School mathematics practices and the games of truth that are school mathematics.

摘要

The persistent practices and inequitable outcomes of school mathematics in the United States, with much rote learning of facts and skills and increasing stratification of students as they get older, have drawn concern from educators and policymakers for over a century. Efforts to reform school mathematics aimed at providing all students with opportunities to learn substantive mathematical concepts frequently find it difficult to alter long-standing habits of practice. This dissertation offers a view of school mathematics shaped from an intense interest in better understanding historical patterns of educational practice in the United States and their relationship to present conditions of schooling.; Using documentary data from the nineteenth and twentieth centuries, this investigation offers an explication and analysis of the emergence of school mathematics in the United States and the ways in which particular truths came to be formed about mathematical knowledge and learners of mathematics. It was found that from the time of its formation in the early nineteenth century to its full emergence by the 1930s, school mathematics was shaped by a desire to universalize content knowledge and standardize the process of learning. A rhetoric of mathematics learning as tied to social progress influenced decisions about which students were allowed access to higher level knowledge.; Tracing the emergence of school mathematics through intersections with the fields of education, mathematics, and educational psychology, a shift in thinking was found whereby mathematical knowledge moved from a position within the mind of the individual to become externalized and confinable within an "objective" public space. Assessment came to be less "subjective" through the use of statistically defined metrics that provided truth about students' differential abilities.; Bringing to the present this historicized understanding of the intellectual perspectives and social circumstances within which now familiar patterns of practice developed, these claims were reflected against exemplars of current practices drawn from teacher observations and interviews. Subsequent analysis sought to bring into relief some of the difficulties faced in reforming school mathematics. It is suggested that meaningful reform requires explicit strategies that challenge the conditions of possibility that exist with respect to school mathematics.