Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.     

Turnaround Students in High School Mathematics: Constructing Identities of Competence Through Mathematical Worlds

This study investigates prospective secondary teachers’ cognitive difficulties and mathematical ideas involved in making connections among representations. We implemented a three-week teaching unit to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to formulating connections among representations, in the context of conic curves. Qualitative analysis of data showed that most undergraduate mathematics majors and minors in this study struggled with variation, the Cartesian Connection, and other affiliated ideas such as graph as a locus of points. Furthermore, they were unable to identify basic metric relations encoded in algebraic expressions such as the distance between points, which further compounded their difficulties in making connections among representations. We argue that mathematics teacher education needs more focus on these ideas so that their graduates can successfully teach these big ideas in their future instruction.     

Rovibrational spectroscopy and intramolecular dynamics of 1,2-trans-d(2)-ethene in the first C-H stretch overtone region

The first overtone region of the C-H stretching vibration of 1,2-trans-d(2)-ethene (HDC=CDH) was monitored via jet-cooled action spectroscopy and room temperature photoacoustic spectroscopy. The spectra include a strong band, which we assigned as the nu(1)+nu(9) C-H stretch vibration, and five additional bands related to transitions to coupled states. The spectral features were modeled in terms of a six-state deperturbation analysis, revealing the energies of the zero-order states and the relatively strong couplings between the initially excited nu(1)+nu(9) state and the doorway states. Considering these energies and the fundamental frequencies of 1,2-trans-d(2)-ethene and presuming that only low-order resonances are involved in the couplings enabled the assignment of the states. The analysis also allowed obtaining insight on energy flow and to find out that the energy oscillations between the C-H stretch state and the doorway states occur on a subpicosecond time scale.     

Disinfection and Mechanistic Insights of Escherichia coli in Water by Bismuth Oxyhalide Photocatalysis

This study demonstrates the potential of a new BiOCl_0.875Br_0.125 photocatalyst to disinfect Escherichia coli in water under simulated solar irradiation. Photocatalytic efficiency was examined for different photocatalyst loadings, solar wavelengths, exposure times, photocatalyst concentration × contact time (Ct) concept and with the use of scavengers. To elucidate the inactivation mechanism, we examined DNA damage, membrane damage, lipid peroxidation and protein release. Both photolysis and photocatalysis were negligible under visible irradiation, but enhanced photocatalytic activity was observed under solar UVA (λ > 320 nm) and UVB (λ > 280 nm), with 1.5 and 3.6 log inactivation, respectively, after 40 min of irradiation. The log inactivation vs Ct curve for E. coli by UVA/BiOCl_0.875Br_0.125 was fairly linear, with Ct = 10 g L^?1 × min, resulting in 2 log inactivation. Photocatalytic treatment led to membrane damage, but without lipid peroxidation. Accordingly, protein was released from the cells after UVA or UVA/BiOCl_0.875Br_0.125 treatment. Photocatalysis also increased endonuclease‐sensitive sites vs photolysis alone, by an unknown mechanism. Finally, E. coli inactivation was not influenced by the addition of tert‐butanol or l ‐histidine, implying that neither hydroxyl radicals nor singlet oxygen reactive species are involved in the inactivation process.     

Disruption of the hexagonal networks of trimesic acid (benzene-1,3,5-tricarboxylic acid, TMA) by acetic acid

The single crystal X-ray structure of the acetic acid solvate of trimesic acid shows the complete disruption of the hydrogen-bonded hexagonal networks of TMA by bonding to an acetic acid molecule.     

Vibrationally mediated photodissociation of ethene isotopic variants preexcited to the fourth C-H stretch overtone

H and D photofragments produced via vibrationally mediated photodissociation of jet-cooled normal ethene (C2H4), 1,2-trans-d2-ethene (HDCCDH), and 1,1-d2-ethene (CH2CD2), initially excited to the fourth C-H stretch overtone region, were studied for the first time. H and D vibrational action spectra and Doppler profiles were measured. The action spectra include partially resolved features due to rotational cooling, while the monitored room temperature photoacoustic spectra exhibit only a very broad feature in each species. Simulation of the spectral contours allowed determination of the band types and origins, limited precision rotational constants, and linewidths, providing time scales for energy redistribution. The H and D Doppler profiles correspond to low average translational energies and show slight preferential C-H over C-D bond cleavage in the deuterated variants. The propensities toward H photofragments emerge even though the energy flow out of the initially prepared C-H stretch is on a picosecond time scale and the photodissociation occurs following internal conversion, indicating a more effective release of the light H atoms.     

Vibrational structure and methyl C-H dynamics in propyne

Our previous study [J. Chem. Phys. 122, 224316 (2005)] presented the photoacoustic and action spectra of the V=2, 3, 4, and 5 manifolds of the C-H methyl stretching vibrations of propyne and their analysis in terms of a simplified joint local mode/normal mode model. In the current paper the C-H transition intensities were calculated using B3LYP6-311++G(d,p) level of theory to obtain the dipole moment functions. The diagonalization of the vibrational Hamiltonian revealed new model parameters obtained by least square fitting of the eigenvalues to the action spectra band origins, while examining the correspondence between the calculated intensities and simulated band areas. The newly derived parameters predict well the band positions and the observed intensities, allowing new assignment of the features. The derived Hamiltonian was also used to obtain the overall temporal behavior of the C-H stretches as a result of the Fermi couplings and interactions with the bath states. These results indicate that any specificity attained by suitable excitation of the methyl C-H stretches is lost on picosecond time scale, primarily due to strong interactions with doorway states in the lower overtone and coupling with bath states in the region of the higher ones.