An Experimental And Computational Study Of Pattern Formation In Insect Cuticle And A Novel Administration Of A Sensemaking Instrument In Physics Education

Though extensively documented, the exact mechanism responsible for pattern formation on insect bristles and scales is not completely understood. Using both scanning and transmission electron microscopy, we assemble a rough time series of pattern formation on butterfly wing scales. We also perform a numerical simulation of the Swift-Hohenberg equation via finite difference analysis to develop an understanding of the phase space of this novel geometry and compare the patterns observed to patterns found on insect bristles. Our work shows that pattern development on wing scales occurs hierarchically and that, during the entire process, extracellular procuticle coats the surface of the growing cell, variations in which align with modulation of the plasma membrane. In simulation, we find a rich phase space of patterns, parameterized by opening angle and cone length, which agree with observed patterns in literature. Our results, though not comprehensive, suggest that a great deal of pattern formation on bristles and wing scales may be the result of a phase transition of extracellular procuticle coupled with modulations in the underlying cellular membrane, in alignment with recent research on similar patterns found elsewhere in nature. The Math Epistemic Games Survey is a diagnostic instrument for gathering information on student sensemaking in introductory physics course, noted for its length and rigor. Previous research has suggested that student effort (and therefore the fidelity of results) may be improved by shortening the instrument. Through an exploratory factor analysis on MEGS data, we identify 10 key factors and divide each to produce two, half length, mutually exclusive tests. We then administer these half tests to a group of ~600 undergraduate introductory physics students at the University of Pennsylvania as pretests and posttests and compare student performance. Our results show that student performance on each test is distributed extremely similarly and that average performance is slightly above that found in previous studies. We therefore conclude that our proposed split administration produces a reliable instrument, which preserves the original validity of the MEGS, and may improve on some of the identified shortcomings of the full MEGS