The phenomenology of the mathematics classroom

This paper describes the mathematics classroom from the perspective of social phenomenology. Here the classroom is seen as an environment of signs, comprising things and people, which impinge on the reality of the individual child. The paper introduces a framework through which mathematical work is seen as taking place in the imagined world through the filter of the world in immediate perception. This provides an approach to structuring evolving mathematical understanding. It is suggested that mathematical ideas are contained and shaped by the child's personal phenomenology, which evolves through time. Further, I argue these ideas are never encountered directly but rather are met through a circular hermeneutic process of reconciling expectation with experience. © 1996 Kluwer Academic Publishers

Supplementary Material for: Endothelial Dysfunction Occurs prior to Clinical Evidence of Polycystic Kidney Disease

<b><i>Objective:</i></b> Polycystic kidney disease (PKD), a monogenic disease with an autosomal dominant or an autosomal recessive form of inheritance (ARPKD), is the most common genetic cause of renal dysfunction and end-stage renal failure. In addition to the development of cysts, the autosomal form of PKD is associated with vascular endothelial dysfunction, a marker of vascular disease. Whether vascular endothelial dysfunction is also present in ARPKD, and its relationship with renal dysfunction remain to be determined. <b><i>Methods:</i></b> ARPKD rats (PCK model) and controls were studied at 6 and 10 weeks of age, and mean arterial pressure and renal function were measured. Aortic endothelial function was assessed using organ chamber techniques. Aortic endothelial cells (ECs) were isolated, characterized and their function studied. <b><i>Results:</i></b> Compared to controls, ARPKD animals had a decrease in the vasorelaxation to endothelium-dependent vasodilators, even prior to changes in mean arterial pressure or renal function. The abnormal vasoreactivity was corrected with L-arginine (a precursor of nitric oxide, NO), while the expression of endothelial NO synthase (eNOS) was unchanged. Furthermore, isolated ECs from 6-week-old ARPKD animals showed increased oxidative stress, with preserved eNOS expression and abnormal patterns of migration and angiogenic capacity (measured by the scratch and tube formation assays, respectively). <b><i>Conclusion:</i></b> ARPKD leads to impairments in aortic vascular function and ECs at an early stage, which can have significant functional consequences, potentially representing a novel therapeutic target in this disease

RURAL AND URBAN POVERTY: AN INCOME&sol;NET WORTH APPROACH

This paper examines rural and urban changes in the distribution of poverty that would result from modifying the conventional poverty measure to include the annuity value of household net worth. Copyright 1988 by The Policy Studies Organization.

The concept and measurement of asset poverty: Levels, trends and composition for the U.S., 1983–2001

American prosperity in the second half of the 1980s together with the booming economy of the 1990s created the impression that American households have done well, particularly in terms of wealth acquisition. In this paper, we develop the concept of “asset poverty” as a measure of economic hardship, distinct from and complementary to the more commonly used concept of “income poverty.” We define a household with insufficient assets to enable it to meet basic needs (as measured by the income poverty line) for a period of three months to be asset poor. The results reveal that in the face of the large growth in overall assets in the U.S. and a fall in standard income poverty over the period from 1983 to 2001, the level of asset poverty increased from 22.4 to 24.5 percent. We also find that asset poverty rates for blacks and Hispanics are over twice those for whites; that asset poverty rates fall monotonically with both age and education; that they are much higher for renters than homeowners; and that by family type they range from a low of 5 percent for elderly couples to 71 percent for female single parents. Copyright Kluwer Academic Publishers 2004demographics, poverty, wealth,

Household wealth and the measurement of economic well-being in the United States

Living standards, Household wealth, Inequality, D31, D6, H4, P16,