http://hdl.handle.net/2027.42/61172 Wed, 22 May 2013 22:40:36 GMT 2013-05-22T22:40:36Z http://hdl.handle.net/2027.42/91279 Mathematical Knowledge for Teaching High School Geometry Herbst, Patricio; Kosko, Karl W. This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. We use this result to propose ways of conceptualizing how instruction-specific considerations might matter in the design of MKT items. Mon, 28 May 2012 00:00:00 GMT http://hdl.handle.net/2027.42/91279 2012-05-28T00:00:00Z http://hdl.handle.net/2027.42/61250 On the Pythagorean hull of Q Pambuccian, Victor Mon, 01 Jan 1990 00:00:00 GMT http://hdl.handle.net/2027.42/61250 1990-01-01T00:00:00Z http://hdl.handle.net/2027.42/61173 Sperner spaces and first-order logic Blass, Andreas; Pambuccian, Victor We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ[sub]∞ω-axiomatizable. We also axiomatize the first-order theory of this class. Mon, 27 Jan 2003 00:00:00 GMT http://hdl.handle.net/2027.42/61173 2003-01-27T00:00:00Z http://hdl.handle.net/2027.42/58127 Asymptotics of rare events in birth–death processes bypassing the exact solutions Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M.; Vanden-Eijnden, Eric We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between any two states are available and the near-continuum expansion of these formulae defines the correct limiting behaviour and is used to check the results of asymptotic analysis of the difference equations. We find that in some cases the asymptotic approach does not lead unequivocally to the proper result. Wed, 14 Feb 2007 00:00:00 GMT http://hdl.handle.net/2027.42/58127 2007-02-14T00:00:00Z