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At Western Oregon University, we offer a College Algebra for Teachers course using the Visual Algebra for College Students [3] materials that we wrote and class tested. Visual Algebra is designed to help middle school teachers gain a deep understanding of basic algebraic skills. Students visually show algebra using a concrete model (algebra pieces), verbally describe the meaning of each algebra piece move, symbolically connect the ideas to standard algebraic algorithms and procedures, and graphically connect the ideas of the visual models and symbolic work. Overall, students think deeply about topics, do not rely on rote memorization or rote rules, and understand ideas so well that they can easily describe, model, and teach core algebraic ideas to their middle grade students in a variety of ways. This allows our future teachers to meet the needs of the different learning styles in their classrooms. Visual Algebra takes students through modeling integer operations with black and red tiles to modeling linear and quadratic patterns with tiles and variable algebra pieces, looking at the general forms of the patterns and then connecting all the ideas to symbolic manipulation, creating data sets, graphing, and finding intercepts and points of intersection. Ideas are then extended to higher order polynomial functions and then to modeling complex number operations with black, red, yellow, and green tiles. Throughout the course, students are able to relate what they learned using visual methods to the standard methods and algorithms they will see every day in their classroom. For example, after factoring quadratic equations using visual methods, students learn factoring by grouping and factoring using the “ac” method. © 2013 by The Mathematical Association of America (Incorporated).

This multi-phased study investigates the learning outcomes of courses taught in the K-14 classroom. Specifically, the methods and practices teachers use to develop and encourage 21st Century Skills including critical thinking skills and technological fluency in all subject areas, STEM and non-STEM related, are of great interest. Currently, these skills are in high demand in fields which develop advanced materials and are the backbone of the National Academies-developed Frameworks for K-12 Science Education. Phase I participants in this study included high school and college educators while Phase II of the study will involve K-14 students. In this study, educators were asked to rate their teaching self-efficacy in two primary areas: critical thinking skills and technological fluency. This included questions related to components in their current curriculum as well as methods of assessment [e.g., rubrics]. The instrument created to measure self-efficacy was based on a modified 'Science Teaching Efficacy Belief Instrument' (STEBI). All participants were from Connecticut. Results indicate that both STEM and non-STEM related subject areas offer an equally rich array of opportunities to effectively teach critical thinking and technological fluency at a variety of educational levels. The impact of Professional Development on teacher self-efficacy was of particular importance, especially in K-12 education. © 2013 Materials Research Society.

Through 1975, the shareholder annual reports of publicly-owned U.S. railroads were exempt from the Securities and Exchange Commission’s accounting regulations, audit and disclosure rules because railroads were common carriers subject to the rules and regulations of the Interstate Commerce Commission (ICC). Pub-liclyowned Class railroads voluntary began to away from ICC-type towards GAAP-type accounting and disclosures in their shareholder reports just after World War II.1 This paper reviews early industry practices with respect to internal and external audits. Using a sample of major Class I railroads from 1946 to 1975, the paper shows: the extent to which certain railroads voluntarily presented audited finan-cial statements before being required, the extent to which particular CPA firms were involved with the railroad industry, and the types of audit reports that issued to these railroads during this period. © 2016, Academy of Accounting Historians. All rights reserved.

Although Palomides in Malory's Morte Darthur and his counterpart in the French Tristan en Prose are usually discussed by their roles, my study selects five scenes linked by woodland settings, wells, and complaints. Accordingly, it demonstrates what each scene shows about the values of reputation, friendship, love, religious conviction, and-in the aftermath of the rupture between Lancelot and Arthur-the capacity for loyalty to Lancelot shown by Palomides and his brother Saphir. © 2013 Project MUSE.

We study almost complete intersection ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics depth or relation type have maximal or minimal values in the class. The focus is on those ideals that lead to almost Cohen-Macaulay algebras, and our treatment is wholly concentrated on the nonlinear relations of the algebras. Several classes of such algebras are presented, some of a combinatorial origin. We offer a different prism to look at these questions with accompanying techniques. The main results are effective methods to calculate the invariants of these algebras. © 2013 Rocky Mountain Mathematics Consortium.

Binary and multiple stellar systems have importance in three main areas of astronomy and astrophysics. First, because of the relatively simple gravitational interaction at work in the case of binary stars, these systems provide a basic check on stellar structure and evolution theory since the masses may be determined through observation. When these masses can be linked to other properties of the two stars, such as luminosity, color, and radius, they can provide very stringent constraints on stellar models. Second, the statistics of binary and multiple star systems provide clues to star formation mechanisms and environmental effects in the galactic gravitational potential and in clusters. Although a number of good results have been obtained in nearby star clusters and associations, knowledge of the field population has been somewhat limited until recently by a lack of large, complete samples of binaries. However, there appears to be a great deal of promise in this area for the coming decade in part due to astrometric satellites such as Hipparcos and Gaia. Third, the binary scenario is invoked to explain several important types of astrophysical phenomena such as Type Ia supernovae, cataclysmic variables, and stellar x-ray sources. Since the first of these mentioned is a standard candle for the extragalactic distance scale, it may even be said binary stars play a minor role in field of cosmology. However, in this chapter, the focus will mainly be on normal stars in binary and multiple-stellar systems. The basic physics of binaries will be reviewed, and the observational methods in use today will be discussed together with their limitations and prospects for the future. Finally, an overview of the current science in the three main areas mentioned where binaries have a significant impact will be given. © Springer Science+Business Media Dordrecht 2013.

Couples who come into therapy with amorphous symptoms often reveal later in treatment that there has been a traumatic event that occurred in the past and that has lingered as a significant disturbance to intimacy. No amount of “talk therapy�? or insight seems to allow these couples to move past the point of emotional treachery. This activity is designed to allow these couples a vehicle for putting the past to rest in a way that allows them to continue their relationship without resentment, revenge, or continual pain. © 1998 by The Haworth Press, Inc. All rights reserved.

Through a multi-country study, Comparative Perspectives on International School Leadership examines the current global spread of educational leadership, occurring rapidly and widely. Exploring five international case studies of leadership policy, preparation, and practice under the framework of policy borrowing and adaptation, Magno attempts to understand and account for commonalities and differences across country contexts. Rather than assuming a particular model or theory to leadership is best, Comparative Perspectives on International School Leadership takes a policy-oriented perspective and considers how and why certain approaches are being formulated and accepted, including an examination of motivations, influencers, actors, institutions, and implementation processes. Magno ultimately argues that efforts toward formalizing educational leadership reflect current global political objectives to improve schools by increasing accountability, transparency, and professionalism. This engaging book will be of interest to scholars and students in the fields of educational leadership and comparative education. © 2013 Taylor & Francis.

The purpose of the study was to examine how international tourists' shopping satisfaction related to their overall satisfaction as tourists and the tourists' expenditure differences by gender. A survey was conducted among U.S. citizens of who were traveling to South Korea (n = 422). The survey took place at transport hubs of the major international airports and seaports in South Korea prior to tourists' departure. The findings of this research concluded that tourist shopping satisfaction was significantly correlated with overall tourist satisfaction. In addition, different shopping patterns were reported among men and women tourists. The results of this study confirm that a positive retail shopping experience is an important aspect of overall international tourism.

A comprehensive analysis of contrast formation mechanisms in scanning tunneling microscopy (STM) experiments on a metal oxide surface is presented with the oxygen-induced (2√2×√2)R45 missing row reconstruction of the Cu(100) surface as a model system. Density functional theory and electronic transport calculations were combined to simulate the STM imaging behavior of pure and oxygen-contaminated metal tips with structurally and chemically different apexes while systematically varying bias voltage and tip-sample distance. The resulting multiparameter database of computed images was used to conduct an extensive comparison with experimental data. Excellent agreement was attained for a large number of cases, suggesting that the assumed model tips reproduce most of the commonly encountered contrast-determining effects. Specifically, we find that depending on the bias voltage polarity, copper-terminated tips allow selective imaging of two structurally distinct surface Cu sites, while oxygen-terminated tips show complex contrasts with pronounced asymmetry and tip-sample distance dependence. Considering the structural and chemical stability of the tips reveals that the copper-terminated apexes tend to react with surface oxygen at small tip-sample distances. In contrast, oxygen-terminated tips are considerably more stable, allowing exclusive surface oxygen imaging at small tip-sample distances. Our results provide a conclusive understanding of fundamental STM imaging mechanisms, thereby providing guidelines for experimentalists to achieve chemically selective imaging by properly selecting imaging parameters. © 2013 American Chemical Society.