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The conceptual framework of mathematical modeling (e.g., Lesh & Doerr, 2003) is a vital area in mathematics education research, and its implementation has potential for deeply involving children in integrated and meaningful learning. In mathematical modeling learners are active agents in content-integrated, real-world problem solving. This emphasis on integrating multiple content areas to answer big questions, the pursuit of mathematical modeling, descends from Dewey’s work. We present the definition, principles, and design of modeling practices for readers who may be familiar with early childhood curriculum but less so with using modeling for learning. We explore the application of mathematical modeling to early childhood classrooms and its compatibility with early childhood pedagogies and philosophies. Young children may often be underestimated, assumed to be unable to pose big questions that can be answered through activity, experience, and data; but we discuss how young children can be engaged in problems through mathematical modeling. Finally, as preservice teacher educators, we discuss preparing preservice and in-service teachers for modeling in their classrooms. We offer examples and guidance for early childhood teachers to engage in authentic practice – meeting children where their interests are and creating integrated problem-solving experiences.

In this chapter, we present our ongoing efforts in developing and sustaining interdisciplinary STEM undergraduate programs at North Carolina A&T State University (NCA&T) – a state-supported HBCU and National Science Foundation (NSF) Historically Black Colleges and Universities Undergraduate Program (HBCU-UP) Institutional Implementation Project grantee. Through three rounds of NSF HBCU-UP implementation grants, a concerted effort has been made in developing interdisciplinary STEM undergraduate research programs in geophysical and environmental science (in round 1), geospatial, computational, and information science (in round 2), and mathematical and computational biology (in round 3) on NCA&T campus. We first present a brief history and background information about the interdisciplinary STEM undergraduate research programs developed and sustained at NCA&T, giving rationales on how these programs had been conceived, and summarizing what have been achieved. Next we give a detailed description on the development of undergraduate research infrastructure including building research facilities through multiple and leveraged funding sources, and engaging a core of committed faculty mentors and research collaborators. We then present, as case studies, some sample interdisciplinary research projects in which STEM undergraduate students were engaged and project outcomes. Successes associated to our endeavor in developing undergraduate research programs as well as challenges and opportunities on implementing and sustaining these efforts are discussed. Finally, we discuss the impact of well-structured undergraduate research training on student success in terms of academic performance, graduation rate and continuing graduate study, and summarize many of the learnings we have gained from implementation and delivery of undergraduate research experiences at HBCUs.

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

Constructing and evaluating behavioral science models is a complex process. Decisions must be made about which variables to include, which variables are related to each other, the functional forms of the relationships, and so on. The last 10 years have seen a substantial extension of the range of statistical tools available for use in the construction process. The progress in tool development has been accompanied by the publication of handbooks that introduce the methods in general terms (Arminger et al., 1995; Tinsley & Brown, 2000a). Each chapter in these handbooks cites a wide range of books and articles on specific analysis topics.

During the last decade or so, philosophers of science have shown increasing interest in scientific models and modeling. The primary impetus seems to have come from the philosophy of biology, but increasingly the philosophy of economics has been drawn into the discussion. This paper will focus on the particular subset of this literature that emphasizes the difference between a scientific model being explanatory and one that provides explanations of specific events. The main differences are in the structure of the models and the characteristics of the explanatory target. Traditionally, scientific explanations have been framed in terms of explaining particular events, but many scientific models have targets that are hypothetical patterns: “patterns of macroscopic behavior across systems that are heterogeneous at smaller scales” (Batterman & Rice, 2014, p. 349). The models with this characteristic are often highly idealized, and have complex and heterogeneous targets; such models are “central to a kind of modeling that is widely used in biology and economics” (Rohwer & Rice, 2013, p. 335). This paper has three main goals: (i) to discuss the literature on such models in the philosophy of biology, (ii) to show that certain economic phenomena possess the same degree of heterogeneity and complexity often encountered in biology (and thus, that hypothetical pattern explanations may be appropriate in certain areas of economics), and (iii) to demonstrate that Hayek’s arguments about “pattern predictions” and “explanations of the principle” are essentially arguments for the importance of this type of modeling in economics.

To provide a comprehensive review of theoretical and research advances in affect control theory from 1988 to 2013 for academic and student researchers in social psychology.

Against the background of a concise history of affect control theory from its beginnings in the 1960s to its maturation in the late 1980s, a comprehensive review of research and publications in the last 25 years is reported in five sections: Theoretical Advances (e.g., self and institutions, nonverbal behavior, neuroscience, artificial intelligence); Technological Advances (e.g., electronic data collection, computer simulations, cultural surveys, equation refinement, small groups analysis); Cross-Cultural Research (archived data and published analyses); Empirical Tests of the Theory; and Substantive Applications (e.g., emotions, social and cultural change, occupations/work, politics, gender/ideology/subcultures, deviance, criminology, stereotyping, physiological behavior).

Reveals an impressive number of publications in this area, including over 120 articles and chapters and four major books, and a great deal of cross-cultural research, including European, Asian, and Middle-Asian cultures.

Because of limitations of space, the review does not cover the large number of theses, dissertations, and research reports.

No other review of affect control theory with this scope and detail exists.