Forms of Knowledge of Advanced Mathematics for Teaching

In this paper, we explore in more detail why knowing advanced mathematics might be beneficial for teachers, specifically in relation to their classroom practice. Rather than by listing courses or specific advanced topics, as though those were the agents of change, we do so by considering advanced mathematical content for teachers in terms of more general forms of knowledge. In particular, we identify five forms of knowledge of advanced mathematics for teaching: peripheral, evolutionary, axiomatic, logical, and inferential. These categories were derived from analysis of an extensive mapping process linking K-12 content to relevant advanced mathematics. We connect these forms of knowledge to particular practices that teachers engage in so as to clarify the perceived relations to classroom practices. We view such work as important to and productive for teacher educators, particularly in conceptualizing and structuring mathematics courses for teachers so that content that truly informs the work of K-12 teaching can be highlighted, and in a manner that facilitates teachers’ formation of those connections

Statistics as Unbiased Estimators: Exploring the Teaching of Standard Deviation

This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator – not just a descriptive statistic for the variation (spread) in data – is related to teachers’ instruction regarding standard deviation, particularly around the issue of division by n-1. In this regard, the study contributes to our understanding about how knowledge of mathematics beyond the current instructional level, what we refer to as nonlocal mathematics, becomes important for teaching. The findings indicate that acquired knowledge of nonlocal mathematics can play a role in altering teachers’ planned instructional approaches in terms of student activity and cognitive demand in their instruction

Secondary Mathematics Teachers’ Planned Approaches For Teaching Standard Deviation

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers to teach in alignment with prior learning experiences, despite professional development. Implications for teacher education and curricular development are offered

A Case for Combinatorics: A Research Commentary

In this commentary, we make a case for the explicit inclusion of combinatorial topics in mathematics curricula, where it is currently essentially absent. We suggest ways in which researchers might inform the field’s understanding of combinatorics and its potential role in curricula. We reflect on five decades of research that has been conducted since a call by Kapur (1970) for a greater focus on combinatorics in mathematics education. Specifically, we discuss the following five assertions: 1) Combinatorics is accessible, 2) Combinatorics problems provide opportunities for rich mathematical thinking, 3) Combinatorics fosters desirable mathematical practices, 4) Combinatorics can contribute positively to issues of equity in mathematics education, and 5) Combinatorics is a natural domain in which to examine and develop computational thinking and activity. Ultimately, we make a case for the valuable and unique ways in which combinatorics might effectively be leveraged within K-16 curricula

Serratamolide is a hemolytic factor produced by Serratia marcescens

Serratia marcescens is a common contaminant of contact lens cases and lenses. Hemolytic factors of S. marcescens contribute to the virulence of this opportunistic bacterial pathogen. We took advantage of an observed hyper-hemolytic phenotype of crp mutants to investigate mechanisms of hemolysis. A genetic screen revealed that swrW is necessary for the hyper-hemolysis phenotype of crp mutants. The swrW gene is required for biosynthesis of the biosurfactant serratamolide, previously shown to be a broad-spectrum antibiotic and to contribute to swarming motility. Multicopy expression of swrW or mutation of the hexS transcription factor gene, a known inhibitor of swrW expression, led to an increase in hemolysis. Surfactant zones and expression from an swrW-transcriptional reporter were elevated in a crp mutant compared to the wild type. Purified serratamolide was hemolytic to sheep and murine red blood cells and cytotoxic to human airway and corneal limbal epithelial cells in vitro. The swrW gene was found in the majority of contact lens isolates tested. Genetic and biochemical analysis implicate the biosurfactant serratamolide as a hemolysin. This novel hemolysin may contribute to irritation and infections associated with contact lens use. © 2012 Shanks et al

A Brane World Perspective on the Cosmological Constant and the Hierarchy Problems

We elaborate on the recently proposed static brane world scenario, where the effective 4-D cosmological constant is exponentially small when parallel 3-branes are far apart. We extend this result to a compactified model with two positive tension branes. Besides an exponentially small effective 4-D cosmological constant, this model incorporates a Randall-Sundrum-like solution to the hierarchy problem. Furthermore, the exponential factors for the hierarchy problem and the cosmological constant problem obey an inequality that is satisfied in nature. This inequality implies that the cosmological constant problem can be explained if the hierarchy problem is understood. The basic idea generalizes to the multibrane world scenario. We discuss models with piecewise adjustable bulk cosmological constants (to be determined by the 5-dimensional Einstein equation), a key element of the scenario. We also discuss the global structure of this scenario and clarify the physical properties of the particle (Rindler) horizons that are present. Finally, we derive a 4-D effective theory in which all observers on all branes not separated by particle horizons measure the same Newton's constant and 4-D cosmological constant.Comment: revtex, 63 pages, 8 figures, one table, revised version, more discussions on the global structure, references adde

C-Jun N-terminal kinase (JNK) isoforms play differing roles in otitis media

BACKGROUND: Innate immunity and tissue proliferation play important roles in otitis media (OM), the most common disease of childhood. CJUN terminal kinase (JNK) is potentially involved in both processes. RESULTS: Genes involved in both innate immune and growth factor activation of JNK are upregulated during OM, while expression of both positive and negative JNK regulatory genes is altered. When compared to wildtypes (WTs), C57BL/6 mice deficient in JNK1 exhibit enhanced mucosal thickening, with delayed recovery, enhanced neutrophil recruitment early in OM, and delayed bacterial clearance. In contrast, JNK2(−/−) mice exhibit delayed mucosal hyperplasia that eventually exceeds that of WTs and is slow to recover, delayed recruitment of neutrophils, and failure of bacterial clearance. CONCLUSIONS: The results suggest that JNK1 and JNK2 play primarily opposing roles in mucosal hyperplasia and neutrophil recruitment early in OM. However, both isoforms are required for the normal resolution of middle ear infection. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12865-014-0046-z) contains supplementary material, which is available to authorized users

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

Infectious Disease Modeling of Social Contagion in Networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for ‘automatic’ (or ‘spontaneous’) non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.National Institutes of Health (U.S.) (grant R01GM078986)National Science Foundation (U.S.)Bill & Melinda Gates FoundationTempleton FoundationNational Institute on Aging (grant P01 AG031093)Framingham Heart Study (contract number N01-HC-25195