Money-income relationships and the exchange rate regime

Demand for money ; Foreign exchange rates

Children\u27s mathematical thinking in different classroom cultures

The relationship between normative patterns of social interaction and children\u27s mathematical thinking was investigated in 5 classes (4 reform and 1 conventional) of 7- to 8-year-olds. In earlier studies, lessons from these classes had been analyzed for the nature of interaction broadly defined; the results indicated the existence of 4 types of classroom cultures (conventional textbook, conventional problem solving, strategy reporting, and inquiry/argument). In the current study, 42 lessons from this data resource were analyzed for children\u27s mathematical thinking as verbalized in class discussions and for interaction patterns. These analyses were then combined to explore the relationship between interaction types and&nbsp; expressed mathematical thinking. The results suggest that increased complexity in children\u27s expressed mathematical thinking was closely related to the types of interaction patterns that differentiated class discussions among the 4 classroom cultures.<br /

White Dwarf Cosmochronometry. I. Monte Carlo Simulations of Proper-Motion ̶ and Magnitude-Limited Samples Using Schmidt’s 1/Vmax Estimator

Observationally, white dwarf stars are a remarkably homogeneous class with a minimum observed Teff ~4000 K. Theoretically, the physics that determines their cooling timescales is relatively more straightforward than that which determines main-sequence evolutionary timescales. As a result, the white dwarf luminosity function has for the last decade been used as a probe of the age and star formation rate of the Galactic disk, providing an estimated local disk age of ~10 Gyr with estimated total uncertainties of roughly 20%. A long-standing criticism of the technique is that the reality of the reported downturn in the luminosity function (LF) hinges on just a handful of stars and on statistical arguments that fainter (older) objects would have been observed were they present. Indeed, the likely statistical variations of these small-number samples represent one of the primary uncertainties in the derived Galactic age, and the behavior of Schmidt\u27s 1/Vmax estimator in this limit is not well understood. In this work, we explore these uncertainties numerically by means of a Monte Carlo population synthesis code that simulates the kinematics and relative numbers of cooling white dwarfs. The “observationally selected” subsamples are drawn using typical proper motion and V-magnitude limits. The corresponding 1/Vmax LFs are then computed and compared to the input-integrated LFs. The results from our (noise-free) data suggest that (1) Schmidt’s 1/Vmax technique is a reliable and well-behaved estimator of the true space density with typical uncertainties of ~50% for 50 point samples and 25% for 200 point samples; (2) the age uncertainties quoted in previously published observational studies of the LF are consistent with uncertainties in the Monte Carlo results ̶ specifically, there is a ~15% and ≤10% observational uncertainty in the ages inferred from 50 point and 200 point samples, respectively; and (3) the large statistical variations in the bright end of these LFs ̶ even in the large-N limit ̶ preclude using the white dwarf LF to obtain an estimate of the recent star formation rate as a function of time

The Distance Geometry of Music

We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\emph{ostinatos}) from traditional world music. We prove that these \emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \emph{evenness}. We also show that essentially all Euclidean rhythms are \emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful property called shelling. All of our results for musical rhythms apply equally well to musical scales. In addition, many of the problems we explore are interesting in their own right as distance geometry problems on the circle; some of the same problems were explored by Erd\H{o}s in the plane.Comment: This is the full version of the paper: "The distance geometry of deep rhythms and scales." 17th Canadian Conference on Computational Geometry (CCCG '05), University of Windsor, Canada, 200

Stakeholder Knowledge and Perceptions of Free-roaming Equids and Their Management at a Western U.S. Land-Grant University

The horse (Equus ferus caballus), originally native to North America, became extinct on the continent approximately 10,000 years ago. Horses that migrated from North America to Eurasia across the Bering Strait continued to evolve and were domesticated along with burros (E. asinus). Both species were then transported to the Americas where they were intentionally released or escaped into the wild, forming feral herds. The Wild Free-Roaming Horses and Burros Act of 1971 (WFRHBA) provided federal oversight and protection for feral horses and burros (hereafter, free-roaming equids) that inhabited designated areas on public lands in the western United States. The Bureau of Land Management (BLM) estimated in 2019 that \u3e90,000 free-roaming equids inhabited 29 million ha on 177 designated herd management areas (HMAs). This population estimate exceeds the designated appropriate management level (AML) of 26,785. To provide BLM managers with insights regarding stakeholder knowledge and perceptions about the management of free-roaming equids in a western U.S. state where HMAs exceed AML, in 2020 we surveyed faculty, staff, and students at the state land-grant university (i.e., Utah State University [USU]). We hypothesized that, because the WFRHBA was passed in 1971, older respondents and those with natural resources education would be more informed and supportive of active free-roaming equid management, such as herd reduction. We received 959 responses (response rate of 12.5%) to our survey (i.e., 14% faculty, 14% staff, and 72% students). Most respondents (60%) were unaware of the WFRHBA, and \u3e50% were unaware that free-roaming equids were protected. Over 45% of our respondents were unsure of HMA AML status or population growth rates. Furthermore, most respondents (65%) did not know that free-roaming equids are ecologically considered feral. Older respondents and those with rural backgrounds and natural resources education were more informed. Our results highlight the need for improved outreach and communication efforts regarding the issues and consequences of free-roaming equid management approaches

Kindergarten Reading Readiness and Developmental Indicators for the Assessment of Learning

The acquisition of early childhood literacy skills is a predictor of academic success in elementary education. In a local school district, 22% of children entering kindergarten were assessed as having a gap in their reading readiness skills (RRS) based on their pre-K scores on the Developmental Indicators for the Assessment of Learning (DIAL-4). The average kindergarten beginning-year difference on the Reading Baseline Inventory (RBI) between the students with a gap and students without a gap was 15 out of 100 points. The purpose of this quantitative research was to examine the change between fall and spring RBI scores of kindergarten students who entered school with a gap and those who entered without a gap to determine if the gap was closed by the end of the school year. The framework for this study was Vygotsky\u27s constructivist theory of how children construct knowledge based on their early experiences. From a census sample of 118 students, 26 students were classified as having a gap in their DIAL-4 readiness scores. Fall pretest and spring posttest RBI scores served as the dependent variable. Within group t tests revealed the group identified as having a reading readiness gap increased their average RBI reading performance by 47% while the group identified as not having a gap increased by 26%, t(26) = -11.47, p \u3c .001. However, the between groups t test comparing the groups\u27 RBI difference scores was also significant, t(116) = -3.12, p = .002, indicating a closed but still significant gap (6.8 points) remaining. A white paper presents the results of the study and will contribute to positive social change by providing school leaders with evidence based practical suggestions to better serve their students. By working to close the reading gap early it will help ensure students have a better chance to reach their full potential for academic success