Analyzing Problem Solving Using Math in Physics: Epistemological Framing via Warrants

Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical processing, computation, blending ancillary information with the math, and reading out physical implications from the math and vice versa. From videotaped observations of intermediate level students solving problems in groups, we note that students often "get stuck" using a limited group of skills or reasoning and fail to notice that a different set of tools (which they possess and know how to use effectively) could quickly and easily solve their problem. We refer to a student's perception/judgment of the kind of knowledge that is appropriate to bring to bear in a particular situation as epistemological framing. Although epistemological framing is often unstated (and even unconscious), in group problem solving situations students sometimes get into disagreements about how to progress. During these disagreements, they bring forth explicit reasons or warrants in support of their point of view. For the context of mathematics use in physics problem solving, we present a system for classifying physics students' warrants. This warrant analysis offers tangible evidence of their epistemological framing.Comment: 23 page

A longitudinal study of cardiac output in normal human pregnancy

OBJECTIVE: Our purpose was to investigate the maternal hemodynamic and cardiac structural changes that occur during pregnancy. STUDY DESIGN: Eighteen women underwent serial echocardiography beginning at 8 to 11 weeks' gestation, then at monthly intervals throughout pregnancy and at 6 and 12 weeks post partum. Cardiac output was measured by pulsed-and continuous-wave Doppler at the aortic valve. Left ventricular chamber size, wall thickness, and mass were determined by M-mode echocardiography. Ventricular diastolic function was assessed by Doppler recording of mitral inflow. RESULTS: Cardiac output by pulsed Doppler increased from 6.7 ± 0.9 L/min at 8 to 11 weeks' gestation to 8.7 ± 1.4 L/min at 36 to 39 weeks' gestation before falling to 5.7 ± 0.7 L/min 12 weeks post partum. Heart rate increased 29%, and stroke volume increased 18%. Left ventricular mass increased because of an increase in wall thickness. Peak mitral A wave velocity increased in late pregnancy. Cardiac output by pulsed and continuous-wave Doppler was similar. CONCLUSION: Cardiac output continues to increase even in late pregnancy. Left ventricular mass increases because of increased wall thickness. The mitral flow velocity findings suggest decreased ventricular compliance or increased preload. (AM J OBSTET GYNECOL 1994;170:849-56.

The fate of homograft conduits in children with congenital heart disease: an angiographic study

The use of homograft conduits in the repair of congenital heart disease is widelym accept. We reviewed the catherization and angiographic data from 20 patients with ho,ograft conduits. All conduits were to the pilmonary arteries. The age at operation was 4.7 ± 5.6 years (mean ± standard deviation) and at follow-up catheterization, 7.8± 6.7 years. At implantation, conduit cross-sectional area and Z value were 219 ± 96 mm2 and 3.5 ± 1.8, respectively. At subsequent catheterization, the conduit diameters were measured in two projections at the shaft, 151 ± 92 mm2 at the annulus, 108 ± 116 mm2 at the valve opening, and 127 ± 84 mm2 at the pulmonary artery insertion. The Z values were -0.9 ± 2.5, -0.9 ± 2.8, -3.8 ± 4.0, and -2.0 ± 3.4, respectively. The crosssectional areas and the Z values at the levels of measurement were significantly smaller than the corresponding values at implantation. The change in cross-sectional areas and Z values exceeded what would be expected from growth alone. These data indicate that there is a decrease, with time, in the functional lumen of homograft conduits, and this may have implications for follow-up strategy after implantation