Mercedes A. McGowen

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The major focus of this study is to trace the cognitive development of students throughout a mathematics course and to seek the qualitative differences between those of different levels of achievement. The aspect of the project described here concerns the use of concept maps constructed by the students at intervals during the course. From these maps,(More)
Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships. In this presentation we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and(More)
While the general notion of 'metaphor' may offer a thoughtful analysis of the nature of mathematical thinking, this paper suggests that it is even more important is to take into account the particular mental structures available to the individual that have been build from experience that the individual has 'met before'. The notion of 'met-before' offers not(More)
The concept of function is considered as foundational in mathematics. Yet it proves to be elusive and subtle for students. In this paper we suggest that a generic image that can act as a cognitive root for the concept is the function box. We see this not as a simple pattern-spotting device, but as a concept that embodies the salient features of the idea of(More)
We describe students' developing understanding of function as an input/output process and as an object by tracing the internalization of the function machine concept as it relates to representations of functions We examine whether function machines serve as a cognitive root for the function concept for undergraduates enrolled in a developmental algebra(More)
OBJECTIVE Client outcomes for the first year of a three-year study were measured in two integrated service agencies (ISAs) for severely mentally ill persons to test the effectiveness of a model combining financing reform (consolidated funding and capitation) with an assertive continuous treatment team approach. METHODS Clients referred to pilot ISAs at an(More)
OBJECTIVE In a three-year controlled study, two California integrated service agency demonstration programs that combined structural and program reforms were tested to see if they produced improved outcomes for a cross-section of clients with severe and persistent mental illness. METHODS Clients at an urban site and a rural site were randomly assigned to(More)
The purpose of this study was to investigate whether students classified as 'developmental' or 'remedial' could, with a suitable curriculum, demonstrate improved capabilities in dealing flexibly and consistently with ambiguous notation using various representations of functions. The stability of their responses over time was also a subject of study. The(More)