Assessing students' conceptual understanding using an online three‐tier diagnostic test

When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general.     

Preparation and characterization study on maleic acid cross-linked poly(vinyl alcohol)/chitin/nanocellulose composites

In the quest on improving composite formulations for environmental sustainability, maleic acid (MA) cross-linked poly(vinyl alcohol) (PVA)-α-chitin composites reinforced by oil palm empty fruit bunch fibers (OPEFB)-derived nanocellulose crystals (NCC) had been successfully prepared. Based on the Fourier transform infrared (FTIR) spectroscopic analysis, it was proven that molecular interactions of the cross-linker to the polymeric networks was through conjugated ester linkage. Differential scanning calorimetry (DSC) showed that the influence of MA was minimal toward crystallization in the PVA/chitin/NCC composite. Maximum tensile strength, elongation at break and Young's modulus of the respective PVA/chitin/NCC composites were achieved at different content of MA, dependent on the PVA/chitin mass ratio. Among all compositions, a maximum Young's modulus was achieved at 30 wt% MA loading in PVA/chitin-30/NCC, amounting to 2,413.81 ± 167.36 MPa. Moreover, the mechanical properties and selected physicochemical properties (swelling, gel content, and contact angle) of the PVA/chitin/NCC composites could be tailored by varying the chitin content (10–30 wt%) and MA content (10–50 wt% based on total mass of composite). In brief, this chemically cross-linked PVA-based biocomposites formulated with sustainable resources exhibited tunable physicochemical and mechanical properties.     

Characterization of biogenic hydroxyapatite derived from animal bones for biomedical applications

In this work, the viability of producing biogenic hydroxyapatite from bio-waste animal bones, namely bovine (cow), caprine (goat) and galline (chicken), through a heat treatment process has been investigated. The animal bones were locally sourced, cleaned to remove collagen and subsequently heat treated in air atmosphere at different temperatures ranging from 600?°C to 1000?°C. From the range of sintering temperatures investigated, it was found that hydroxyapatite derived from bovine bone showed good thermal stability while those produced from caprine and galline bones exhibited phase instability with traces of tri-calcium phosphate (TCP) being detected after heat treatment beyond 700?°C. The porous nature of the bone samples can be observed from the microstructures obtained and supported by low relative density. Heating the bovine and caprine bones at selected temperatures yielded porous HA body, having hardness values that are comparable with human cortical bone. However, the sintered galline bone sample showed higher porosity levels and low hardness when compared to the other two bone types.     

Collection efficiency of liquid‐based samplers for fungi in indoor air

This study assessed the collection efficiency (CE) of two popularly used sampling devices (BioSampler and Coriolis sampler) for fungal aerosols. Phosphate‐buffered saline (PBS) supplemented with or without surfactant (Tween‐20, Tween‐80, or Triton X‐100) and antifoam agent was prepared and used as collection liquids. The agar impactor (BioStage) was simultaneously operated with liquid‐based samplers to collect fungi from seven sites located at a university building, public library, and animal farming. Fungal concentrations determined by liquid samplers were divided by those by BioStage, and the ratio values represented CE. Results indicate that the CE of BioSampler was superior to that of Coriolis (P = 0.0001) and the PBS containing surfactant collected fungi better than that without surfactant (P < 0.0001), whereas antifoam agent showed no influence (P = 0.8). Moreover, fungal concentrations determined by BioSampler with surfactant‐added PBS were statistically indifferent from those by BioStage (P > 0.05) with a Spearman correlation coefficient of 0.81‐0.83 (P < 0.01). In addition to sampler and collection liquid, sampling location was also identified as a significant CE factor (P = 0.006), implying potential influences by fungal genera in the studied fields. Overall, BioSampler with surfactant‐supplemented PBS (eg, Triton X‐100) is recommended considering the great CE and compatibility with a variety of analytical assays.     

An efficient approach for the S‐shaped penalty function

Interval goal programming (IGP) with a marginal penalty function (PF) was first proposed by Charnes and Collomb in 1972, and further improved by Kvanli and other researchers. Recently, Lu and Chen proposed an efficient logarithmic method to formulate IGP with an S‐shaped PF. However, their method requires adding many binary variables when the problem size becomes large, which increases the computational burden in the solution process. This study proposes an efficient approach for the S‐shaped PF. The arbitrary PF frequently appears in the fields of business and industry. However, none of the previous approaches have addressed arbitrary PFs without adding binary variables. The proposed approach can be easily extended to formulate an arbitrary PF in which binary variables are no longer required, regardless of the number of break points. The proposed method can improve the efficiency of IGP for solving large size management and decision problems in considering PFs. In order to demonstrate the correctness, usefulness of the proposed model, illustrative examples are provided.     

Affixing poly(methyl methacrylate-co-acrylic acid) nanospheres with trimethoxyvinylsilane on silicon solar module to enhance its power conversion efficiency

Poly(methyl methacrylate-co-acrylic acid) [P(MMA-co-AA)] incorporated with 0–9 wt% of trimethoxyvinylsilane (TMVS) has been studied to investigate the effect of TMVS on the adhesion properties of P(MMA-co-AA) nanospheres coated on silicon substrate as well as on the power conversion efficiency (PCE) of silicon solar module coated with the polymer nanospheres. The incorporation of 7 and 9 wt% of TMVS into the copolymer has been found to render the copolymer stronger adhesion to glass substrate than the samples with lower amount of TMVS in them. The coating of the P(MMA-co-AA) nanospheres on the glass surface of solar module increases the light harvesting efficiency by serving as an anti-reflective layer. Solar module coated with an array of P(MMA-co-AA) nanospheres with 7 wt% of TMVS yielded the highest PCE enhancement of 98% under the illumination of an AM1.5 solar simulator. The natural weathering results indicate that the copolymer with 7% of TMVS was able to withstand prolonged natural weathering exposure and remained reasonably effective in PCE enhancement up to 130 days of outdoor exposure. This study demonstrates a cost-effective technique to bind [P(MMA-co-AA)] nanospheres onto the silicon surface of solar module via siloxane linkages and thus increases the PCE of the solar module effectively. The T_g of the copolymer increased linearly from 110.31 to 118.42 °C when 0–9 wt% of TMVS was added into it. Thermogravimetry results indicate that the incorporation of TMVS does not give any significant effect on the T_d of the copolymer, which occurs at about 390 °C.