Teaching and cognitive outcomes in A-levels and Advanced GNVQ's: Case studies from Science and Business Studies Classrooms

The purpose of the paper is to demonstrate how a research diary methodology, designed to analyse A-level and GNVQ classrooms, can be a powerful tool for examining pedagogy and quality of learning at the level of case study. Two subject areas, science and business studies, are presented as cases. Twelve teachers and thirty-four students were studied over a four-week period in May 1997 and contrasts were drawn between lessons from three A-level physics teachers/three Advanced GNVQ science teachers and two A-level business/economics teachers/four Advanced GNVQ business teachers. Lessons were analysed within a cognitive framework which distinguishes between conceptual and procedural learning and emphasizes the importance of metacognition and epistemological beliefs. Two dimensions of lessons were identified: pedagogical activities (e.g. teacher-led explanation, teacher-led guidance on a task, question/answer sessions, group discussions, working with IT) and cognitive outcomes (e.g. structuring and memorizing facts, understanding concepts and arguments, critical thinking, problem-solving, learning core skills, identifying values). Immediately after each lesson, teachers and students (three per class) completed structured research diaries with respect to the above dimensions. Data from the diaries reveal general and unique features of the lessons. Time-ofyear effects were evident (examinations pending in May), particularly in A-level classrooms. Students in business studies classes reported a wider range of learning activities and greater variety in cognitive outcomes than did students in science classes. Science students self-rating of their ability to manage and direct their own learning was generally low. The phenomenological aspects of the classrooms were consistently linked to teachers' lesson plans and what their teaching objectives were for those particular students at that particular time of the year.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Qubit state guidance without feedback

We study a protocol for two-qubit-state guidance that does not rely on feedback mechanisms. In our scheme, entanglement can be concentrated by arranging the interactions of the qubits with a continuous variable ancilla. By properly post-selecting the outcomes of repeated measurements performed on the state of the ancilla, the qubit state is driven to have a desired amount of purity and entanglement. We stress the primary role played by the first iterations of the protocol. Inefficiencies in the detection operations can be fully taken into account. We also discuss the robustness of the guidance protocol to the effects of an experimentally motivated model for mixedness of the ancillary states.

Greenberger-Horne-Zeilinger nonlocality in arbitrary even dimensions

We generalize Greenberger-Horne-Zeilinger (GHZ) nonlocality to every even-dimensional and odd-partite system. For the purpose we employ concurrent observables that are incompatible and nevertheless have a common eigenstate. It is remarkable that a tripartite system can exhibit the genuinely high-dimensional GHZ nonlocality.