Secondary Student Metacognition Compared to Actual Participation in the Classroom

Many times in a conflict there are three different accounts of what happened: person one’s side, person two’s side, and the truth. As often as this saying gets made and joked about, it does reveal truth about how perception and truth don’t always align. With this thought, I want to compare a student’s perceived participation in comparison with actual class participation. In many secondary and collegiate level classrooms, course grades are partially determined on class participation. Because of this, it would seem relevant to consider perceptions with reality so that students can better understand themselves. When a student has a good grasp on his or herself, then he or she is more likely to modify behavior for improvement. As for the actual measuring of data, a survey will be given out after one session of recording, then to also be followed by a second session. During each recording session, the primary principal/co-principal investigator will record how often each student raises their hand, how often each student is called on with and without their hand raised separately by tallies. The students will also turn in their assignment, not for a grade but for a completion of finished, half finished, or not finished as a score. Assignments will be tallied on two different situations: one prior to the survey and one after the survey. After all data has been collected and coded to protect identities, surveys will be compared to before and after survey recordings and then compared through mean, mode and median

Mutations of puzzles and equivariant cohomology of two-step flag varieties

We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks to the equivariant version of the `quantum equals classical' result, our formula specializes to a Littlewood-Richardson rule for the equivariant quantum cohomology of Grassmannians.Comment: In this version illegal puzzle pieces have been renamed to temporary puzzle pieces. Conjecture 4.7 has been replaced with a counterexample. This is the final version to appear in Annals of Mathematic

The saturation conjecture (after A. Knutson and T. Tao)

In this exposition we give a simple and complete treatment of A. Knutson and T. Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the saturation conjecture, which asserts that the Littlewood-Richardson semigroup is saturated. The main tool is Knutson and Tao's hive model for Berenstein-Zelevinsky polytopes. In an appendix of W. Fulton it is shown that the hive model is equivalent to the original Littlewood-Richardson rule.Comment: Latex document, 12 pages, 24 figure

A Note on Solid-State Maxwell Demon

Starting from 2002, at least two kinds of laboratory-testable, solid-state Maxwell demons have been proposed that utilize the electric field energy of an open-gap n-p junction and that seem to challenge the validity of the Second Law of Thermodynamics. In the present paper we present some arguments against the alleged functioning of such devices.Comment: 9 pages, 4 figures. Foundations of Physics, forthcoming. arXiv admin note: substantial text overlap with arXiv:1101.505