, of the daytime sky, and yet few people pay much attention to it beyond worrying about the weather. Only a meager proportion—and Introduction this does not just apply to city-dwellers—could, for example, orient themselves from the time of day and the position of the sun, or could accurately describe the way in which the sun’s daily arc through the sky changes with the seasons. As a result, it can be difficult for us to imagine just how great an impact the sky, whether by night or day, had upon human cultures in the past. Yet we need look no further than the many indigenous peoples today for whom the sky continues to be of immense importance. In addition to this, certain world religions such as Islam continue to tie daily and annual observances very explicitly to the appearance of the sun and moon (see ISLAMIC ASTRONOMY). And one only has to talk to some of the older people living in rural areas, even in the world’s most densely populated and developed nations, to discover that an immense amount of practical, everyday sky knowledge was possessed even within living memory. Who, sky watchers of the past might wonder, could fail to notice the regular cycle of lunar phases keeping time with the human menstrual cycle? Who could fail to recognize the changing path taken by the sun through the sky, higher in summer and lower in winter? Who, even in an unfamiliar place, could fail to be able to tell directions and hence find their way about by night or day using the sun or stars? Perceptions of the Skies in the Past ARCHAEOASTRONOMY can be defined as the study of beliefs and practices concerning the sky in the past, especially in prehistory, and the uses to which people’s knowledge of the skies were put. It has been recognized in recent years as a legitimate and worthwhile academic pursuit, but it also strikes a popular chord, bringing together two of the most attractive sciences, archaeology and astronomy. It combines the excitement of the cosmos with the romance of the past. Books making spectacular claims about ancient astronomical knowledge often find themselves on bestseller lists. But why should studying people’s perceptions of the skies in history, let alone in prehistory, be of particular interest or importance to scholars, not to mention anyone else, in the twenty-first century? One reason is that archaeoastronomy gives us important insights into how people in the past made sense of the world within which they dwelt. People’s lives were governed by observations of objects and events in the world around them. On one level, it is obvious that human communities needed to keep track of various seasonal markers in order to control and maintain their food supply through the year. This would be true whether they subsisted by harvesting plants, fruits, and tubers, by fishing, by hunting, by herding animals or by growing crops, or (most commonly) by a combination of these. CALENDARS, however rudimentary, were necessary for survival in all types of human society: for the smallest bands of hunter-gatherers; for farming villages controlled by local chiefs; and for complex urban societies seeking to support the higher social echelons of elite specialists, craftsmen, priests, and kings. But humans share a deeper need to understand the world that they inhabit. This does not necessarily mean seeing humankind (or the human mind) as existing within the “objective reality” of the natural environment, as is the modern scientific view, but more generally perceiving the cosmos as a conceptual whole with oneself and one’s own community embedded within it. In such a view of the world, the human body, or the dwelling house, or the sacred temple, is often seen as a microcosm reflecting and reinforcing the nature and structure of the cosmos as a whole. Such a worldview makes people strive to be at one with the cosmos of which they are a part and achieve a harmony of existence that enables individuals and whole communities to survive and flourish. This harmony is sustained by continually observing what is happening in the world and keeping one’s own actions in tune. The sky was an integral and prominent part of the perceived cosmos. Its familiar sights and unceasing cycles were part of the fabric of life. Its rhythms were correlated with the time of day and with the seasons. In fact, although we know these cycles to be unfailingly regular and reliable, to past peoples they may not have appeared any more so than a host of other seasonal indicators in the world around them. The important point for us is that, unlike the rest of their perceived world, the sky is a part that we can visualize directly. Landscapes change: patterns of settlement and land use alter, people move around, plants constantly grow and die. We only have indirect knowledge of the appearance of past landscapes. But thanks to modern astronomy, we can reconstruct mathematically the actual appearance of the sky (or, at least, the regular aspects of it—that is, the appearance of the sun, moon, planets, and stars) at any place on earth at any time in the past and visualize it on a computer display or in a planetarium. This gives us a “direct view” of a prominent part of the world that was perceived by peoples in the past. By studying knowledge passed down orally through myth and story, as well as a variety of other types of evidence available to the historian and the archaeologist, we can begin to appreciate the many different ways in which human societies came to understand what they saw in the skies, and how they came to “use” that knowledge for cultural ends. The sky could, for instance, affirm the POWER of cultural elites, as in the case of the Inca rulers, whose right to rule stemmed from their avowed relationship to the sun god himself (see CEQUE SYSTEM; CUSCO SUN PILLARS). Then again, it could reinforce the status of a shaman or priest who, by performing the appropriate rites at the appropriate times, could be seen as able to affect what happened in the sky—for example by reversing the direction of the sun at the winter solstice and preventing the days from getting ever shorter and colder. Likewise, people tend to lay out buildings in tune with the cosmos, in other words, reflecting perceived links with the wider world (see, for example, NAVAJO HOGAN; PAWNEE EARTH LODGE). Where these links relate to the sky—for instance, to the rising or setting position of the sun, moon, or stars—then we have particular hope of recognizing them, since we know where these celestial bodies ap- peared in the past (see HOW THE SKY HAS CHANGED OVER THE CENTURIES). By studying architectural alignments upon sky phenomena, we can obtain valuable insights into the worldviews that engendered them. There is no reason investigations of people’s perceptions of the skies should be limited to past societies, and a field known as ETHNOASTRONOMY has emerged in recent years alongside archaeoastronomy, concerned with studies of beliefs and practices relating to the sky among modern indigenous peoples. Since there is no hard line between past and present, many scholars prefer to merge the two fields and to speak instead of cultural astronomy. Regardless of how the subject is divided up, the study of people’s perceptions of the skies has a deep resonance and helps us appreciate the richness and diversity of human cognition and belief (see COGNITIVE ARCHAEOLOGY). This said, our knowledge of particular practices is always indirect, whether the evidence we are working with is ethnographic, historical, or archaeological, and questions of METHODOLOGY are highly important. For example, when studying an astronomical alignment (such as a building or temple oriented upon solstitial sunrise) it is necessary to have reasonable confidence that the alignment was actually intentional. This is not self-evident, since everything must, after all, point somewhere. In the 1970s, an abyss developed between two groups of academics regarding the interpretation of British megalithic monuments (see MEGALITHIC MONUMENTS OF BRITAIN AND IRELAND). On the one side were those who paid great attention to STATISTICAL ANALYSIS but little to anthropological theory and tended to argue that “MEGALITHIC ASTRONOMY” was highly mathematically sophisticated. On the other were those who did the reverse and reached the diametrically opposite conclusion: that ancient peoples had no interest in the sky at all. To get past this impasse, it is important to distinguish between “our” science, which provides tried and tested methods for fairly selecting and assessing evidence, and “their” science, the worldview (ancient, historical, or indigenous) we are interested in (see PALAEOSCIENCE; SCIENCE OR SYMBOLISM?). Those who are mathematically adept but anthropologically naive tend to try to show, in a proprietary way, that people in the past were our intellectual equals by demonstrating that they were capable of sophisticated mathematics and astronomy. The flaw, and also the irony, in this approach lies in the desire to measure the achievements of a past society against the yardstick of our own. This tendency, well known to anthropologists as ETHNOCENTRISM, amounts to putting our own culture on a pedestal. It is necessary to recognize that the worldview we are studying might well be logical enough in its own terms even though it does not conform in every respect to our rationality, since it is built upon different assumptions and principles. A few thousand years is nothing in human evolutionary terms, and thus people living a few thousand years ago were undoubtedly our intellectual equals: however, their way of thinking was different. We pay respect to that difference by trying to understand their way of thinking in its own terms rather than trying to make it conform to ours. It is for this reason that many prefer to avoid using the singular term astronomy to describe ancient peoples’ interest in the skies, speaking instead, if they use the term at all, of ancient astronomies. All people develop a personal view of the world. It is influenced by their own memories and experiences in which any things that may be perceived—objects, places, events, people and their actions, other living creatures, and plants—can acquire particular meanings, as can the relationships perceived to exist between them. What is more, among the countless things that make up an individual’s experience, some come to acquire more significance than others, in a selection process that can seem, to an outsider, highly arbitrary. A “discovery” that seems important to one person may be entirely overlooked or simply of no interest to another. Thus one of the Mursi, a modern group of cultivators and herders living in southwestern Ethiopia, determined the number of days that had elapsed between the planting and first harvesting of his sorghum crop by wearing a cord round his ankle and tying a new knot in it each day. However, those to whom he proudly announced the result were mildly surprised that anyone should have taken so much trouble to deduce something so irrelevant to their daily lives— something that added nothing to their total stock of knowledge about the world. Groups of people living together do, however, tend to develop common mindsets—sets of common perceptions and understandings. These worldviews are reinforced by shared experiences and social convention, and by regular communication, which in small groups is likely to take place by means of a common language. In the framework of modern Western thought, we organize what we perceive in nature according to the principles of Linnaean classification (deriving from the work of the eighteenth-century Swedish botanist Carolus Linnaeus)— that is, into a hierarchical structure of groups (taxa) based upon their observable characteristics. We also tend to believe that the universe is an empirical reality existing independently of the human mind that can progressively be understood through rational argument and scientific experimentation. Other worldviews, however, do not generally classify objects and phenomena into taxa familiar from a Western viewpoint: categories and relationships are not determined by “objective” criteria but simply by whether enough people agree on them. As a result there is generally no clear distinction between the sacred and the mundane, the animate and the inanimate, the empirically real and the fantastic; nor indeed between the terrestrial and the celestial. In traditional cultures, creatures such as fish-man or bird-woman may be seen as fellow beings, every bit as much a part of the perceived universe as entities a Westerner would identify as physically real. As an example, Old Star, chief protector of the inhabitants of the sacred He world of the Barasana of the Colombian Amazon, is at once a short trumpet, a constellation corresponding to ORION, the fierce thunder jaguar, and a human warrior. The sky is a crucial component in practically every indigenous worldview. For earlier peoples and for many indigenous groups around the world today, what we in the modern Western world separate out and categorize as astronomical and meteorological phenomena were an integral part of the environment as a whole. This total environment, including things both real and imagined, was the cosmos; the words COSMOLOGY (as widely used in anthropological literature) and cosmovisión are broadly synonymous with worldview. In non-Western worldviews, direct associations between the terrestrial and the celestial are commonplace. A good example of this is the BARASANA “CATERPILLAR JAGUAR” CONSTELLATION, whose behavior is believed to relate directly to that of earthly caterpillars, which fall out of trees and provide an important food source at a certain time of the year. Myths and Monuments Where we have first-hand informants or can actually still witness long-standing cultural practices, we are in the strongest position to recognize aspects of other worldviews. Examples such as the modern Yucatec Maya village of Yalcobá in southern Mexico, where the structure of the cosmos is reflected in a whole variety of aspects of social behavior, show just how rich and complex these practices can be. Yet ethnographers can be misled by informants, especially if they ask the wrong questions—all too easy if they have very little initial understanding of the nature of the worldview they are studying. Added to this, sacred information is often withheld, or the anthropologist may not be at liberty to pass it on. There is also the additional danger that the ethnographer may succeed, unwittingly, in influencing the very worldview he or she is trying to investigate, so that a subsequent investigator is misled into thinking that certain modern knowledge was in fact indigenous. Finally, most of us are limited to approaching the cultural information indirectly, at best at second hand, which imposes a selectivity that is not of our choosing and a filter—that of the ethnographer’s interpretations— through which we are forced to view everything. Historical accounts, whether by indigenous people themselves or by past ethnographers, are subject to all the problems just mentioned together with some additional ones. For one thing, an author who is no longer alive cannot be questioned, so there is no possibility of clarification or elaboration. For another, in interpreting a historical account it may be critical to appreciate the context in which it was produced. Ancient written records directly relating to astronomy exist not only among the civilizations of the Middle and Far East (see for example CHINESE ASTRONOMY). Perhaps the most extraordinary example produced in the American continent is the Maya DRESDEN CODEX, a pre-Columbian astronomical (or, more accurately, astrological) almanac. Both its complexity and level of detail are exceptional. In some cultures, other types of recording device encapsulated sacred information, including astronomical knowledge or calendrical data. One intriguing example is the QUIPU, bundles of knotted strings used in the Inca empire. A much more widespread practice, which did not produce any form of written record, was to embed sky knowledge and cosmological beliefs within myths that were transmitted from generation to generation orally. Storytelling may have been entertaining, but it could also have the deeper purpose of passing on wisdom. Creation myths often served to confirm a community’s rightful place in space and time, or to establish the genealogical credentials, and hence the social standing, of a king or leader. (Genealogies were not limited to human forbears. The KUMULIPO, a 2,000-line long Hawaiian creation chant composed in the eighteenth century, recounted in detail how chief Ka-‘»-i-mamao was related, ultimately, to everything in the world.) Some sacred stories were carefully learned and recounted, often in the context of formal ceremonies. Other tales might change in the telling, bringing many variations down to us but leaving intact the essential underlying substance and meaning. The further we delve into the past, the more we find ourselves limited to the archaeological record—the material remains of past human activity. Silent alignments of stone temples and tombs, interplays of sunlight and shade that light up dark spaces only on rare occasions, symbols with unfathomable meanings but which resemble the sun or moon or familiar groups of stars—these form many of the most famous manifestations of ancient astronomy. But they also present the serious scholar with serious methodological problems. Every oriented structure must point towards some point on the horizon, and in all likelihood to one or more identifiable astronomical targets. Similarly, the majority of entrances and openings will let in a shaft of sunlight at some time of the year and day. The mere existence of (say) a solar alignment is no guarantee that this meant anything to the builders of a house, temple, or tomb. Since astronomical alignments can—and frequently will—occur completely by chance, we must do more than simply “butterfly collect” them if we are interested in what they actually meant to people in the past. There are two ways of proceeding: either to seek statistical confirmation— for example, by identifying a group of several monuments in which a certain type of astronomical alignment occurs repeatedly—or by finding corroborating archaeological evidence of different forms. An example of the former is the RECUMBENT STONE CIRCLES of northeast Scotland, which have a consistent orientation relating to the moon. Two different examples of the latter, also from Neolithic and Bronze Age Britain, are the THORNBOROUGH henges (large round embanked enclosures) in Yorkshire, England, and the cairns at Balnuaran of Clava in Inverness, Scotland (see CLAVA CAIRNS). In some cases, such as pre-Columbian Mesoamerica, we have both archaeological and other forms of evidence, including ethnohistory (accounts recorded during the early years of European contact), iconography, and written records (see “BROWN” ARCHAEOASTRONOMY). Integrating these diverse forms of evidence can be a considerable challenge. This problem is illustrated by the prolonged controversy that surrounded the putative Venus alignment at the so-called Governor’s Palace at the Maya city of Uxmal (see GOVERNOR’S PALACE AT UXMAL). Inscriptions on the building attest to a strong interest in the planet Venus, but the apparent orientation of the building toward an extreme rising point of the planet has generated much debate. In ancient Mesoamerica in general, the historical evidence relating to astronomy and calendrics is strong, and the archaeological evidence—for example in the form of alignments—tends to strengthen and corroborate this. If it were not for the accounts of the early Spanish chroniclers, the calendrical inscriptions, and the vital bark books (codices), we would simply have no idea of the sophistication and complexity of Mesoamerican astronomy. In other places there can be a finer balance. The origins of a piece of oral history are typically much more obscure than the historical context of written records or inscriptions. It can be extremely difficult to separate genuine traditions and stories that stretch back over many generations from more modern inventions or infiltrations. In Hawai’i, a very rich oral heritage existed until the early nineteenth century, of which only fragments now survive (see HAWAIIAN CALENDAR; POLYNESIAN AND MICRONESIAN ASTRONOMY). Yet in assessing the significance of temple alignments in these islands, some of those surviving fragments may contain vital gems of information (see POLYNESIAN TEMPLE PLATFORMS AND ENCLOSURES). They are of uncertain provenance, so must be used with extreme caution, but one would be unwise to simply ignore them and revert to statistics alone. Where the only available evidence is archaeological, it is possible to use analogies from different cultures where other forms of evidence exist to suggest interpretations. Thus in the 1970s, the Scottish archaeologist Euan MacKie attempted to use the analogy of Maya society to argue (in support of theories, popular at the time, that many of the British megaliths were high-precision observatories) for the existence of highly skilled astronomer-priests in Neolithic Britain (see “MEGALITHIC ASTRONOMY”; “MEGALITHIC” CALENDAR). However, this direct use of ethnographic or historical analogy is generally fraught with problems. Most archaeologists concluded, for a variety of reasons, that MacKie’s efforts were badly misguided. On the other hand, analogies can be very useful in challenging assumptions that might have been made too unquestioningly, and hence in suggesting new interpretative possibilities. It is generally assumed, for example, that any people who observed the changing rising and setting position of the sun on the horizon over the year must have understood that this regulated seasonal events. Yet while it is true that some of the Mursi, already mentioned, track the changing rising position of the sun on the horizon, the MURSI CALENDAR is based upon the moon. The sun is regarded as no more reliable a seasonal indicator than the behavior of various birds, animals, or plants. The Mursi example stops us leaping to conclusions about practices in the past by showing us that the range of possibilities is wider than we might have imagined. In summary, where we have only archaeological evidence to go on, it may be possible to gain insights into prehistoric worldviews by recognizing symbolic asxvi sociations in the material record. Analogy may be useful in the process of interpretation, but our conclusions will never be categorical. We can only ever have a certain degree of belief that a specific association had meaning to a particular group of people, although our belief may be strengthened or weakened by further evidence. From Tally Marks to Calendars How did people begin to make links between different cycles of activity they observed around them and hence begin to understand and control the periodic changes in the natural world as they perceived it? At what stage did they start consciously to plan their own actions in accordance with those perceptions? Groups of people from the earliest times would certainly have varied their subsistence activities in accordance with the seasons, whether these involved searching for edible plants and animals, fishing, or hunting. But in this alone they were little different from many others in the animal kingdom: many birds, after all, undertake seasonal migrations. Two characteristics that have distinguished humankind for several tens of thousands of years are people’s capacity for abstract thought—making connections between things in order to satisfy the desire to make sense of them—and the use of symbolic representation to express ideas. There is ample evidence of the latter in the Upper Palaeolithic, in the form of systematic markings on many small portable objects such as pieces of bone. Their meaning is much debated, but it has been suggested that some at least represented rudimentary lunar calendars—tallies of days or some other sort of symbolic notation relating to the lunar phase cycle. The most famous example is a fragment of eagle’s wing found in a cave at Abri Blanchard in southern France, dating to around 30,000 B.C.E. (see ABRI BLANCHARD BONE). Some much more recent, and less controversial, examples of possible lunar tallies among hunter-gatherers are found in rock art from northeastern Mexico. The site of PRESA DE LA MULA, near Monterrey, is one of two petroglyphs that seem to record counts of days stretching over seven synodic (lunar-phase-cycle) months, divided up according to the appearance of the moon. However, these designs were not calendars: they were clearly not intended for regulating future activities. Rather, they were first-hand observational records, with all the vagaries and imperfections this implies. Counting days, as such, is unlikely to have been an overriding issue for most people in the past. They had to be aware of many different cycles of activity in their lives. One of the most effective ways of keeping track of things is through myth and appropriately timed ritual performance. These were invariably tied in, along with many aspects of living and being, with the unchanging entities in the sky and the ceaseless cycles in which they were seen to move. Stories help describe the world and explain why things are as they are. Ceremonies serve in a very active way to affirm the natural order. Stories and ceremonies also involve an ele- Introduction

Rooted In Evil

Author : Natalie Joy Andrews
ISBN : 9781683481867
Genre : Fiction
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: “I could hear the crackling of the blazing fires and even feel the smoke swirl around my body. The faint odor of blood filled my nostrils until I was overwhelmed by the stench of death.” Moving to a small town and beginning her senior year at a new school proved to be much more than a typical high school nightmare of being the new kid on campus; for Addy, it was a tug-of-war for her soul. Enticed by a mysterious and powerful group of peers, she uncovers unexpected secrets hidden away in the coastal town of Ledo and must face the most important decision of her life, but it may cost her just that…her life.

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