Unpacking the logic of mathematical statements

This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61students in six small sections of a “bridge" course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion of proof framework to indicate the top-level logical structure of a proof. For simplified informal calculus statements, just 8.5% of unpacking attempts were successful; for actual statements from calculus texts, this dropped to 5%. We infer that these students would be unable to reliably relate informally stated theorems with the top-level logical structure of their proofs and hence could not be expected to construct proofs or evaluate their validity

Asymmetry of Caddo Ceramics from the Washington Square Mound Site: An Exploratory Analysis

While pursuing a study of 3D geometric morphometrics for ceramic burial vessels that often articulate with the Native American Graves Protection and Repatriation Act (NAGPRA) from the ancestral Caddo region, there have been no shortage of potentially meaningful observations, one of which--rotational asymmetry in coil-built vessels--is discussed here. Using Geomagic Design X (reverse-engineering software) and Geomagic Control X (inspection software), metrics associated with rotational asymmetry were generated then analyzed. Results indicate variable asymmetry among the different vessel shapes (i.e., bottles, jars, etc.), which may augment and strengthen studies and discussion of vessel form. Future directions include the incorporation of directional and--possibly--fluctuating asymmetry measures for the widest vessel profiles. Preliminary results point toward substantive analytical gains that can be used to augment more traditional ceramic analyses as well as geometric morphometric studies of ceramic vessel shape