Beyond Classical

The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

Amid enormous changes in higher education, audience and music listener preferences, and the relevant career marketplace, music faculty are increasingly aware of the need to reimagine classical music performance training for current and future students. But how can faculty and administrators, under urgent pressure to act, be certain that their changes are effective, strategic, and beneficial for students and institutions? In this provocative yet measured book, Michael Stepniak and Peter Sirotin address these questions with perspectives rooted in extensive experience as musicians, educators, and arts leaders. Building on a multidimensional analysis of core issues and drawing upon interviews with leaders from across the performing arts and higher education music fields, Stepniak and Sirotin scrutinize arguments for and against radical change, illuminating areas of unavoidable challenge as well as areas of possibility and hope. An essential read for education leaders contemplating how classical music can continue to thrive within American higher education.

From about 2000 BCE onward, Egypt served as an important nexus for cultural exchange in the eastern Mediterranean, importing and exporting not just wares but also new artistic techniques and styles. Egyptian, Greek, and Roman craftsmen imitated one another’s work, creating cultural and artistic hybrids that transcended a single tradition. Yet in spite of the remarkable artistic production that resulted from these interchanges, the complex vicissitudes of exchange between Egypt and the Classical world over the course of nearly 2500 years have not been comprehensively explored in a major exhibition or publication in the United States. It is precisely this aspect of Egypt’s history, however, that Beyond the Nile uncovers. Renowned scholars have come together to provide compelling analyses of the constantly evolving dynamics of cultural exchange, first between Egyptians and Greeks—during the Bronze Age, then the Archaic and Classical periods of Greece, and finally Ptolemaic Egypt—and later, when Egypt passed to Roman rule with the defeat of Cleopatra. Beyond the Nile, a milestone publication issued on the occasion of a major international exhibition, will become an indispensable contribution to the field. With gorgeous photographs of more than two hundred rare objects, including frescoes, statues, obelisks, jewelry, papyri, pottery, and coins, this volume offers an essential and inter-disciplinary approach to the rich world of artistic cross-pollination during antiquity.

Classical and quantal nonrelativistic scattering between simple atomic systems is reviewed, and most approximations currently used in calculations on electron capture are discussed. The OBK interaction is generalized to include capture from neutral atoms by singly charged many-electron ions; the sum over the squares of the vector coupling coefficients is affected in the formula for the OBK cross section for p-orbital capture by protons into H(ns). The cross section for H(+) + H(1s) to H(Sigma n1) + H(+) at high impact energies is determined classically. The second Born amplitudes at high impact energies for H(+) + H(1s) to H(1s) + H(+) and H(+) + D(1s) to H(1s) + D(+) are evaluated approximately using the Green's function of the post Hamiltonian. Two modifications of Thomas' classical model for heavy atoms are proposed, and corresponding cross sections are calculated for H(+) + B to H(Sigma n1) + B(+) with B = O, N, Ne, A, Kr, Xe. A semiclassical theory is developed for charge transfer in alkali atom-alkali-ion collision at low impact velocities, and cross sections are obtained for H, Li, Na, K, Rb, Cs. OBK cross sections are calculated for s-orbital capture from He(1s(2)), N((4)S), O((3)P), and p-orbital capture from N((4)S), O((3)P), all for incident protons capturing into H(1s). Born prior and post cross sections are calculated for H(+) + O((3)P) to H(1s) + O(+)((4)S) and H(1s) + H(1s) to H( - )(1s(2)) + H(+).

Why is classical music predominantly the preserve of the white middle classes? Contemporary associations between classical music and social class remain underexplored, with classical music primarily studied as a text rather than as a practice until recent years. In order to answer this question, this book outlines a new approach for a socio-cultural analysis of classical music, asking how musical institutions, practices, and aesthetics are shaped by wider conditions of economic inequality, and how music might enable and entrench such inequalities or work against them. This approach is put into practice through a richly detailed ethnography which locates classical music within one of the cultures that produces it - middle-class English youth - and foregrounds classical music as bodily practice of control and restraint. Drawing on the author's own background as a classical musician, this closely observed account examines youth orchestra and youth choir rehearsals as a space where young people learn the unspoken rules of this culture of weighty tradition and gendered control. It highlights how the middle-classes' habitual roles - boundary drawing around their protected spaces and reproducing their privilege through education - can be traced within the everyday spaces of classical music. These practices are camouflaged, however, by the ideology of 'autonomous art' that classical music carries. Rather than solely examining the social relations around the music, the book demonstrates how this reproductive work is facilitated by its very aesthetic, of 'controlled excitement', 'getting it right', precision, and detail. This book is of particular interest at the present moment, thanks to the worldwide proliferation of El Sistema-inspired programmes which teach classical music to children in disadvantaged areas. While such schemes demonstrate a resurgence in defending the value of classical music, there has been a lack of debate over the ways in which its socio-cultural heritage shapes its conventions today. This book locates these contestations within contemporary debates on class, gender and whiteness, making visible what is at stake in such programmes.

Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.

As distinct from the extant studies of ancient canonical texts, which focus either on literary (Greco-Roman) or religious (Judeo-Christian) canons, the present volume aims at bridging between these two fields by proposing the first comparative study of canon. An international team of experts discusses the processes of canon-formation in societies of the ancient world, addressing such issues as canon and the articulation of identity; the hermeneutical attitude toward canonical texts; textual fixity and openness; oral and written canons; methods of transmission, and more. Among the topics discussed are Mesopotamian canons; Zoroastrianism; the Bible; Homer; literary and philosophical canons in ancient Greece and Rome; the New Testament; the Roman law; Rabbinic Judaism and Kabbalistic literature. The future of the so-called Western Canon is one of the most hotly debated issues of the day. There is reason to believe that what is perceived today as a unique crisis, can be put into perspective by students of ancient societies, for the simple reason that the ancient world offers us the historical perspective of civilizations as a whole and allows us to study cultural phenomena in the longue durée.