Teacher voice and ownership of curriculum change

We comment critically on the notion that teachers can experience ownership of curriculum change. The evidence base for this commentary is our work on two curriculum development projects in health and physical education between 1993 and 1998. Applying a theoretical framework adapted from Bernstein's writing on the social construction of pedagogic discourse, we contend that the possibilities for teacher ownership of curriculum change are circumscribed by the anchoring of their authority to speak on curriculum matters in the local context of implementation. We argue that this anchoring of teacher voice provides a key to understanding the perennial problem of the transformation of innovative ideas from conception to implementation. We also provide some insights into the extent to which genuine participation by teachers in education reform might be possible, and we conclude with a discussion of the possibilities that exist for partnerships in reforming health and physical education.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.