Mathematical thinking of undergraduate students when using three types of software

The research investigates how conceptual understanding of mathematics is promoted when using three types of software: black-box (no mathematical intermediate steps shown), glass-box (intermediate steps shown) and open-box (interaction at each intermediate step). Thirty-eight students were asked to think-aloud and give detailed explanations whilst answering three types of tasks: mechanical (mostly procedural), interpretive (mostly conceptual) and constructive (mixture of conceptual and procedural). The software types had no impact on how students answered the mechanical tasks; however students using the black-box did better on the constructive tasks because of their increased explorations. Students with low maths confidence resorted to using real-life explanations when answering tasks that were application related

An Illustration of Students’ Engagement with Mathematical Software using Remote Observation

Students using three types of spreadsheet calculators for understanding expected value were observed remotely. This remote observation involves the use of webcams and application sharing for observing students learning mathematics. The study illustrates how remote observation can be used for collecting mathematical education data and raises questions about the extent to which such a method can be used in future experiments

Technology - Empowering the Educational Researcher through Remote Observation

Observing students using computers often occurs through three methods: user-lab, on-site and remote data logging. Whilst each of these have their advantages with the new type of students such as elearners, an alternative method called web-conferencing remote observation is presented for observing students at a distance. This method collects both audio and video data of the observer through webcams and voice/video conversations. Students are able to interact with the software through application sharing facilities. Further, it allows both quantitative and qualitative data to be collected. This proof-of-concept method is presented here where it has been used in two previous studies using Windows Messenger and Netviewer. Although, video quality is not high the quality is sufficient for observational data

Exotic magnetism on the quasi-FCC lattices of the d3d^3 double perovskites La2_2NaB′'O6_6 (B′' == Ru, Os)

We find evidence for long-range and short-range ($\zeta$ $=$ 70 \AA~at 4 K) incommensurate magnetic order on the quasi-face-centered-cubic (FCC) lattices of the monoclinic double perovskites La$_2$NaRuO$_6$ and La$_2$NaOsO$_6$ respectively. Incommensurate magnetic order on the FCC lattice has not been predicted by mean field theory, but may arise via a delicate balance of inequivalent nearest neighbour and next nearest neighbour exchange interactions. In the Ru system with long-range order, inelastic neutron scattering also reveals a spin gap $\Delta$ $\sim$ 2.75 meV. Magnetic anisotropy is generally minimized in the more familiar octahedrally-coordinated $3d^3$ systems, so the large gap observed for La$_2$NaRuO$_6$ may result from the significantly enhanced value of spin-orbit coupling in this $4d^3$ material.Comment: 5 pages, 4 figure

Muon spin rotation/relaxation measurements of the non-centrosymmetric superconductor Mg10Ir19B16

We have searched for time-reversal symmetry breaking fields in the non-centrosymmetric superconductor Mg$_{10}$Ir$_{19}$B$_{16}$ via muon spin relaxation in zero applied field, and we measured the temperature dependence of the superfluid density by muon spin rotation in transverse field to investigate the superconducting pairing symmetry in two polycrystalline samples of signficantly different purities. In the high purity sample, we detected no time-reversal symmetry breaking fields greater than 0.05 G. The superfluid density was also found to be exponentially-flat as T$\to$0, and so can be fit to a single-gap BCS model. In contrast, the lower purity sample showed an increase in the zero-field $\mu$SR relaxation rate below T$_c$ corresponding to a characteristic field strength of 0.6 G. While the temperature-dependence of the superfluid density was also found to be consistent with a single-gap BCS model, the magnitude as T$\to$0 was found to be much lower for a given applied field than in the case of the high purity sample. These findings suggest that the dominant pairing symmetry in high quality Mg$_{10}$Ir$_{19}$B$_{16}$ samples corresponds to the spin-singlet channel, while sample quality drastically affects the superconducting properties of this system.Comment: 6 pages, 5 figures, revised version resubmitted to PR

Comparison of black-box, glass-box and open-box software for aiding conceptual understanding

Three mathematical software types: black-box (no steps shown), glass-box (steps shown) and open-box (interactive steps) were used by 32 students to solve conceptual and procedural tasks on the computer via remote observation. Comparison of the three software types suggests that there is no difference in the scores that students receive for conceptual understanding tasks. Students using the black-box are more likely to explore answers than students using the glass and open-box software