Using Metaphors to Unpack Student Beliefs About Mathematics

This paper reports on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States. These beliefs were revealed using contemporary metaphor theory. A thematic analysis of the students' metaphors for mathematics indicated that students had well developed and complex views about mathematics including math as: an Interconnected Structure, a Hierarchical Structure, a Journey of Discovery, an Uncertain Journey, and a Tool. Another prevalent theme revealed by the metaphors was that students believe perseverance is needed for success in mathematics. The data also suggest an impact of gender and tracking on students beliefs about mathematics. Creating metaphors for mathematics provided a catalyst for student reflection, class discussion, and qualitative data, which could aid program evaluation. Several areas for future research were identified through this exploratory study.     

Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics

We present the results of inelastic neutron scattering experiments for Cr₂O₃ carried out using the single-crystal time-of-flight spectrometer PRISMA at ISIS (U.K.) as well as the three-axis spectrometer TAS-1 at JAERI(J). The collected data are analysed on the basis of phenomenological shell models showing convincing agreement between calculation and experiment both for the frequencies and intensities. All together the dispersion relations of 12 out of 20 phonon branches along the three-fold axis are determined. By a comparison with the Cr₂O₃ iso-type sapphire (Al₂O₃) it is found that the dynamical response of the oxygen ion is only little affected by the ionic substitution. The chromiumd electrons find their expression mainly in a strengthening of the metal-oxygen bonding. The problem of ionic polarizabilities is addressed in detail both for the oxygen and chromium ions.     

Trapping quasiminimizing submanifolds in spaces of negative curvature

LetM be a Hadamard manifold with all sectional curvatures bounded above by some negative constant. A well-known lemma essentially due to M. Morse states that every quasigeodesic segment inM lies within an a priori bounded distance from the geodesic arc connecting its endpoints. In this paper we establish an analogue of this fact for quasiminimizing surfaces in all dimensions and codimensions; the only additional requirement is that the sectional curvatures ofM be bounded from below as well. We apply this estimate to obtain new solutions to the asymptotic Plateau problem in various settings. The second author was supported by the Swiss National Science Foundation and enjoyed the hospitality of the University of Bonn. The collaboration between the authors was facilitated by the program GADGET II.     

Eine Methode zur gleichzeitigen elementaranalytischen Bestimmung von Kohlenstoff, Wasserstoff und Stickstoff

Ohne Zusammenfassung     

Study of solid-state polymerization by positron lifetime measurements

The positron lifetime measurement technique was applied to analyze the structural changes occurring in solid-state polymerization of acrylamide and trioxane. Positronium (Ps) parameters, τ₂ and I₂, which show a marked change as a function of the γ-ray irradiation dose, signaled the presence of three clearly defined stages in the polymerization process: initiation, propagation, and saturation. The initial increase in τ₂, may very well be the result of efficient trapping of Ps in vacancies created around the polymer nuclei. The complicated behavior of I₂ may be explained as a chemical reaction between Ps precursors and the radiolysis products of this polymerization process.