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Leveling transparency via situated intermediary learning objectives (SILOs)
When designers set out to create a mathematics learning activity, they have a fair sense of its objectives: students will understand a concept and master relevant procedural skills. In reform-oriented activities, students first engage in concrete situations, wherein they achieve situated, intermediary learning objectives (SILOs), and only then they rearticulate their solutions formally. We define SILOs as heuristics learners devise to accommodate contingencies in an evolving problem space, e.g., monitoring and repairing manipulable structures so that they model with fidelity a source situation. Students achieve SILOs through problem-solving with media, instructors orient toward SILOs via discursive solicitation, and designers articulate SILOs via analyzing implementation data. We describe the emergence of three SILOs in developing the activity Giant Steps for Algebra. Whereas the notion of SILOs emerged spontaneously as a framework to organize a system of practice, i.e. our collaborative design, it aligns with phenomenological theory of knowledge as instrumented action
Evidence for two spin-glass transitions with magnetoelastic and magnetoelectric couplings in the multiferroic (BiBa)(FeTi)O system
For disordered Heisenberg systems with small single ion anisotropy, two spin
glass transitions below the long range ordered phase transition temperature has
been predicted theoretically for compositions close to the percolation
threshold. Experimental verification of these predictions is still
controversial for conventional spin glasses. We show that multiferroic spin
glass systems can provide a unique platform for verifying these theoretical
predictions via a study of change in magnetoelastic and magnetoelectric
couplings, obtained from an analysis of diffraction data, at the spin glass
transition temperatures. Results of macroscopic and microscopic (x-ray and
neutron scattering) measurements are presented on disordered BiFeO3, a
canonical Heisenberg system with small single ion anisotropy, which reveal
appearance of two spin glass phases SG1 and SG2 in coexistence with the LRO
phase below the A-T and G-T lines. It is shown that the temperature dependence
of the integrated intensity of the antiferromagnetic peak shows dips with
respect to the Brillouin function behaviour around the SG1 and SG2 transition
temperatures. The ferroelectric polarisation changes significantly at the two
spin glass transition temperatures. These results, obtained using microscopic
techniques, clearly demonstrate that the SG1 and SG2 transitions occur on the
same magnetic sublattice and are intrinsic to the system. We also construct a
phase diagram showing all the magnetic phases in BF-xBT system. While our
results on the two spin glass transitions support the theoretical predictions,
it also raises several open questions which need to be addressed by revisiting
the existing theories of spin glass transitions by taking into account the
effect of magnetoelastic and magnetoelectric couplings as well as
electromagnons.Comment: 59 pages 21 figure
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