Photocatalytic activity and biodegradation of polyhydroxybutyrate films containing titanium dioxide

This study aims to evaluate the photocatalytic activity and biodegradation of polyhydroxybutyrate (PHB) films containing titanium dioxide (TiO₂). Nanosized TiO₂ photocatalysts were immobilized onto PHB film to overcome the difficulty of the recovery process. PHB is a suitable base material as it is naturally biodegradable and is produced from renewable resources. The photocatalytic degradation of organic compounds, photocatalytic sterilization activity and biodegradation rate in garden soil of PHB-TiO₂ composite films were investigated. After an hour under solar illumination, 96% of methylene blue solution was decolorized. The antibacterial activity against Escherichia coli (E. coli) using PHB-TiO₂ composite film exhibited enhanced photocatalytic sterilization activity over time. As for the ability to biodegrade, PHB-TiO₂ composite films placed on soil surface with no direct solar illumination showed slower degradation rate compared to those receiving direct solar illumination. Interestingly, the latter composite films showed faster degradation rates compared to pure PHB films indicating that the degradation is mainly due to photocatalytic activity. PHB-TiO₂ composite films buried in soil generally showed slower degradation rates compared to pure PHB films and were dependent on the soil microbial activity.     

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.     

Application of Löwdin's canonical orthogonalization method to the Slater‐type orbital configuration‐interaction basis set

We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.