IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: • Algebra: Setting the Scene • Some Lessons From History • Seeing Algebra Through the Eyes of a Learner • Emphases in Algebra Teaching • Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.
This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration. The survey’s final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics. The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level.
This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration. The survey's final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics. The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level.
IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: • Algebra: Setting the Scene • Some Lessons From History • Seeing Algebra Through the Eyes of a Learner • Emphases in Algebra Teaching • Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.
This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration. The survey’s final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics. The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level.
The first volume in a landmark commentary on an important and influential work of ancient philosophy This is the first volume of a groundbreaking commentary on one of the most important works of ancient philosophy, the Enneads of Plotinus—a text that formed the basis of Neoplatonism and had a deep influence on early Christian thought and medieval and Renaissance philosophy. This volume covers the first three of the six Enneads, as well as Porphyry's Life of Plotinus, a document in which Plotinus’s student—the collector and arranger of the Enneads—introduces the philosopher and his work. A landmark contribution to modern Plotinus scholarship, Paul Kalligas’s commentary is the most detailed and extensive ever written for the whole of the Enneads. For each of the treatises in the first three Enneads, Kalligas provides a brief introduction that presents the philosophical background against which Plotinus’s contribution can be assessed; a synopsis giving the main lines and the articulation of the argument; and a running commentary placing Plotinus’s thought in its intellectual context and making evident the systematic association of its various parts with each other.
Eighty years ago, Walter Bauer promulgated a bold and provocative thesis about early Christianity. He argued that many forms of Christianity started the race, but one competitor pushed aside the others, until this powerful 'orthodox' version won theday. The victors rewrote history, marginalizing all other perspectives and silencing their voices, even though the alternatives possessed equal right to the title of normative Christianity. Bauer's influence still casts a long shadow on early Christian scholarship. Were heretical movements the original forms of Christianity? Did the heretics outnumber the orthodox? Did orthodox heresiologists accurately portray their opponents? And more fundamentally, how can one make any objective distinction between 'heresy' and 'orthodoxy'? Is such labeling merely the product of socially situated power? Did numerous, valid forms of Christianity exist without any validating norms of Christianity? This collection of essays, each written by a relevant authority, tackles such questions with scholarly acumen and careful attention to historical, cultural-geographical, and socio-rhetorical detail. Although recognizing the importance of Bauer's critical insights, innovative methodologies, and fruitful suggestions, the contributors expose numerous claims of the Bauer thesis (in both original and recent manifestations) that fall short of the historical evidence.
This “knowledgeable account” of the emperor who brought Christianity to Rome “provides valuable insight into Constantine’s era” (Kirkus Reviews). “By this sign conquer.” So began the reign of Constantine. In 312 A.D. a cross appeared in the sky above his army as he marched on Rome. In answer, Constantine bade his soldiers to inscribe the cross on their shield, and so fortified, they drove their rivals into the Tiber and claimed Rome for themselves. Constantine led Christianity and its adherents out of the shadow of persecution. He united the western and eastern halves of the Roman Empire, raising a new city center in the east. When barbarian hordes consumed Rome itself, Constantinople remained as a beacon of Roman Christianity. Constantine is a fascinating survey of the life and enduring legacy of perhaps the greatest and most unjustly ignored of the Roman emperors—written by a richly gifted historian. Paul Stephenson offers a nuanced and deeply satisfying account of a man whose cultural and spiritual renewal of the Roman Empire gave birth to the idea of a unified Christian Europe underpinned by a commitment to religious tolerance. “Successfully combines historical documents, examples of Roman art, sculpture, and coinage with the lessons of geopolitics to produce a complex biography of the Emperor Constantine.” —Publishers Weekly
This study explores the meaning and function of water as a literary symbol in the Gospel of John. Jones first gives an account of symbol: it points beyond itself, it defies clear and definitive perceptual expression, and it in some way embodies that which it represents. Then he examines the narrative sections of John that involve water, plotting the expanding meaning and function of the symbol as the narrative unfolds. The study concludes that water serves primarily as a symbol of the Spirit and therein symbolizes Jesus. The symbol of water calls a wide variety of readers to a decision and functions as a bridge linking the new identity believers receive when they come to faith in Jesus with the traditions from which they came.
Richard Verstegan is the usual English name of a man who went through early life as Richard Rowlands, before reverting to his ancestral Dutch surname in exile. Born in Mid-Tudor London around 1550 and dying in the Baroque Antwerp of 1640, his ninety-odd years of life saw numerous religious, political and military conflicts, in some of which he was a minor player and on almost all of which he commented in his writings. After studying at Oxford without taking a degree, training as a goldsmith and illegally printing a Catholic book, he fled to France, where he worked as a propagandist for the faction of the Duke of Guise. Imprisoned in France for these activities, he fled to Rome, and eventually settled in Antwerp, where he worked for almost fifty years as, variously, a newswriter, engraver, publisher, editor, translator, polemicist, antiquarian, cloth merchant, poet and satirist. He is one of the earliest identifiable European newspaper journalists, having worked on Abraham Verhoeven's Nieuwe Tijdinghen (Antwerp, 1620-1629).
This study offers an extensive survey of previous literature dealing with the provenance of the song in Deuteronomy 32, a renewed discussion of its text and language as well as an analysis of its poetic structure with the help of a new method. The author tests the tenability of older theories and proposes a new theory based on systematic research into the intertextual links with other parts of the Hebrew Bible and extra-biblical literature of the Ancient Near East. Separate sections are dedicated to the song's descriptions of the relationship between YHWH and the gods and to the identity of the hostile people to which the song refers. The author concludes that a pre-exilic date is extremely likely for the song in its entirety.
The alignment splits in the Neo-Aramaic languages display a considerable degree of diversity, especially in terms of agreement. While earlier studies have generally oversimplified the actual state of affairs, Paul M. Noorlander offers a meticulous and clear account of nearly all microvariation documented so far, addressing all relevant morphosyntactic phenomena. By means of fully glossed and translated examples, the author shows that this vast variation in morphological alignment, including ergativity, is unexpected from a functional typological perspective. He argues the alignment splits are rather the outcome of several construction-specific processes such as internal system harmonization and grammaticalization, as well as language contact.
Clinical Anesthesia, Seventh Edition covers the full spectrum of clinical options, providing insightful coverage of pharmacology, physiology, co-existing diseases, and surgical procedures. This classic book is unmatched for its clarity and depth of coverage. *This version does not support the video and update content that is included with the print edition. Key Features: • Formatted to comply with Kindle specifications for easy reading • Comprehensive and heavily illustrated • Full color throughout • Key Points begin each chapter and are labeled throughout the chapter where they are discussed at length • Key References are highlighted • Written and edited by acknowledged leaders in the field • New chapter on Anesthesia for Laparoscopic and Robotic Surgery Whether you’re brushing up on the basics, or preparing for a complicated case, the digital version will let you take the content wherever you go.
A survey of previous literature about the provenance of the song in Deuteronomy 32 and a discussion of its text and poetic structure. The author concludes that the song dates from the pre-exilic period.
In Mani at the Court of the Persian Kings the authors explore evidence arising from their project to edit the Chester Beatty Kephalaia codex. This new text presents Mani at the heart of Sasanian Iran in dialogue with its sages and nobles, acting as a cultural mediator between East and West and interpreter of Christian, Iranian, and Indian traditions. Nine chapters study Mani’s appropriation of the ‘law of Zarades’ and of Iranian epic; suggest a new understanding of his last days; and analyse his formative role in the history of late antique religions. These interdisciplinary studies advance research in several fields and will be of interest to scholars of Manichaeism, Sasanian Iran, and the development of religions in Late Antiquity.
This study contextualizes the achievement of a strategically crucial figure in Byzantium's turbulent seventh century, the monk and theologian Maximus the Confessor (580-662). Building on newer biographical research and a growing international body of scholarship, as well as on fresh examination of his diverse literary corpus, Paul Blowers develops a profile integrating the two principal initiatives of Maximus's career: first, his reinterpretation of the christocentric economy of creation and salvation as a framework for expounding the spiritual and ascetical life of monastic and non-monastic Christians; and second, his intensifying public involvement in the last phase of the ancient christological debates, the monothelete controversy, wherein Maximus helped lead an East-West coalition against Byzantine imperial attempts doctrinally to limit Jesus Christ to a single (divine) activity and will devoid of properly human volition. Blowers identifies what he terms Maximus's "cosmo-politeian" worldview, a contemplative and ascetical vision of the participation of all created beings in the novel politeia, or reordered existence, inaugurated by Christ's "new theandric energy". Maximus ultimately insinuated his teaching on the christoformity and cruciformity of the human vocation with his rigorous explication of the precise constitution of Christ's own composite person. In outlining this cosmo-politeian theory, Blowers additionally sets forth a "theo-dramatic" reading of Maximus, inspired by Hans Urs von Balthasar, which depicts the motion of creation and history according to the christocentric "plot" or interplay of divine and creaturely freedoms. Blowers also amplifies how Maximus's cumulative achievement challenged imperial ideology in the seventh century--the repercussions of which cost him his life-and how it generated multiple recontextualizations in the later history of theology.
The influence of Arabic-Islamic science on European astronomy is still evident in the number of terms and star names which derive from the Arabic. These articles examine what the Arabs - and other peoples of the Islamic world - knew about the fixed stars and the constellations, and the astrological traditions they associated with them. Professor Kunitzsch shows how the early folk astronomy of the Arabs was radically altered, without being swept away, by the discovery of ancient Greek, also Indian and Persian, sources; by far the most important of these was the Almagest of Ptolemy. This knowledge was then transmitted to medieval Europe, to Byzantium and, especially, to Spain, as the articles go on to describe, and was a vital factor in stimulating the development of scientific thought in the West.
This new version of the late fourth-century diary of journeys in and around the Holy Land known as the Itinerarium Egeriae provides a more literal translation of the Latin text than earlier English renderings, with the aim of revealing more of the female traveler’s personality. The substantial introduction to the book covers both early pilgrimage as a whole, especially travel by women, and the many liturgical rites of Jerusalem that Egeria describes. Both this and the verse-by-verse commentary alongside the translated text draw on the most recent scholarship, making this essential reading for pilgrims, students, and scholars seeking insight into life and piety during one of Christianity’s most formative periods.
When the First Crusade ended with the conquest of Jerusalem in 1099, jubilant crusaders returned home to Europe bringing with them stories, sacred relics, and other memorabilia, including banners, jewelry, and weapons. In the ensuing decades, the memory of the crusaders' bravery and pious sacrifice was invoked widely among the noble families of western Christendom. Popes preaching future crusades would count on these very same families for financing, leadership, and for the willing warriors who would lay down their lives on the battlefield. Despite the great risks and financial hardships associated with crusading, descendants of those who suffered and died on crusade would continue to take the cross, in some cases over several generations. Indeed, as Nicholas L. Paul reveals in To Follow in Their Footsteps, crusading was very much a family affair.Scholars of the crusades have long pointed to the importance of dynastic tradition and ties of kinship in the crusading movement but have failed to address more fundamental questions about the operation of these social processes. What is a "family tradition"? How are such traditions constructed and maintained, and by whom? How did crusading families confront the loss of their kin in distant lands? Making creative use of Latin dynastic narratives as well as vernacular literature, personal possessions and art objects, and architecture from across western Europe, Paul shows how traditions of crusading were established and reinforced in the collective memories of noble families throughout the twelfth and thirteenth centuries. Even rulers who never fulfilled crusading vows found their political lives dominated and, in some ways, directed by the memory of their crusading ancestors. Filled with unique insights and careful analysis, To Follow in Their Footsteps reveals the lasting impact of the crusades, beyond the expeditions themselves, on the formation of dynastic identity and the culture of the medieval European nobility.
In Stanzaic Syntax in the Madrashe of Ephrem the Syrian, which focuses on madrāšê V and VI in the Paradise cycle, Paul S. Stevenson looks at Ephrem’s poetic art from the point of view of a linguist. This study goes beyond the traditional levels of analysis, the clause and the sentence, and examines the structure of whole stanzas as units. The result is a surprisingly rich tapestry of syntactic patterning, which can justly be considered the key to Ephrem’s prosody. The driving force behind Ephrem’s poetry turns out not to be meter or sound play, but a variety of syntactic templates, which include even vertical patterning of constituents.
Paul Bradshaw, one of the world's foremost scholars on the history of Christian liturgy, has shared this expertise in several works that have become standard texts for students of liturgy. In Rites of Ordination, Bradshaw turns his attention to the ways that Christians through the ages have understood what it means to ordain someone as a minister and how that has been expressed in liturgical practice. Bradshaw considers the typological background to ordained ministry some have drawn from the Old Testament and what ministry meant to the earliest Christian communities. He explores the ordination rites and theology of the early church, the Christian East, the medieval West, the churches of the Reformation, and the post-Tridentine Roman Catholic Church. Rites of Ordination promises to serve as an enriching resource for seminary students, students of liturgy and church history, and anyone fascinated by the history and theology of Christian liturgy and ministry.
In The Ethics of The Tripartite Tractate (NHC I, 5), Paul Linjamaa explores the theoretical foundations and practical implications of the ethics in the longest Valentinian text extant today. As such, it is one of the first serious explorations of early Christian determinism.
The famous Nile Mosaic of Palestrina, ancient Praeneste in central Italy, dating to c. 100 B.C., is one of the earliest large mosaics which have been preserved from the classical world. It presents a unique, comprehensive picture of Egypt and Nubia. The interpretation of the mosaic is disputed, suggestions ranging from an exotic decoration to a topographical picture or a religious allegory. The present study demonstrates that the mosaic depicts rituals connected with Isis and Osiris and the yearly Nile flood. The presence of these Egyptian religious scenes at Praeneste can be explained by the assimilation of isis and Fortuna, the tutelary goddess of Praeneste, and by the interpretation of the mosaic as a symbol of divine providence.
In examining and analyzing these practices, Griffiths develops a picture of the intellectual and moral commitments involved in being a religious person. Griffiths favorably contrasts the practices and pedagogies of traditional religious cultures with those of our own fragmented and secularized culture and insists that religious reading should be preserved. He concludes with the controversial proposal that the modern university should make room for traditional scholastics."--BOOK JACKET.
A comprehensive new history of the Eastern Roman Empire based on the science of the human past. As modern empires rise and fall, ancient Rome becomes ever more significant. We yearn for Rome’s power but fear Rome’s ruin—will we turn out like the Romans, we wonder, or can we escape their fate? That question has obsessed centuries of historians and leaders, who have explored diverse political, religious, and economic forces to explain Roman decline. Yet the decisive factor remains elusive. In New Rome, Paul Stephenson looks beyond traditional texts and well-known artifacts to offer a novel, scientifically minded interpretation of antiquity’s end. It turns out that the descent of Rome is inscribed not only in parchments but also in ice cores and DNA. From these and other sources, we learn that pollution and pandemics influenced the fate of Constantinople and the Eastern Roman Empire. During its final five centuries, the empire in the east survived devastation by natural disasters, the degradation of the human environment, and pathogens previously unknown to the empire’s densely populated, unsanitary cities. Despite the Plague of Justinian, regular “barbarian” invasions, a war with Persia, and the rise of Islam, the empire endured as a political entity. However, Greco-Roman civilization, a world of interconnected cities that had shared a common material culture for a millennium, did not. Politics, war, and religious strife drove the transformation of Eastern Rome, but they do not tell the whole story. Braiding the political history of the empire together with its urban, material, environmental, and epidemiological history, New Rome offers the most comprehensive explanation to date of the Eastern Empire’s transformation into Byzantium.
The NIV Application Commentary helps you communicate and apply biblical text effectively in today's context. To bring the ancient messages of the Bible into today's world, each passage is treated in three sections: Original Meaning. Concise exegesis to help readers understand the original meaning of the biblical text in its historical, literary, and cultural context. Bridging Contexts. A bridge between the world of the Bible and the world of today, built by discerning what is timeless in the timely pages of the Bible. Contemporary Significance. This section identifies comparable situations to those faced in the Bible and explores relevant application of the biblical messages. The author alerts the readers of problems they may encounter when seeking to apply the passage and helps them think through the issues involved. This unique, award-winning commentary is the ideal resource for today's preachers, teachers, and serious students of the Bible, giving them the tools, ideas, and insights they need to communicate God's Word with the same powerful impact it had when it was first written.
Paul explores the relationship between films set in the ancient world and the classical epic tradition, arguing that there is a connection between the genres. Through this careful consideration of how epic manifests itself through different periods and cultures, we learn how cinema makes a claim to be a modern vehicle for a very ancient tradition.
This book studies the research perspective in which the literary inhabitants of Late Antique and medieval Constantinople remembered its past and conceptualised its existence as a Greek city that was the political capital of a Christian Roman state. Initial reactions to Constantine’s foundation noted its novel Christian orientation, but the memorial mode of writing about the city that developed from the sixth century recollected the traditional civic cultural heritage that Constantinople claimed both as the New Rome, and as the continuation of ancient Byzantion. This research culture increasingly became the preserve of the imperial bureaucracy, and focused on the city’s sculptured monuments as bearers of eschatological meaning. Yet from the tenth century, writers progressively preferred to define the wonder and spectacle of Constantinople in the aesthetic mode of urban praise inherited from late antiquity, developing the notion of the city as a cosmic theatre of excellence.
Die Festschrift vereinigt 29 Beitrage, die folgende Sachgebiete betreffen: arabische und mittelalterlich-europaische Mathematik, Uberlieferungsgeschichte der indisch-arabischen Ziffern, die arabisch-islamische Astronomie, die volkstumliche arabische Himmelskunde, das Astrolab und seine Nomenklatur, antike und spatgriechische astronome Traditionen, weitere Fragen bzw. Texte zur Uberlieferung der Wissenschaften im griechisch-syrisch-arabisch-lateinischen Traditionsraum. Alle Arbeiten sind originell und beruhen auf einschlagigen Originalquellen. Mehrere griechische, syrische, arabische und lateinische Texte bzw. Auszuge daraus sind auch ediert. Die Sammlung enthalt somit wichtige, neue Bausteine fur unser Gesamtbild von den arabischen Wissenschaften, ihrem Nachleben in Europa und weiteren Ausstrahlungen auf die europaische Geistesgeschichte.
Containing over 300 entries, this guide presents an overview of the most recent developments in Dutch architecture and urban design from the 1980s to the present day. Its compact shape, practical layout and extensive indexes make this guide an indispensable source of inspiration and reference work on the practice of Dutch architecture today. Includes work by Koolhaas, Mecanoo, Arets, van Berkel, van Egeraat, Foster, De Geyter, Hertzberger, Krier, MVRDV, Neutelings Riedijk, Graves, Benthem Crouwel, Nox, and many others.
This volume consists of an introduction, the text of book 4 of Valerius Flaccus' Argonautica, commentary, bibliography and index. However, it is not a standard philological commentary. Although it contains textual criticism (but only where meaning and appreciation are substantially affected) and explanation of sense and references (a vital basis for critical analysis), above all there is literary appreciation of Valerius' fourth book, which should help to bring about a revaluation of this largely neglected and sadly underestimated author. The book alerts readers to important aspects of Valerius' highly intellectual poetry, such as wit, humor, elegance, point, subtlety, narrative skill, and creative engagement with forerunners, especially Apollonius of Rhodes and Virgil.
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