SEEKING CULTURAL FAIRNESS IN A MEASURE OF RELATIONAL REASONING

Relational reasoning, or the ability to identify meaningful patterns within any stream of information, is a fundamental cognitive ability associated with academic success across a variety of domains of learning and levels of schooling. However, the measurement of this construct has been historically problematic. For example, while the construct is typically described as multidimensional—including the identification of multiple types of higher-order patterns—it is most often measured in terms of a single type of pattern: analogy. For that reason, the Test of Relational Reasoning (TORR) was conceived and developed to include three other types of patterns that appear to be meaningful in the educational context: anomaly, antinomy, and antithesis. Moreover, as a way to focus on fluid relational reasoning ability, the TORR was developed to include, except for the directions, entirely visuo-spatial stimuli, which were designed to be as novel as possible for the participant. By focusing on fluid intellectual processing, the TORR was also developed to be fairly administered to undergraduate students—regardless of the particular gender, language, and ethnic groups they belong to. However, although some psychometric investigations of the TORR have been conducted, its actual fairness across those demographic groups has yet to be empirically demonstrated. Therefore, a systematic investigation of differential-item-functioning (DIF) across demographic groups on TORR items was conducted. A large (N = 1,379) sample, representative of the University of Maryland on key demographic variables, was collected, and the resulting data was analyzed using a multi-group, multidimensional item-response theory model comparison procedure. Using this procedure, no significant DIF was found on any of the TORR items across any of the demographic groups of interest. This null finding is interpreted as evidence of the cultural-fairness of the TORR, and potential test-development choices that may have contributed to that cultural-fairness are discussed. For example, the choice to make the TORR an untimed measure, to use novel stimuli, and to avoid stereotype threat in test administration, may have contributed to its cultural-fairness. Future steps for psychometric research on the TORR, and substantive research utilizing the TORR, are also presented and discussed.

Relations among Topic Knowledge, Individual Interest, and Relational Reasoning, and Critical Thinking in Maternity Nursing

Critical thinking in learners is a goal of educators and professional organizations in nursing as well as other professions. However, few studies in nursing have examined the role of the important individual difference factors topic knowledge, individual interest, and general relational reasoning strategies in predicting critical thinking. In addition, most previous studies have used domain-general, standardized measures, with inconsistent results. Moreover, few studies have investigated critical thinking across multiple levels of experience. The major purpose of this study was to examine the degree to which topic knowledge, individual interest, and relational reasoning predict critical thinking in maternity nurses. For this study, 182 maternity nurses were recruited from national nursing listservs explicitly chosen to capture multiple levels of experience from prelicensure to very experienced nurses. The three independent measures included a domain-specific Topic Knowledge Assessment (TKA), consisting of 24 short-answer questions, a Professed and Engaged Interest Measure (PEIM), with 20 questions indicating level of interest and engagement in maternity nursing topics and activities, and the Test of Relational Reasoning (TORR), a graphical selected response measure with 32 items organized in scales corresponding to four forms of relational reasoning: analogy, anomaly, antithesis, and antinomy. The dependent measure was the Critical Thinking Task in Maternity Nursing (CT2MN), composed of a clinical case study providing cues with follow-up questions relating to nursing care. These questions align with the cognitive processes identified in a commonly-used definition of critical thinking in nursing. Reliable coding schemes for the measures were developed for this study. Key findings included a significant correlation between topic knowledge and individual interest. Further, the three individual difference factors explained a significant proportion of the variance in critical thinking with a large effect size. While topic knowledge was the strongest predictor of critical thinking performance, individual interest had a moderate significant effect, and relational reasoning had a small but significant effect. The findings suggest that these individual difference factors should be included in future studies of critical thinking in nursing. Implications for nursing education, research, and practice are discussed.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.