The aqueous chemistries of two transition metal cations, Zr⁴⁺ and Nb⁵⁺, are examined and then used to develop inorganic precursor solutions. The oxides of these cations (ZrO₂ and Nb₂O₅) are deposited and characterized, and their morphological and optical properties discussed. Due to the obstacles created by niobium's aqueous chemistry, an...
The purpose of this study was to detail mathematical knowledge that supports the work of teaching proof and to investigate how such knowledge is evidenced in professional development (PD). To advance the construct of mathematical knowledge for teaching (MKT) in the context of proof, I developed a framework of MKT...