Intermittent power sources such as wind and solar are increasingly penetrating electrical grids, mainly motivated by global warming concerns and government policies. These intermittent and non-dispatchable sources of power affect the operation and control of the power system because of the uncertainties associated with their output power. Depending on the penetration level of intermittent sources of power, the electric grid may experience considerable changes in power flows and synchronizing torques associated with system stability, because of the variability of the power injections, among several other factors. Thus, adequate and efficient techniques are required to properly analyze the system stability under such uncertainties. A variety of methods are available in the literature to perform power flow, transient, and voltage stability analyses considering uncertainties associated with electrical parameters. Some of these methods are computationally inefficient and require assumptions regarding the probability density functions (pdfs) of the uncertain variables that may be unrealistic in some cases. Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches for voltage and transient stability assessment of power systems, considering uncertainties associated with power injections due to intermittent sources of power. In the proposed AA-based methods, the estimation of the output power of the intermittent sources and their associated uncertainty are modeled as intervals, without any need for assumptions regarding pdfs. This is a more desirable characteristic when dealing with intermittent sources of power, since the pdfs of the output power depends on the planning horizon and prediction method, among several other factors. The proposed AA-based approaches take into account the correlations among variables, thus avoiding error explosions attributed to other self-validated techniques such as Interval Arithmetic (IA).

The purpose of this study is to analyze certain recent trends in the teaching of arithmetic, particularly those trends which have dealt with the reconstruction of the curriculum, and to determine to what extent the advocated theories seem to have been put into practice in the elementary school, according to reports in various school magazines and bulletins.

The purpose of this study is threefold: (1) to review briefly important studies and recommendations relating to curriculum construction in elementary arithmetic; (2) to develop a set of criteria for judging elementary arithmetic textbooks; and (3) to apply the criteria to a selected number of elementary arithmetic textbooks.

Thesis advisor: Elida V. Laski / Strategy selection is an essential aspect of problem-solving, particularly within the domain of mathematics. This dissertation examines the mechanisms that guide children’s arithmetic strategy selection in order to advance theoretical understanding of this essential component of cognitive development. Better understanding of arithmetic strategy selection is important because individual differences in children’s arithmetic strategies are predictive of arithmetic accuracy and later math achievement. The current study builds upon prior research that has identified cognitive processes associated with strategy selection by considering the role of metacognitive judgments. The study investigated the direct and indirect effects of cognitive and metacognitive factors on strategy selection in a group of first and second grade students (n = 126). The majority of students generated metacognitive judgments of their competence using decomposition (an advanced strategy at this age) that were consistent with their actual ability. In these cases, their judgments of competence were related to the frequency with which they used decomposition strategies. Additionally, children’s metacognitive judgments of the anticipated amount effort required to execute decomposition mediated the association between children’s cognitive processes/pre-requisite knowledge (working memory and fact fluency) and the frequency with which they used it. Theoretical and practical implications of these findings are discussed. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Counseling, Developmental and Educational Psychology.

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