Matematik Öğretmeni Adaylarının Dörtgenleri Sınıflandırma Becerilerinin İncelenmesi

This study aimed to explore prospective teachers’ performance on recognizing quadrilaterals with their special cases and constructing a hierarchical classification of them. The participants consisted of 44 freshmen studying at a public university’s elementary school mathematics education department. Data was collected with a question form containing two questions at the first day of the geometry course taught in the second term of the first year. For quantifying the data of the first question, while students who identify the prototypes of quadrilaterals and their special cases were given 1 and 2 points for each correct answer respectively, -1 point was given for each incorrect answer. The similarity index was employed to quantify students’ concept maps. We investigated that students could detect the prototypes of the quadrilaterals but not their special cases. Additionally, the similarity index between majority of freshmen’ concept maps and the referent map was found as low or moderate.

Understanding catalytic reactions over zeolites: A density functional theory study of selective catalytic reduction of NOX by NH3 over Cu-SAPO-34

Metal exchanged CHA-type (SAPO-34 and SSZ-13) zeolites are promising catalysts for selective catalytic reduction (SCR) of NOx by NH3. However, the understanding of the process at the molecular level is still limited, which hinders the identification of its mechanism and the design of more efficient zeolite catalysts. In this work, modelling the reaction over Cu-SAPO-34, a periodic density functional theory (DFT) study of NH3-SCR was performed using hybrid functional with the consideration of van der Waals (vdW) interactions. A mechanism with a low N–N coupling barrier is proposed to account for the activation of NO. The redox cycle of Cu2+ and Cu+, which is crucial for the SCR process, is identified with detailed analyses. Besides, the decomposition of NH2NO is shown to readily occur on the Brønsted acid site by a hydrogen push-pull mechanism, confirming the collective efforts of Brønsted acid and Lewis acid (Cu2+) sites. The special electronic and structural properties of Cu-SAPO-34 are demonstrated to play an essential role the reaction, which may have a general implication on the understanding of zeolite catalysis.