An industry-sponsored, school-focused model for continuing professional development of technology teachers

Traditionally a divide has existed between faculties of education at higher education institutions (HEIs) and trade and industry, but the business sector is increasingly buying into community development with corporate social investment, especially regarding technology education. We report on a continuing professional teacher development (CPTD) model, which entails trade and industry sponsoring learning and teacher support material (LTSM) for technology education in under-resourced schools, paying for LTSM through their corporate social investment funds, and sponsoring CPTD of technology teachers where they are trained to use LTSM more efficiently. Trade and industry, together with HEIs and Departments of Education (DoE), could change the traditional concept that CPTD is the responsibility of DoEs into a new model where the business sector shares some of the responsibility for equipping teachers so that they can provide quality education. We argue that custom-made and sponsored LTSM and CPTD play an important role in the training and empowerment of technology teachers. Keywords: continuing professional development; learning and teacher support material; technology education South African Journal of Education Vol. 27 (4) 2007: pp. 579-59

Methodology and Practicum (Engineering Graphics and Design Technology)

Exam paper (Supplementary) for second semester B.Ed. (FET and Senior Phase

Conservation Laws and Integral Relations for the Boussinesq Equation

We are concerned with conservation laws and integral relations associated with rational solutions of the Boussinesq equation, a soliton equation solvable by inverse scattering, which was first introduced by Boussinesq in 1871. The rational solutions are logarithmic derivatives of a polynomial, are algebraically decaying, and have a similar appearance to rogue-wave solutions of the focusing nonlinear Schrödinger equation. For these rational solutions, the constants of motion associated with the conserved quantities are zero and they have some interesting integral relations, which depend on the total degree of the associated polynomial

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.Comment: 4 pages, RevTex, 1 EPS figure To appear in Physical Review Letter

Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Stable multicolor periodic-wave arrays

We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons.Comment: 12 pages, 3 figure

An instrument to determine the technological literacy levels of upper secondary school students

In this article, an instrument for assessing upper secondary school students’ levels of technological literacy is presented. The items making up the instrument emerged from a previous study that employed a phenomenographic research approach to explore students’ conceptions of technology in terms of their understanding of the nature of technology and their interaction with technological artefacts. The instrument was validated through administration to 1,245 students on completion of their 12 years of formal schooling. A factor analysis was conducted on the data and Cronbach alpha reliability coefficients determined. The results show that a five-dimension factor structure (namely, artefact, process, direction/instruction, tinkering, and engagement) strongly supported the dimensions as developed during the original phenomenographic study. The Cronbach alpha reliability co-efficient of each dimension was satisfactory. Based on these findings, the instrument has been shown to be valid and reliable and can be used with confidence