Characteristics of Feedback that Influence Student Confidence and Performance during Mathematical Modeling

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when they are in an environment where they iteratively develop models based on effective feedback

Crystallization of the Ca2+-ATPase of Sarcoplasmic Reticulum by Calcium and Lanthanide Ions

Two-dimensional crystalline arrays of Ca2+-ATPase molecules develop in sarcoplasmic reticulum vesicles exposed to Ca2+ or lanthanide ions. The Ca2+- or lanthanide-induced crystals are presumed to represent the E1 conformation of the Ca2+-ATPase, and their crystal form is clearly different from the earlier described E2 crystals induced by Na3VO4 in the presence of ethylene glycol bis(beta aminoethyl ether)-N,N,N',N'-tetraacetic acid (Taylor, K. A., Dux, L., and Martonosi, A. (1984) J. Mol. Biol. 174, 193-204). Analysis of the crystalline arrays by negative staining or freeze-fracture electron microscopy reveals obliquely oriented rows of particles corresponding to individual Ca2+-ATPase molecules. Computer analysis of the negatively stained lanthanide-induced crystalline Ca2+-ATPase arrays shows that the molecules are arranged in a P1 lattice. The pear-shaped profiles of Ca2+-ATPase molecules seen in projection in the density maps are similar to those seen in vanadate-induced crystals. The space group and unit cell dimensions of the E1 crystals are consistent with Ca2+-ATPase monomers as structural units, while the vanadate-induced E2 crystals form by lateral aggregation of chains of Ca2+-ATPase dimers. The transition between the E1 and E2 conformations may involve a shift in the monomer-oligomer equilibrium of the Ca2+-ATPase. The formation of E1 crystals by PrCl3 is promoted by inside negative membrane potential, presumably through stabilization of the E1 conformation of the enzyme. Cleavage of the Ca2+-ATPase by trypsin into two major fragments (A and B) did not interfere with the Ca2+- or the Pr3+-induced crystallization