How can universities support beginning teachers?

Many beginning teachers struggle in teaching, consequently, tertiary education has been criticised for not preparing preservice teachers well enough. This qualitative study uses interviews and questionnaires to investigate 10 first-year teachers’ understandings of how universities can support them more effectively. The findings indicated that university preparation needed more literacy (particularly reading and spelling), numeracy, catering for lower socio-economic students, understanding behaviour differentiation, and communicating with parents. A two-prong approach may support beginning teachers: (1) timely induction and mentoring within school settings, and (2) research for advancing teacher education coursework to ensure currency of addressing beginning teachers’ needs

Action-gradient-minimizing pseudo-orbits and almost-invariant tori

Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring integrable system. "Almost invariant" tori with rational rotation number can be defined using continuous families of periodic \emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number tori can be defined by nesting with sequences of such rational tori. Three definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin), \emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on variants of Hamilton's Principle, use different strategies to extremize the action as closely as possible. Equivalent Lagrangian (configuration-space action) and Hamiltonian (phase-space action) formulations, and a new approach to visualizing action-minimizing and minimax orbits based on AGMin pseudo-orbits, are presented.Comment: Accepted for publication in a special issue of Communications in Nonlinear Science and Numerical Simulation (CNSNS) entitled "The mathematical structure of fluids and plasmas : a volume dedicated to the 60th birthday of Phil Morrison