No description available.

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 124-131). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (M.A.)--York University, 2002. Graduate Programme in Psychology. / Typescript. Includes bibliographical references (leaves 71-78). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ71623.

This study explores characteristics of students’ repertoires of representations in two mathematical contexts: whole number multiplication and the comparison of common fractions. A repertoire of representations refers to a set of representations which a student can reconstruct as needed. Of particular interest are (1) how multiplicative relationships among units were represented, and (2) whether continuous measurement was an underlying conceptual framework for their representations. In addition, the characteristics of students’ representations and interpretation of units of linear and area measurement were explored. Data were collected through a series of interviews with Grade 5 and Grade 7 students. Some results of the study were as follows. Each repertoire of representations was exemplified by a dominant form of units, either discrete or contiguous. Within a repertoire, all forms of units were related, first through a common system of measurement (either numerosity or area), and second through their two-dimensional characteristic. In the multiplication context, some repertoires were comprised only of representations with discrete units, but others also included some representations with contiguous units. Students sought characteristics in their representations which reflected those based on continuous measurement, however linear or area measurement was not used as a conceptual framework. Instead, all representations were based on the measurement of numerosity. Also, students exhibited different limits in their representation of multiplicative relationships among units. Some represented no multiplicative relationships, but most represented at least a multiplicative relationship between two units. Relationships among three units were seldom constructed and difficult to achieve. Common fraction repertoires were based on the measurement of either numerosity or area, but the physical characteristics of the units varied. Some repertoires had only contiguous representations of units, others also included representations with discrete units, and a few did not represent fractional units at all. Students’ representations reflected characteristics of area-based representations, however area measurement was not necessarily a conceptual framework. In addition, students’ beliefs about what constituted units of area measurement were variable. As a result, they either represented no multiplicative relationships among units, or fluctuated between representing two-unit and three-unit relationships. Linear measurement was notably absent as a basis for representations in both mathematical contexts. The one-dimensional characteristic of linear measurement did not fit students’ dominant framework for constructing mathematical representations. With respect to measurement, students represented linear units in terms of discrete points or line segments. Counting points and interpreting the count in terms of the numerosity of line segments was problematic for nearly all students. When partitioning regions into units of area, a few students also equated the number of lines with the number of parts. The direct relationship of action and result in counting discrete objects was generalized without consideration of other geometric characteristics. When comparing quantities having linear or area units, numerical reasoning was not always used. Alternatively, either quantities were transformed to facilitate a direct comparison, or only perceptual judgements were made. No students consistently used numerical reasoning to compare fractional units of area. In the latter situations, the part-whole relationship among units seldom was observed. In general, there was no direct relationship between the forms of representations used by students in the two mathematical contexts and the characteristics of their representations of units of the measurement contexts. The development of repertoires of representations appears to be context specific. The repertoires were strictly limited in terms of the forms of representations of which they were comprised.

Thesis (Ph. D.)--University of Wyoming, 2005. / Title from PDF title page (viewed on Oct. 16, 2007). Includes bibliographical references (p. 36-39).

Thesis (Ph. D.)--Open University. BLDSC no. DX196536.

Thesis (Ph. D.)--UCLA, 2009. / Vita. Description based on print version record. Includes bibliographical references (leaves 200-210).

This study explores characteristics of students’ repertoires of representations in two mathematical contexts: whole number multiplication and the comparison of common fractions. A repertoire of representations refers to a set of representations which a student can reconstruct as needed. Of particular interest are (1) how multiplicative relationships among units were represented, and (2) whether continuous measurement was an underlying conceptual framework for their representations. In addition, the characteristics of students’ representations and interpretation of units of linear and area measurement were explored. Data were collected through a series of interviews with Grade 5 and Grade 7 students. Some results of the study were as follows. Each repertoire of representations was exemplified by a dominant form of units, either discrete or contiguous. Within a repertoire, all forms of units were related, first through a common system of measurement (either numerosity or area), and second through their two-dimensional characteristic. In the multiplication context, some repertoires were comprised only of representations with discrete units, but others also included some representations with contiguous units. Students sought characteristics in their representations which reflected those based on continuous measurement, however linear or area measurement was not used as a conceptual framework. Instead, all representations were based on the measurement of numerosity. Also, students exhibited different limits in their representation of multiplicative relationships among units. Some represented no multiplicative relationships, but most represented at least a multiplicative relationship between two units. Relationships among three units were seldom constructed and difficult to achieve. Common fraction repertoires were based on the measurement of either numerosity or area, but the physical characteristics of the units varied. Some repertoires had only contiguous representations of units, others also included representations with discrete units, and a few did not represent fractional units at all. Students’ representations reflected characteristics of area-based representations, however area measurement was not necessarily a conceptual framework. In addition, students’ beliefs about what constituted units of area measurement were variable. As a result, they either represented no multiplicative relationships among units, or fluctuated between representing two-unit and three-unit relationships. Linear measurement was notably absent as a basis for representations in both mathematical contexts. The one-dimensional characteristic of linear measurement did not fit students’ dominant framework for constructing mathematical representations. With respect to measurement, students represented linear units in terms of discrete points or line segments. Counting points and interpreting the count in terms of the numerosity of line segments was problematic for nearly all students. When partitioning regions into units of area, a few students also equated the number of lines with the number of parts. The direct relationship of action and result in counting discrete objects was generalized without consideration of other geometric characteristics. When comparing quantities having linear or area units, numerical reasoning was not always used. Alternatively, either quantities were transformed to facilitate a direct comparison, or only perceptual judgements were made. No students consistently used numerical reasoning to compare fractional units of area. In the latter situations, the part-whole relationship among units seldom was observed. In general, there was no direct relationship between the forms of representations used by students in the two mathematical contexts and the characteristics of their representations of units of the measurement contexts. The development of repertoires of representations appears to be context specific. The repertoires were strictly limited in terms of the forms of representations of which they were comprised. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

No description available.

O presente trabalho teve como objetivo investigar a dinâmica psíquica de crianças vítimas de uma enfermidade grave e a possibilidade de permitir maior mobilidade da dinâmica psíquica dessas crianças por meio da técnica lúdica e do trabalho de busca de representabilidade, a partir da premissa de que a enfermidade grave na infância é uma situação traumática dentre tantas outras possíveis. Delineamos, para tal entendimento, um percurso que se inicia nas primeiras inscrições psíquicas e na construção de representações e, em seguida, apresentamos a maneira como uma situação traumática pode fragilizar a mente. Enfatizamos a possibilidade de representação, mediante as intervenções psicanalíticas, partindo do princípio de que é por intermédio da condição simbólica que o indivíduo se desenvolve. Realizamos um estudo teórico-clínico de duas crianças que foram submetidas à operação para correção de cardiopatia congênita e, consequentemente, internação em unidade de terapia intensiva. O estudo consistiu de intervenções psicanalíticas que privilegiaram o oferecimento de um continente com rêverie, com uma proposta de acompanhar a criança no confronto com questões que fogem da esfera de representações, por intermédio do brincar, favorecendo a não paralisação e o não congelamento de sua rede simbólica e de significados. O Procedimento de Desenhos-estórias foi utilizado no início e final do processo como apoio para as intervenções e avaliações. Por meio das intervenções psicanalíticas, dos recursos teóricos-técnicos utilizados, observamos algumas modificações na linha de representação dos conflitos e um início de mudança na forma das crianças brincarem e se expressarem graficamente / This study aimed to investigate the psychological dynamics of child victims of a serious illness and possibility of allowing greater mobility of the psychological dynamics of these children through recreational technical and search representative from the premise that serious illness in childhood is a traumatic situation among many others possible. Outline for such an understanding, a journey that starts in the first registration and the construction of mental representations and then present how a traumatic situation may weaken the mind. We emphasize the possibility of representation by the psychoanalytic interventions, assuming that it is through the symbolic condition that the individual develops. We conducted a theoretical and clinical study of two children who underwent surgery for repair of congenital heart disease and, consequently, admission to the intensive care unit. The study consisted of psychoanalytic interventions which recommended the offer of a continent with reverie, with a proposal to accompany the child in confronting issues that are beyond the realm of representations, through the play, not favoring the strike and not freeze your symbolic condition. The Drawing-stories was used at the beginning and end of the process as support for interventions and evaluations. Through psychoanalytic interventions, theoretical-technical resources used, we observed some changes in the line representing the beginning of a conflict and change in the way children play and express themselves graphically