Building Middle-Level Mathematics Teachers\u27 Capacities as Teachers and Leaders: The Math in the Middle Institute Partnership

This article describes professional development for middle-level mathematics teachers offered through the Math in the Middle Institute Partnership, a National Science Foundation-funded project to build teachers’ capacities to improve mathematics learning for all students. An overview of the project, including descriptions of its goals and curriculum are provided. Detailed descriptions of two mathematics courses and one pedagogy course are offered. The mathematics courses included here are the introductory course to the Math in the Middle Institute, as well as one of the final math courses of the Institute in which participants apply mathematical knowledge and processes to real-world problems. The pedagogy course features curriculum that enables teachers to acquire an understanding of the nature and purpose of action research, and launches teachers into planning and implementing systematic inquiry in their own mathematics classrooms around topics of their choosing. The varied abilities of teachers, as well as growth in teachers’ mathematical and pedagogical capacities, are represented by several samples of student work provided within the article. In addition, mathematical and pedagogical products of student work are also provided through the project’s URL links. Improving teacher quality is identified as a national need in mathematics education and one many universities and schools across the country are working in partnership to try to address. This article describes a professional development project aimed at improving mathematics teaching and learning in the middle grades. An overview of the project, along with a close look at several of its course offerings, are presented highlighting mathematical and pedagogical goals, challenges, and accomplishments

Understanding Teacher Leadership in Middle School Mathematics: A Collaborative Research Effort

We report findings from a collaborative research effort designed to examine how teachers act as leaders in their schools. We find that teachers educated by the Math in the Middle Institute act as key sources of advice for colleagues within their schools while drawing support from a network consisting of other teachers in the program and university-level advisors. In addition to reporting on our findings, we reflect on our research process, noting some of the practical challenges involved, as well as some of the benefits of collaboration

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found `in vivo' in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs

Embodying functionally relevant action sounds in patients with spinal cord injury

Growing evidence indicates that perceptual-motor codes may be associated with and influenced by actual bodily states. Following a spinal cord injury (SCI), for example, individuals exhibit reduced visual sensitivity to biological motion. However, a dearth of direct evidence exists about whether profound alterations in sensorimotor traffic between the body and brain influence audio-motor representations. We tested 20 wheelchair-bound individuals with lower skeletal-level SCI who were unable to feel and move their lower limbs, but have retained upper limb function. In a two-choice, matching-to-sample auditory discrimination task, the participants were asked to determine which of two action sounds matched a sample action sound presented previously. We tested aural discrimination ability using sounds that arose from wheelchair, upper limb, lower limb, and animal actions. Our results indicate that an inability to move the lower limbs did not lead to impairment in the discrimination of lower limb-related action sounds in SCI patients. Importantly, patients with SCI discriminated wheelchair sounds more quickly than individuals with comparable auditory experience (i.e. physical therapists) and inexperienced, able-bodied subjects. Audio-motor associations appear to be modified and enhanced to incorporate external salient tools that now represent extensions of their body schema

Lensed CMB power spectra from all-sky correlation functions

Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Non-perturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0.3-1% level. We describe a new, accurate and fast, full-sky correlation-function method for computing the lensing effect on CMB power spectra to better than 0.1% at l<2500 (within the approximation that the lensing potential is linear and Gaussian). We also discuss the effect of non-linear evolution of the gravitational potential on the lensed power spectra. Our fast numerical code is publicly available.Comment: 16 pages, 4 figures. Changes to match PRD version including new section on non-linear corrections. CAMB code available at http://camb.info

How linear features alter predator movement and the functional\ud response

In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator–prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them

Moving towards a geocentric, polycultural theory of organizational paradox

Purpose This paper comments on “Global implications of the indigenous epistemological system from the east” (Li, 2016), which provides an indigenous Chinese perspective on organizational paradox. Li introduces Yin-Yang balancing as an epistemological system that can help scholars examine and practitioners manage paradoxes. In this commentary, the purpose of this paper is to discuss the merits of Yin-Yang balancing and how this approach and other indigenous theories might enrich organizational paradox theory. Design/methodology/approach The authors provide a commentary and suggestions for future research. The authors distinguish between Yin-Yang balancing as a normative theory, a meta-theory and a lay theory. The authors encourage both geocentrism and polycentrism as goals for future paradox research, enabling attention to the diversity of ideas across and within varied cultures. Originality/value The commentary connects Yin-Ying balancing with extant research on organizational paradox

Ion-ion dynamic structure factor, acoustic modes and equation of state of two-temperature warm dense aluminum

The ion-ion dynamical structure factor and the equation of state of warm dense aluminum in a two-temperature quasi-equilibrium state, with the electron temperature higher than the ion temperature, are investigated using molecular-dynamics simulations based on ion-ion pair potentials constructed from a neutral pseudoatom model. Such pair potentials based on density functional theory are parameter-free and depend directly on the electron temperature and indirectly on the ion temperature, enabling efficient computation of two-temperature properties. Comparison with ab initio simulations and with other average-atom calculations for equilibrium aluminum shows good agreement, justifying a study of quasi-equilibrium situations. Analyzing the van Hove function, we find that ion-ion correlations vanish in a time significantly smaller than the electron-ion relaxation time so that dynamical properties have a physical meaning for the quasi-equilibrium state. A significant increase in the speed of sound is predicted from the modification of the dispersion relation of the ion acoustic mode as the electron temperature is increased. The two-temperature equation of state including the free energy, internal energy and pressure is also presented