An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Modification of polystyrene maleic anhydride for efficient energy storage applications

Journal of Solid State Electrochemistry - The development of new energy storage devices has been gaining momentum in the wake of the energy crisis faced worldwide. New materials have been tried and...     

ThH5: An Actinide-Containing Superhalogen Molecule

Thorium and its compounds have been widely investigated as important nuclear materials. Previous research focused on the potential use of thorium hydrides, such as ThH₂, ThH₄, and Th₄H₁₅, as nuclear fuels. Here, we report studies of the anion, ThH₅⁻, by anion photoelectron spectroscopy and computations. The resulting experimental and theoretical vertical detachment energies (VDE) for ThH₅⁻ are 4.09 eV and 4.11 eV, respectively. These values and the agreement between theory and experiment facilitated the characterization of the structure of the ThH₅⁻ anion and showed its neutral counterpart, ThH₅ to be a superhalogen. ThH₅⁻, which exhibits a C_4v structure with five Th−H single bonds, possesses the largest known H/M ratio among the actinide elements, M. The adaptive natural density partitioning (AdNDP) method was used to further analyze the chemical bonding of ThH₅⁻ and to confirm the existence of five Th−H single bonds in the ThH₅⁻ molecular anion.