Children’s numeracy competencies are not only relevant for their academic achievement, but also later in life. The development of early numeracy competencies is influenced by children’s learning environment. Here, the home numeracy environment and parent’s own beliefs about mathematics play an important role for children’s numeracy competencies. However, only a few studies explicitly tested these associations separately for mothers and fathers. In our study, we assessed mothers’ and fathers’ mathematical gender stereotypes, self-efficacy and their beliefs on the importance of mathematical (...) activities at home, and tested their associations with parents’ numeracy activities and children’s numeracy competencies in a sample of N = 160 children with an average age of M = 59.15 months. Both, fathers and mothers regarded boys as being more competent in mathematics than girls. Fathers when compared to mothers reported a greater mathematical self-efficacy. Further, only mothers’ self-efficacy was associated with the frequency of numeracy activities with the study child. In contrast, only fathers’ beliefs on the importance of mathematics was associated with their numeracy activities which, in turn, predicted children’s numeracy competencies. However, the non-invariant constructs and varying results lead to the question whether a revision of existing scales assessing parental beliefs and home numeracy activities is needed to investigate differences of mothers and fathers and their potential associations with children’s numeracy outcomes. (shrink)

George Birtwistle (1877–1929) published The New Quantum Mechanics in 1928. His stated aim was to give a detailed account of work which had brought the relatively new subject of quantum mechanics to the fore in the previous few years. The earlier chapters give a restatement of Alfred Landé's theory of multiplets which reconciles it with the new mechanics which follow. Later chapters present the matrix theory of Heisenberg, the q-number theory of Dirac and the wave mechanics of Schroedinger, and (...) synthesise new theories, statistics and controversies in the work of de Broglie, Bose, Einstein, Fermi and Dirac. The book gives a complete overview of the state of quantum mechanics at the end of the second decade of the twentieth century, making it a valuable benchmark for historians of science and mathematicians alike. (shrink)

The theme of The Planetary Clock is the representation of time in postmodern culture and the way temporality as a global phenomenon manifests itself differently across an antipodean axis. To trace postmodernism in an expansive spatial and temporal arc, from its formal experimentation in the 1960s to environmental concerns in the twenty-first century, is to describe a richer and more complex version of this cultural phenomenon. Exploring different scales of time from a Southern Hemisphere perspective, with a special emphasis on (...) issues of Indigeneity and the Anthropocene, The Planetary Clock offers a wide-ranging, revisionist account of postmodernism, reinterpreting literature, film, music, and visual art of the post-1960 period within a planetary framework. By bringing the culture of Australia and New Zealand into dialogue with other Western narratives, it suggests how an antipodean impulse, involving the transposition of the world into different spatial and temporal dimensions, has long been an integral (if generally occluded) aspect of postmodernism. Taking its title from a Florentine clock designed in 1510 to measure worldly time alongside the rotation of the planets, The Planetary Clock ranges across well-known American postmodernists (John Barth, Toni Morrison) to more recent science fiction writers (Octavia Butler, Richard Powers), while bringing the US tradition into juxtaposition with both its English (Philip Larkin, Ian McEwan) and Australian (Les Murray, Alexis Wright) counterparts. By aligning cultural postmodernism with music (Messiaen, Ligeti, Birtwistle), the visual arts (Hockney, Blackman, Fiona Hall), and cinema (Rohmer, Haneke, Tarantino), this volume enlarges our understanding of global postmodernism for the twenty-first century. (shrink)

Recent encounters with structuralist and poststructuralist critical theory, linguistics, and cognitive sciences have brought the theory and analysis of music into the orbit of important developments in present-day intellectual history. Without seeking to impose an explicit redefinition of either theory or analysis, this book explores the limits of both. Essays on decidability, ambiguity, metaphor, music as text, and music analysis as cognitive theory are complemented by studies of works by Debussy, Schoenberg, Birtwistle and Boulez.

This fully revised new edition re-establishes Paul Griffiths's survey as the definitive study of music since the Second World War. The disruptions of the war, and the struggles of the ensuing peace, were reflected in the music of the time: in Pierre Boulez's radical reforming of compositional technique and in John Cage's move into zen music, in Milton Babbitt's settling of the serial system and in Dmitry Shostakovich's unsettling symphonies, in Karlheinz Stockhausen's development of electronic music and in Luigi Nono's (...) pursuit of the universally human, in Iannis Xenakis's view of music as sounding mathematics and in Luciano Berio's consideration of it as language. The initiatives of these composers and their contemporaries opened prospects that have continued to unfold. This constant expansion of musical thinking since 1945 has left us with no single history of music. Paul Griffiths's study accordingly follows several different paths, showing how and why they converge and diverge. In addition to the composers mentioned above, others whose music is discussed include Steve Reich, Jean Barraque, Elliott Carter, Olivier Messiaen, Gyorgy Kurtag, Harrison Birtwistle, and Gyorgy Ligeti. Publication and recording details are given for the works of all these composers and many others. (shrink)